Answer:
(a) Amount remaining after 15 days = 27 mg
(b) Amount remaining after t days = [216(0.5)^t/5] mg
Explanation:
Nt = No(0.5)^t/t1/2
No (initial amount) = 216 mg, t = 15 days, t1/2 (half-life) = 5 days
N15 (amount remaining after 15 days) = 216(0.5)^15/5= 216(0.5)^3 = 216 × 0.125 = 27 mg
(b) Nt (amount remaining after t days) = 216(0.5)^t/5
Answer:
(a). 27 mg, (b). N = 216 (1/2)^ (t/5 days).
Explanation:
From the question, we are given that the half-life of bismuth-210, 210Bi = 5 days, a sample mass = 216 mg, the amount remaining after 15 days= ???(unknown).
Using the equation (1) below we can solve for the amount remaining after 15 days.
N= N° (1/2)^(t/th).-------------------------(1).
Where N = is the amount remaining, N° = is the initial amount, t= is time and th= half life.
Therefore,amount remaining, N = 216mg (1/2)^(15 days/5 days).
=====> Amount remaining, N =216 mg (1/2)^3.
=====> Amount remaining, N= 216 mg × 0.125. = 27 mg.
OR
We can solve it by using; 1/2 M°. Where M° is the initial mass.
Therefore, after 5 days, 1/2 × 216 = 108 mg remains.
After 10 days, 1/2 × 108 mg = 54 mg remains.
After 15 days; 1/2 × 54 mg = 27 mg remains.
(b). We are to find the amount remaining after time, t.
The amount remaining after time,t ==> N= N° (1/2)^(t/th)
===> N = 216 (1/2)^ (t/5 days).
With this we can calculate the amount of the sample at particular time if the time is given.
If a mixture of gases contained 78% nitrogen at a pressure of 984 torr and 22% carbon dioxide at 345 torr, what is the total pressure of the system?
Answer:
P(total) = 1329 torr
Explanation:
Given data:
Pressure of nitrogen = 984 torr
Pressure of carbon dioxide = 345 torr
Total pressure of system = ?
Solution:
The given problem will be solve through the Dalton law of partial pressure of gases.
According to the this law,
The total pressure exerted by the mixture of gases is equal to the sum of partial pressure of individual gas.
Mathematical expression,
P(total) = P₁ + P₂ +.......+ Pₙ
Here we will put the values in formula,
P₁ = partial pressure of nitrogen
P₂ = partial pressure of carbon dioxide
P(total) = 984 torr + 345 torr
P(total) = 1329 torr
Final answer:
The total pressure of the system is calculated by adding the partial pressures of the individual gases, resulting in a total pressure of 843.42 torr.
Explanation:
To calculate the total pressure of a mixture of gases, you use Dalton's Law of Partial Pressures which implies that the overall pressure exerted by a mixture of non-reacting gases is equal to the sum of their partial pressures.
In this case,
The partial pressure of nitrogen (N₂) is given as 78% of 984 torr, which is 767.52 torr.
The partial pressure of carbon dioxide (CO₂) is given as 22% of 345 torr, which is 75.9 torr.
The total pressure is the sum of these partial pressures:
767.52 torr (N₂) + 75.9 torr (CO₂) = 843.42 torr
The total pressure of the system is 843.42 torr.
Suppose the half-life is 35.5 s for a first order reaction and the reactant concentration is 0.0700 M 28.6 s after the reaction starts. How many seconds after the start of the reaction does it take for the reactant concentration to decrease to 0.0063 M?
Answer:
It takes 151.9 s for the reactant concentration to decrease to 0.0063 M
Explanation:
k = ln2 / t1/2
k = ln2 / 35.5 s = 0.0195 s^-1
ln [A]t = -kt + ln [A]o
ln (0.0063) = -0.0195t + ln (0.0700)
t = 123.32 s
Since t is counted from 28.6 s as the initial time, the time after start of reaction to reach 0.0063 M is
28.6 + 123.32 s = 151.9 s
Two equivalents of molecular halogen will react with and add to an alkyne. Complete the mechanism and draw the organic product. Include all lone pairs and nonzero formal charges.
Answer:
The drawing of the mechanism and the organic product is shown below.
Explanation:
Alkynes react with bromine to form a dihaloalkene (with an equivalent of the halogen) or a tetrahaloalkane derivative (with two equivalents of the halogen), which is this case. The triple bond adds two halogen molecules as shown in the drawing, an anti addition occurring.
Use electron configurations to account for the stability of the lanthanide ions Ce⁴⁺ and Eu²⁺.
Answer:
Explanation:
The Ce metal has electronic configuration as follows
[Xe] 4f¹5d¹6s²
After losing 4 electrons , it gains noble gas configuration ,. So Ce ⁺⁴ is stable.
Eu has electronic configuration as follows
[ Xe ] 4 f ⁷6s²
[ Xe ] 4 f ⁷
Its outermost orbit contains 2 electrons so Eu²⁺ is stable. Its +3 oxidation state is also stable.
Ce⁺²
What is the electric force on a proton 2.5 fmfm from the surface of the nucleus? Hint: Treat the spherical nucleus as a point charge. Express your answer to two significant figures and include the appropriate units.
Explanation:
It is known that charge on xenon nucleus is [tex]q_{1}[/tex] equal to +54e. And, charge on the proton is [tex]q_{2}[/tex] equal to +e. So, radius of the nucleus is as follows.
r = [tex]\frac{6.0}{2}[/tex]
= 3.0 fm
Let us assume that nucleus is a point charge. Hence, the distance between proton and nucleus will be as follows.
d = r + 2.5
= (3.0 + 2.5) fm
= 5.5 fm
= [tex]5.5 \times 10^{-15} m[/tex] (as 1 fm = [tex]10^{-15}[/tex])
Therefore, electrostatic repulsive force on proton is calculated as follows.
F = [tex]\frac{1}{4 \pi \epsilon_{o}} \frac{q_{1}q_{2}}{d^{2}}[/tex]
Putting the given values into the above formula as follows.
F = [tex]\frac{1}{4 \pi \epsilon_{o}} \frac{q_{1}q_{2}}{d^{2}}[/tex]
= [tex](9 \times 10^{9}) \frac{54e \times e}{(5.5 \times 10^{-15})^{2}}[/tex]
= [tex](9 \times 10^{9}) \frac{54 \times (1.6 \times 10^{-19})^{2}}{(5.5 \times 10^{-15})^{2}}[/tex]
= 411.2 N
or, = [tex]4.1 \times 10^{2}[/tex] N
Thus, we ca conclude that [tex]4.1 \times 10^{2}[/tex] N is the electric force on a proton 2.5 fm from the surface of the nucleus.
If 200 ml of 0.30 M formic acid is added to 400 ml of water, what is the resulting pH of the solution? Round the answer to one decimal place. pKa= 3.75
Answer:
The pH of the resultant solution is 2.4
Explanation:
From the data
[HCOOH]_0 is 0.30V_w is 400 mlV_a is 200 mlV_total is given asV_total=V_w+V_a
V_total=400+200 ml
V_total=600mlNow the concentration of solution is given as
[tex]M_1V_1=M_2V_2\\M_2=\frac{M_1V_1}{V_2}\\M_2=\frac{0.30 \times 0.2}{0.6}\\M_2=0.1 M\\[/tex]
The reaction equation is given as
Equation [tex]HCOOH + H_2O \rightarrow HCOO^- +H_3O^+\\[/tex]
Initial Concentration is 0.1 0 0
Change is -x x x
_______________________________________________
At Equilibrium 0.1-x x x
Now the equation for K_a is given as
[tex]K_a=\frac{[HCOO^-][H_3O^+]}{[HCOOH]}[/tex]
Here Ka, for pKa-=3.75, is given as
[tex]K_a=10^{-pKa}\\K_a=10^{-3.75}\\K_a=1.78 \times 10^{-4}[/tex]
Substituting this and concentrations at equilibrium in equation of Ka gives
[tex]K_a=\frac{[HCOO^-][H_3O^+]}{[HCOOH]}\\1.78 \times 10^{-4}=\frac{xx}{0.1-x}\\[/tex]
Solving for x
[tex]1.78 \times 10^{-4} (0.1-x)=x^2\\[/tex]
Here 0.1-x≈0.1 so
[tex]1.78 \times 10^{-5} =x^2\\x=\sqrt{1.78 \times 10^{-5}}\\x=4.219 \times 10^{-3}[/tex]
As [tex][H_3O^+]=[H^+][/tex]=x so its value is 4.219 x10^(-3) so pH is given as
[tex]pH=-log[H^+]\\pH=-log (4.219 \times 10^{-3})\\pH=2.37 \approx 2.4[/tex]
So the pH of the resultant solution is 2.4
Answer:
2.4
Explanation:
Given that:
Initial Concentration (M₁) of our formic acid from the question= 0.30 M
Initial volume (V₁) of the formic acid = 200 mL
Volume of water added = 400 mL
pKa= 3.75
∴ we can determine the total volume of the final solution by the addition of (Initial volume (V₁) of the formic acid) + (Volume of water added)
= 200 mL + 400 mL
= 600 mL
We can find the final concentration using the formula;
M₁V₁ = M₂V₂
M₂= [tex]\frac{0.30*200}{600}[/tex]
M₂= 0.1M
∴ The concentration of the diluted formic acid(since water is added to the initial volume) = 0.1M
From our pKa which is = 3.75
Ka of formic acid (HCOOH) = [tex]10^{-3.75}[/tex]
= 1.78 × 10⁻⁴
If water is added to the formic acid; the equation for the reaction can be represented as;
HCOOH + H₂O ⇒ HCOO⁻ + H₃O
Initial 0.1 0 0
Change -x +x +x
Equilibrium 0.1-x x x
Ka = [tex]\frac{x^2}{0.1-x}[/tex] = 1.78 × 10⁻⁴
x² = (0.1 × 1.78 × 10⁻⁴) since x = 0
x² = 1.78 × 10⁻⁵
x = [tex]\sqrt{1.78*10^{-5}}[/tex]
x = 0.004217
x = [tex][H_3O^+]=[H^+][/tex] = 0.004217 M
pH = [tex]-log[H^+][/tex]
= -log (0.004217)
= 2.375
≅ 2.4 (to one decimal place)
We can thereby conclude that the final pH of the formic acid solution = 2.4
A pure titanium cube has an edge length of 2.64 in . How many titanium atoms does it contain? Titanium has a density of 4.50g/cm3.
Answer:
1.71 × 10²⁵ atoms
Explanation:
A pure titanium cube has an edge length of 2.64 in. In centimeters,
2.64 in × (2.54 cm/ 1 in) = 6.71 cm
The volume of the cube is:
V = (length)³ = (6.71 cm)³ = 302 cm³
Titanium has a density of 4.50 g/cm³. The mass corresponding to 302 cm³ is:
302 cm³ × 4.50 g/cm³ = 1.36 × 10³ g
The molar mass of titanium is 47.87 g/mol. The moles corresponding to 1.36 × 10³ g are:
1.36 × 10³ g × (1 mol/47.87 g) = 28.4 mol
1 mol of Ti contains 6.02 × 10²³ atoms of Ti (Avogadro's number). The atoms in 28.4 moles are:
28.4 mol × (6.02 × 10²³ atoms/1 mol) = 1.71 × 10²⁵ atoms
The initial reaction rate for the elementary reaction 2A + B → 4C was measured as a function of temperature when the concentration of A was 2 M and that of B was 1.5 M. (a) What is the activation energy? (b) What is the frequency factor? (c) What is the rate constant as a function of temperature using Equation (S3-5) and T0 = 27°C as the base case?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a) The activation energy is 124.776[tex]\frac{kJ}{mole}[/tex]
b) The frequency factor is 1.77 ×[tex]10^{18}[/tex]
c) The rate constant is 0.00033 [tex](\frac{dm^{3} }{mole} )^{2}[/tex][tex]\frac{1}{s}[/tex]
Explanation:
From the question the elementary reaction for A and B is given as
2A + B → 4C
The rate equation the elementary reaction is
-[tex]r_{A}[/tex] = [tex]k[/tex][tex][A]^{2}[/tex][tex][B][/tex]
= [tex]k[2]^{2}[1.5][/tex]
= 6k
[tex]k = \frac{-r_{A} }{6}[/tex]
When temperature changes, the rate constant change an this causes the rate of reaction to change as shown on the second uploaded image.
The relationship between temperature and rate constant can be deduced from these equation
[tex]k = Aexp(-\frac{E_{a} }{RT} )[/tex]
taking ln of both sides we have
[tex]lnk =ln A - (\frac{E_{a} }{R}) \frac{1}{T}[/tex]
Considering the graph for the rate constant [tex]ln k[/tex] and [tex](\frac{1}{T} )[/tex] the slope from the equation is [tex]-(\frac{E_{a} }{R})[/tex] and the intercept is [tex]ln A[/tex]
From the given table we can generate another table using the equation above as shown on the third uploaded image
The graph of [tex]ln k[/tex] vs [tex](\frac{1}{T} )[/tex] is shown on the fourth uploaded image
From the graph we can see that the slope is [tex]-(\frac{E_{a} }{R} ) = - 15008[/tex]
Now we can obtain the activation energy [tex]E_{a}[/tex] by making it the subject in the equation also generally R which is the gas constant is [tex]8.145 \frac{J}{kmole}[/tex]
[tex]E_{a} = 15008 × 8,3145\frac{J}{molK}[/tex]
[tex]= 124\frac{KJ}{mole}[/tex]
Hence the activation energy is [tex]= 124\frac{KJ}{mole}[/tex]
b) From the graph its intercept is [tex]ln A = 42.019[/tex]
[tex]A = exp(42.019)[/tex]
[tex]=1.77 × 10^{18}[/tex]
Hence the frquency factor A is [tex]=1.77 × 10^{18}[/tex]
c) From the equation of rate constant
[tex]lnk =ln A - (\frac{E_{a} }{R}) \frac{1}{T}[/tex]
We have
[tex]ln k = 42.019 - 15008 * (\frac{1}{300} )[/tex]
[tex]k = 0.00033(\frac{dm^{3} }{mole} )^{2} \frac{1}{s}[/tex]
Hence the rate constant is [tex]k = 0.00033(\frac{dm^{3} }{mole} )^{2} \frac{1}{s}[/tex]
A scuba diver that ascends to the surface too quickly can experience decompression sickness, which occurs when nitrogen that dissolves in the blood under high pressure, forms bubbles as the pressure decreases during the ascent. Therefore an understanding of the gas laws is an important part of a scuba diver\'s training. In fresh water the pressure increases by 1 atm every 34 ft below the water surface a diver descends. If a diver ascends quickly to the surface from a depth of 68 ft without exhaling, by what factor will the volume of the diver\'s lungs change upon arrival at the surface? Assume the atmospheric pressure at the surface of the water is 1 atm.
Final answer:
The volume of the diver's lungs would increase by a factor of three when ascending from a depth of 68 feet to the surface, due to the pressure change from 3 ATM to 1 ATM.
Explanation:
The question asks us to calculate the change in volume of a diver's lungs when ascending from a depth of 68 feet in fresh water to the surface, where the pressure is 1 ATM, assuming they do not exhale. According to the information given, in fresh water, pressure increases by 1 ATM every 34 feet. Therefore, at 68 feet, the pressure would be 3 ATM (including 1 ATM of atmospheric pressure at the surface). Using Boyle's Law, which states that pressure is inversely proportional to volume when temperature is constant (P1V1 = P2V2), the volume of the diver's lungs at the surface would be three times the volume underwater because the pressure decreases from 3 ATM to 1 ATM during ascent.
The following values are the only allowable energy levels of a hypothetical one-electron atom:
E₆ = -2 x 10⁻¹⁹ J
E₅ = -7 x 10⁻¹⁹ J
E₄ = -11 x 10⁻¹⁹ J
E₃ = -15 x 10⁻¹⁹ J
E₂ = -15 x 10⁻¹⁹ J
E₁ = -15 x 10⁻¹⁹ J
(a) If the electron were in the n = 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted? (b) What is the ionization energy (in kJ/mol) of the atom in its ground state? (c) If the electron were in the n = 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?
Answer:
Explanation:
a ) All the electronic levels below n = 3 have same energy so there will not be any evolution of energy in electronic transition from n=3 to n=2 or to n= 1 .
b ) Ionisation energy of ground state = 15 x 10⁻¹⁹ J per electron
= 15 x 10⁻¹⁹ x 6.02 x 10²³ J / mol
= 90 x 10⁴ J/mol
= 900 kJ / mol
c ) the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization will correspond to n = 4 to n = 6
= (11 - 2 ) x 10⁻¹⁹ J
= 9 X 10⁻¹⁹ J
= 9 X 10⁻¹⁹ J / 1.6 X 10⁻¹⁹
= 5.625 eV
= 1244 / 5.625 nm
= 221.155 nm
How many electrons in an atom can have each of the following quantum number or sublevel designations?
(a) 4p
(b) n = 3, l = 1, ml = +1
(c) n = 5, l = 3
Answer :
(a) Number of electrons in an atoms is, 6
(b) Number of electrons in an atoms is, 2
(c) Number of electrons in an atoms is, 14
Explanation :
There are 4 quantum numbers :
Principle Quantum Numbers : It describes the size of the orbital. It is represented by n. n = 1,2,3,4....
Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...
Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as . The value of this quantum number ranges from . When l = 2, the value of
Spin Quantum number : It describes the direction of electron spin. This is represented as . The value of this is for upward spin and for downward spin.
Number of electrons in a sublevel = 2(2l+1)
(a) 4p
n = 4
Value of 'l' for 'p' orbital : l = 1
At l = 1, [tex]m_l=+1,0,-1[/tex]
Number of electrons in an atoms = 2(2l+1) = 2(2×1+1) = 6
(b) n = 3, l = 1, ml = +1
As we know that, a sublevel of 'p' orbital can accommodate 6 electrons but 1 orbital can accommodate only 2 electrons. So,
Number of electrons in an atoms for (ml = +1) = 2
(b) n = 5, l = 3
Number of electrons in an atoms = 2(2l+1) = 2(2×3+1) = 14
There are a given specific number of electrons that can be found in a particular orbital or energy level.
In an atom, electrons are arranged in orbitals. These orbitals lie within specific energy levels. There is a maximum number of electrons that can be found in a particular energy level as well as in a particular orbital.
The maximum number of electrons that can be found in the following orbitals and energy levels are shown below;
The 4p orbital contains six electrons since the p level is triply degenerate.The orbital designated by n = 3, l = 1, ml = +1 can only contain two electronsThe orbital designated as n = 5, l = 3 refers to a 5f orbital which is seven fold degenerate hence it can contain a maximum of 14 electrons.Learn more: https://brainly.com/question/13439771
KBr(aq) AgNO3(aq) Classify each chemical reaction: reaction type of reaction (check all that apply) combination precipitation single replacement combustion double replacement acid-base decomposition combination precipitation single replacement combustion double replacement acid-base decomposition combination precipitation single replacement combustion double replacement acid-base decomposition combination precipitation single replacement combustion double replacement acid-base decomposition
The question is incomplete, here is the complete question:
[tex]KBr(aq.)+AgNO_3(aq.)\rightarrow KNO_3(aq.)+AgBr(s)[/tex]
Classify the type of the reaction (check all that apply)
1. Combination
2. Precipitation
3. Single replacement
4. Combustion
5. Double replacement
6. Acid-base
7. Decomposition
Answer: The given reaction is a type of precipitation and double displacement reaction.
Explanation:
Combination reaction is defined as the reaction in which smaller substances combine to form a larger substance.
[tex]A+B\rightarrow AB[/tex]
Precipitation reaction is defined as the reaction in which an insoluble salt is formed when two solutions are mixed containing soluble substances. The insoluble salt settles down at the bottom of the reaction mixture.
Single displacement reaction is defined as the reaction in which more reactive element displaces a less reactive element from its chemical reaction.
[tex]A+BC\rightarrow AC+B[/tex]
Combustion reaction is defined as the reaction in which a hydrocarbon reacts with oxygen gas to produce carbon dioxide gas and water molecule.
[tex]\text{Hydrocarbon}+O_2\rightarrow CO_2+H_2O[/tex]
Double displacement reaction is defined as the reaction in which exchange of ions takes place.
[tex]AB+CD\rightarrow CB+AD[/tex]
An acid-base reaction is known as neutralization reaction. This reaction is defined as the reaction in which an acid reacts with a base to produce a salt and water molecule.
[tex]HX+BOH\rightarrow BX+H_2O[/tex]
Decomposition reaction is defined as the reaction in which a large substance breaks down into smaller substances.
[tex]AB\rightarrow A+B[/tex]
For the given chemical equation:
[tex]KBr(aq.)+AgNO_3(aq.)\rightarrow KNO_3(aq.)+AgBr(s)[/tex]
As, ions are getting exchanges and also a solid salt is getting formed. The above reaction is a type of double displacement and precipitation reaction.
Hence, the given reaction is a type of precipitation and double displacement reaction.
The reaction between KBr(aq) and AgNO3(aq) is a double replacement reaction, where the bromide and nitrate anions switch cations. This results in the formation of AgBr(s), a precipitate, and KNO3(aq).
Explanation:The equation represents a double replacement reaction. When potassium bromide (KBr) and silver nitrate (AgNO3) are combined in an aqueous solution, they undergo a double replacement reaction.
In a double replacement reaction, the cations and anions of the two reactants switch places, forming two new compounds. In this case, KBr(aq) + AgNO3(aq) will yield AgBr(s) and KNO3(aq), with AgBr being a precipitate.
It's called a double replacement because both K and Ag exchange their anions (bromide and nitrate respectively). So this reaction doesn't fall under the categories of combination, precipitation, single replacement, combustion, acid-base or decomposition reaction, but it's specifically a double replacement reaction.
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Explain in detail how you would prepare 100 mL of a 0.00200 M solution of NaCl by diluting 0.500 M stock solution. The only glassware available for you to use are 1-mL, 5- mL, and 10-mL volumetric pipets and 100-mL volumetric flask.
To prepare a 0.00200 M NaCl solution from a 0.500 M stock, dilute 0.4 mL of the stock to 100 mL with water using volumetric pipets and a flask.
Explanation:To prepare 100 mL of a 0.00200 M NaCl solution from a 0.500 M stock solution, you need to perform a dilution. First, use the dilution equation C1V1 = C2V2, where C1 is the concentration of the stock solution, V1 is the volume of the stock solution needed, C2 is the concentration of the diluted solution, and V2 is the volume of the diluted solution. Plugging in the values, you get (0.500 M) V1 = (0.00200 M)(100 mL), which simplifies to V1 = (0.00200 M)(100 mL) / (0.500 M) = 0.4 mL. This is the volume of the stock solution you need to pipet into the 100-mL volumetric flask. As we only have 1-mL, 5-mL, and 10-mL volumetric pipets available, you can use the 1-mL pipet to add 0.4 mL of the stock solution to the volumetric flask, then fill the flask with water up to the 100-mL mark to achieve the desired concentration.
A stream of hot wat at 85 deg C at a rate of 1 kg/s is needed for the pasteurizing unit in a milk bottling plant. Such a stream is not readily available, and will be produced in a well-insulated mixing tank by directly injecting st rem from a boiler plant at 10 bar and 200 deg C into city water available at 1 bar and 20 deg C. a) Calculate the flow rates of city water and stream needed. b) Calculate the rate of entropy production in the mixing tank. Any help would be greatly appreciated
Answer:
the flow rate for steam from the boiler plant = [tex]0.099kg/s[/tex]
the flow rate from the city water = 0.901 kg/s
the rate of entropy production in the mixing tank = 0.2044 kJ/k
Explanation:
In a well-insulated mixing tank where:
[tex]Q_{cv} = 0[/tex] & [tex]W_{cv}=0[/tex]
The mass flow rates can be calculated using the formula:
[tex]Q_cv+m_1h_1+m_2h_2=m_3h_3+W_{cv[/tex] ------ equation (1)
so;
[tex]0+m_1h_1+m_2h_2=m_3h_3+0[/tex] ------- equation (2)
Given that:
From the steam in the boiler plant;
The temperature (T₁) = 200°C
Pressure (P₁) = 10 bar
The following data from compressed water and super-heated steam tables were also obtained at: T₁ = 200°C
h₁ = 2828.27 kJ/kg
s₁ = 6.95 kJ/kg K
m₁ (flow rate for steam in the boiler plant) = ????
Also, for city water
The temperature (T₂) = 20°C
Pressure (P₂) = 1 bar
Data obtained from compressed water and super-heated steam tables are as follows:
h₂ = 84.01 kJ/kg
s₂ = 0.2965 kJ/kg K
m₂ (flow rate for city water) = ???
For stream of hot wat at 85 deg C
Temperature (T₃) = 85°C
h₃([tex]h_f[/tex]) = 355.95 kJ/kg
s₃([tex]s_f[/tex]) = 1.1344 kJ/kg K
m₃ = 1 kg/s
so since:
m₁ + m₂ = m₃ (since m₃ = 1)
m₂ = 1 - m₁
From equation (2);
[tex]0+m_1h_1+m_2h_2=m_3h_3+0[/tex]
= [tex]m_1(2828.27)+(1-m_1)(84.01)=1(355.95)[/tex]
= [tex]2828.27m_1+(84.01-84.01m_1)=(355.95)[/tex]
= [tex]2828.27m_1-84.01m_1=355.95-84.01[/tex]
= [tex]m_1(2828.27-84.01)=355.95-84.01[/tex]
[tex]m_1 = \frac{355.95-84.01}{2828.27-84.01}[/tex]
[tex]m_1 = \frac{271.94}{2744.26}[/tex][tex]m_1 = 0.099 kg/s[/tex]
∴ the flow rate for steam from the boiler plant = [tex]0.099kg/s[/tex]
since; m₂ = 1 - m₁
m₂ = 1 - 0.099 kg/s
m₂ = 0.901 kg/s
∴ the flow rate from the city water = 0.901 kg/s
b)
rate of entropy production in the mixing tank can be determined using the formula:
Δ[tex]S_{production} = m_3}s_3-(m_1s_1+m_2s_2)[/tex]
Δ[tex]S_{production}[/tex] [tex]= (1)(1.1344)-(0.099)(6.6955)-0.901(0.2965)[/tex]
Δ[tex]S_{production}[/tex] [tex]= 1.1344-0.6628545-0.2671465[/tex]
Δ[tex]S_{production}[/tex] [tex]= 1.1344 - 0.930001[/tex]
Δ[tex]S_{production}[/tex] [tex]= 0.204399[/tex]
Δ[tex]S_{production}[/tex] ≅ 0.2044 kJ/k
∴ the rate of entropy production in the mixing tank = 0.2044 kJ/k
Oxygen is much less soluble in water than carbon dioxide at 0.00412 g/ 100 mL at 20°C and 760 mmHg. Calculate the solubility of oxygen gas in water at 20°C and a pressure of 1150 mmHg
Answer:
Solubility of CO2 = 0.045 g/l
Explanation:
Using Henry’s law which states that the quantity of an ideal gas that dissolves in a definite volume of liquid is directly proportional to the pressure of the gas.
C = k * Pg
Where C = concentration of the gas
Pg = pressure of the gas
k = proportionality constant
Calculating k,
k = C/Pg
Converting g/100ml to g/l,
0.00412 g/100ml; 0.00412g/100ml * 1000ml/1l
= 0.0412 g/l
Pressure in bar,
Pg = 1.01 bar
k = 0.0412/1.01 bar
= 0.0412 g/l.bar
Molar mass of CO2 = 12 + (16*2)
= 44 g/mol
Molar concentration of CO2 = k/molar mass
= 0.000936 mol/l.bar
Pressure of oxygen = 1.533 bar
Molar mass of O2 = 32 g/mol
Solubility of O2 = molar mass * molar concentration * pressure (bar)
= 32 * 0.000936 * 1.533
= 0.0459 g/l
Pressure in mmHg,
Pg = 760 mmHg
k = 0.0412/760
= 0.000054 g/l.mmHg
Molar mass of CO2 = 12 + (16*2)
= 44 g/mol
Molar concentration of CO2 = k/molar mass
= 0.00000123 mol/l.mmHg
Pressure of oxygen = 1150 mmHg
Molar mass of O2 = 32 g/mol
Solubility of O2 = molar mass * molar concentration * pressure (mmHg)
= 32 * 0.00000123 * 1150
= 0.0453 g/l
Final answer:
To calculate the solubility of oxygen in water at a new pressure, apply Henry's Law using the given solubility at a standard pressure, adjusting for the new pressure using a simple formula.
Explanation:
The student is asking about calculating the solubility of oxygen gas in water at a different pressure using Henry's law. Henry's Law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. Therefore, to calculate the solubility of oxygen at a pressure of 1150 mmHg, we use the known solubility at a standard pressure (760 mmHg or 1 atm) and adjust for the new pressure.
Given that the solubility of oxygen is 0.00412 g/100 mL at 20°C and 760 mmHg, and we are asked to find its solubility at 1150 mmHg. We can use the formula from Henry's Law:
S1 / P1 = S2 / P2
Where S1 is the solubility at the initial pressure (0.00412 g/100 mL), P1 is the initial pressure (760 mmHg), S2 is the solubility at the new pressure, and P2 is the new pressure (1150 mmHg).
Rearranging the equation to solve for S2 gives us:
S2 = S1 * (P2 / P1) = 0.00412 * (1150 / 760)
Solving this gives us the solubility of oxygen in water at 20°C and a pressure of 1150 mmHg. Remember, the actual calculations were omitted here, but applying this formula with the given values will provide the answer.
The nonvolatile, nonelectrolyte testosterone, C19H28O2 (288.40 g/mol), is soluble in benzene C6H6. Calculate the osmotic pressure generated when 12.4 grams of testosterone are dissolved in 168 ml of a benzene solution at 298 K.
Answer: 6.26atm
Explanation:Please see attachment for explanation
Answer:
The osmotic pressure is 6.26 atm
Explanation:
Step 1: Data given
Mass of testosterone = 12.4 grams
Volume of benzene = 168 mL
Temperature = 298 Kelvin
Step 2: Calculate moles of testosterone
Moles testosterone = mass / molar mass
Moles testosterone = 12.4 grams / 288.42 g/mol
Moles testosterone = 0.0430 moles
Step 3: Calculate molarity
Molarity = moles / volume
Molarity = 0.0430 moles / 0.168 L
Molarity = 0.256 M
Step 4 : Calculate the osmotic pressure
π = iMRT
⇒ with i = The Van't hoff factor = 1 (since testosterone is nonelectrolyte)
⇒ with M = the molair concentration = 0.256 M
⇒ with R = the gas constant = 0.08206 L*atm/k*mol
⇒ with T = the temperature = 298 K
π = 1*0.256*0.08206*298
π = 6.26 atm
The osmotic pressure is 6.26 atm
100. mg of an unknown protein are dissolved in enough solvent to make 5.00mL of solution. The osmotic pressure of this solution is measured to be 0.0766 atm at 25.0 degree C .
Calculate the molar mass of the protein. Be sure your answer has the correct number of significant digits.
Answer: The molar mass of the unknown protein is 6387.9 g/mol
Explanation:
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
[tex]\pi=iMRT[/tex]
or,
[tex]\pi=i\times \frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}\times RT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 0.0766 atm
i = Van't hoff factor = 1 (for non-electrolytes)
Mass of protein = 100. mg = 0.100 g (Conversion factor: 1 g = 1000 mg)
Molar mass of protein = ?
Volume of solution = 5.00 mL
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]25^oC=[25+273]K=298K[/tex]
Putting values in above equation, we get:
[tex]0.0766atm=1\times \frac{0.100\times 1000}{\text{Molar mass of protein}\times 5}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 298K\\\\\pi=\frac{1\times 0.100\times 1000\times 0.0821\times 298}{0.0766\times 5}=6387.9g/mol[/tex]
Hence, the molar mass of the unknown protein is 6387.9 g/mol
A lithium flame has a characteristic red color due to emissions of wavelength 671 nm. What is the mass equivalence of 1 mol of photons of this wavelength (1 J = 1 kg·m²/s²)?
Answer:
1.98x10⁻¹² kg
Explanation:
The energy of a photon is given by:
E= hc/λh is Planck's constant, 6.626x10⁻³⁴ J·s
c is the speed of light, 3x10⁸ m/s
and λ is the wavelenght, 671 nm (or 6.71x10⁻⁷m)
E = 6.626x10⁻³⁴ J·s * 3x10⁸ m/s ÷ 6.71x10⁻⁷m = 2.96x10⁻¹⁹ JNow we multiply that value by Avogadro's number, to calculate the energy of 1 mol of such protons:
1 mol = 6.023x10²³ photons2.96x10⁻¹⁹ J * 6.023x10²³ = 1.78x10⁵ JFinally we calculate the mass equivalence using the equation:
E=m*c²m=E/c²m = 1.78x10⁵ J / (3x10⁸ m/s)² = 1.98x10⁻¹² kgThe mass equivalence of 1 mole of photons of this wavelength is equal to [tex]1.78 \times 10^{-11} \;kg[/tex]
Given the following data:
Wavelength = 671 nm = [tex]6.71 \times 10^{11}[/tex] m.We know that the speed of light is [tex]3 \times 10^8[/tex] m/s.
Planck constant = [tex]6.626 \times 10^{-34}\;J.s[/tex]
Avogadro constant = [tex]6.02 \times 10^{23}[/tex]
To determine the mass equivalence of 1 mole of photons of this wavelength:
First of all, we would calculate the energy associated with the photons of this wavelength by using the Planck-Einstein relation:
Mathematically, Planck-Einstein relation for photon energy is given by the formula:
[tex]E = hf = h\frac{v}{\lambda}[/tex]
Where:
E is the maximum kinetic energy.h is Planck constant.f is photon frequency.[tex]\lambda[/tex] is the wavelength.v is the speed of light.Substituting the parameters into the formula, we have;
[tex]E = \frac{6.626 \times 10^{-34} \; \times \;3 \times 10^8 }{6.71 \times 10^{-7}} \\\\E = \frac{1.99 \times 10^{-25}}{6.71 \times 10^{-7}} \\\\E=2.96 \times 10^{-19} \;Joules[/tex]
For the energy of 1 mole of photons:
[tex]E = 2.96 \times 10^{-19} \times 6.02 \times 10^{23}\\\\E = 1.78 \times 10^5 \; Joules[/tex]
Now, we can find the mass equivalence of 1 mole of photons by using the formula:
[tex]E = mc^2\\\\m = \frac{E}{c^2} \\\\m = \frac{1.78 \times 10^5}{(3.0 \times 10^8)^2} \\\\m = \frac{1.78 \times 10^5}{(9.0 \times 10^{16})}\\\\m = 1.78 \times 10^{-11} \;kg[/tex]
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A cubic box with sides of 20.0 cm contains 2.00 × 1023 molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10-27 kg. What is the average pressure exerted by the molecules on the walls of the container? (The Boltzmann constant is 1.38 × 10-23 J/K and the ideal gas constant is R = 8.314 J/mol•K .) (12 pts.)
Answer:
1.133 kPa is the average pressure exerted by the molecules on the walls of the container.
Explanation:
Side of the cubic box = s = 20.0 cm
Volume of the box ,V= [tex]s^3[/tex]
[tex]V=(20.0 cm)^3=8000 cm^3=8\times 10^{-3} m^3[/tex]
Root mean square speed of the of helium molecule : 200m/s
The formula used for root mean square speed is:
[tex]\mu=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
= root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature = 370 K
M = mass helium = [tex]3.40\times 10^{-27}kg/mole[/tex]
[tex]N_A[/tex] = Avogadro’s number = [tex]6.022\times 10^{23}mol^{-1}[/tex]
[tex]T=\frac{\mu _{rms}^2\times M}{3kN_A}[/tex]
Moles of helium gas = n
Number of helium molecules = N =[tex]2.00\times 10^{23}[/tex]
N = [tex]N_A\times n[/tex]
Ideal gas equation:
PV = nRT
Substitution of values of T and n from above :
[tex]PV=\frac{N}{N_A}\times R\times \frac{\mu _{rms}^2\times M}{3kN_A}[/tex]
[tex]PV=\frac{N\times R\times \mu ^2\times M}{3k\times (N_A)^2}[/tex]
[tex]R=k\times N_A[/tex]
[tex]PV=\frac{N\times \mu ^2\times M}{3}[/tex]
[tex]P=\frac{2.00\times 10^{23}\times (200 m/s)^2\times 3.40\times 10^{-27} kg/mol}{3\times 8\times 10^{-3} m^3}[/tex]
[tex]P=1133.33 Pa =1.133 kPa[/tex]
(1 Pa = 0.001 kPa)
1.133 kPa is the average pressure exerted by the molecules on the walls of the container.
The question asks for the average pressure exerted by helium gas molecules on the walls of a cubic container. Using the equation PV = Nmv^2, we can calculate pressure by substituting the given values for volume, number of molecules, mass of one molecule, and root-mean-square speed.
Explanation:The question is asking to calculate the average pressure exerted by helium gas molecules on the walls of a cubic container. The important formula relating pressure (P), volume (V), number of molecules (N), mass of a molecule (m), and the square of the rms speed (v2) of the molecules in a gas is:
PV = Nmv2,
First, we need to determine the volume of the container, which is the cube of one side, so V = (20 cm)3 = (0.2 m)3. Inserting the given values into the equation and solving for P gives us the desired answer. Recall that the rms speed is given, so no temperature calculations are needed.
Therefore, using all given data points:
Volume (V) = (0.2 m)3
Number of molecules (N) = 2.00 × 1023
Mass of one helium molecule (m) = 3.40 × 10-27 kg
Root-mean-square speed (vrms) = 200 m/s
By substituting these values, we can find the pressure exerted by the gas. This represents an application of kinetic theory of gases which assumes the behavior of an ideal gas.
In what region of the periodic table will you find elements with relatively high IEs? With relatively low IEs?
High ionization energies are common in elements found on the right side of the periodic table, notably the Noble Gases due to their full electron shells. In contrast, low ionization energies are associated with elements on the left side of the periodic table, particularly metals like those of the Alkali Metal group with just one or two electrons in their outermost shell.
Explanation:In the periodic table, elements with relatively high IEs (Ionization Energies) are generally located on the right side, specifically in the group of Noble Gases. Noble gases like Helium or Neon have high IEs because they have full electron shells, and thus it requires a large amount of energy to remove an electron. On the other hand, the elements with relatively low IEs are located on the left side of the periodic table. This is because metals, such as those in the Alkali Metal group, have only one or two electrons in their outermost shell. These electrons are relatively easy to remove, resulting in a low ionization energy.
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Compare the wavelengths of an electron (mass = 9.11 x 10⁻³¹ kg) and a proton (mass = 1.67 x 10²⁷ kg), each having (a) a speed of 3.4 x 10⁶ m/s; (b) a kinetic energy of 2.7 x 10⁻¹⁵ J.
Answer:
Part A:
For electron:
[tex]\lambda_e=2.1392*10^{-10} m[/tex]
For Proton:
[tex]\lambda_p=1.16696*10^{-13} m[/tex]
Part B:
For electron:
[tex]\lambda_e=9.44703*10^{-12} m[/tex]
For Proton:
[tex]\lambda_p=2.20646*10^{-13} m[/tex]
Explanation:
Formula for wave length λ is:
[tex]\lambda=\frac{h}{mv}[/tex]
where:
h is Planck's constant=[tex]6.626*10^{-34}[/tex]
m is the mass
v is the velocity
Part A:
For electron:
[tex]\lambda_e=\frac{6,626*10^{-34}}{(9.11*10^{-31})*(3.4*10^6)} \\\lambda_e=2.1392*10^{-10} m[/tex]
For Proton:
[tex]\lambda_p=\frac{6,626*10^{-34}}{(1.67*10^{-27})*(3.4*10^6)} \\\lambda_p=1.16696*10^{-13} m[/tex]
Wavelength of proton is smaller than that of electron
Part B:
Formula for K.E:
[tex]K.E=\frac{1}{2}mv^2\\v=\sqrt{2 K.E/m}[/tex]
For Electron:
[tex]v_e=\sqrt{\frac{2*2.7*10^{-15}}{9.11*10^{-31}}} \\v_e=76990597.74\ m/s[/tex]
Wavelength for electron:
[tex]\lambda_e=\frac{6,626*10^{-34}}{(9.11*10^{-31})*(76990597.74)} \\\lambda_e=9.44703*10^{-12} m[/tex]
For Proton:
[tex]v_p=\sqrt{\frac{2*2.7*10^{-15}}{1.67*10^{-27}}} \\v_p=1798202.696\ m/s[/tex]
Wavelength for proton:
[tex]\lambda_p=\frac{6,626*10^{-34}}{(1.67*10^{-27})*(1798202.696)} \\\lambda_p=2.20646*10^{-13} m[/tex]
Wavelength of electron is greater than that of proton.
The structures of TeF4 and TeCl4 in the gas phase have been studied by electron diffraction.
a. Would you expect the TeiX (axial) distances in these molecules to be longer or shorter than than TeiX (equatorial) distances? Explain briefly.
b. Which compound would you predict to have the smaller X(axial)iTeiX(axial) angles? The smaller X(equatorial)iTeiX(equatorial) angles? Explain briefly
Answer:
a)
From VSPER theory, the compound TeF₄ and TeCl₄ AX₄E type of models. Hence, the molecular geometry of this molecule is trigonal bipyramidal. The plausible structure of this molecule are shown on the first uploaded image
Looking at the image we see that structure 1 has three lone pairs repulsion with 90° angle. From VSPER theory, the repulsive force between the electron pair is given as
lone pair - lone pair > lone pair - bond pair > bond pair - bond pair
The above shows that bond pair -bond pair has less repulsion than lone pair- bond pair, and next is lone pair - lone pair
This means that structure 2 is more stable structure for TeF₄ or TeCl₄ .,because the lone pair is present at equatorial position.
This stable structure is shown on the second uploaded image
A lone pair of electron occupy more space around the central atom than a bond pair electron that are present at axial positions, the two atoms that are present at axial position are tilt away from the lone pair
We can see the structure on the third uploaded image
Due to the repulsive interaction , the bond distance between Te - X(axial) increases, which means that the Te - X(axial) distance is longer than Te - X(equitorial) distance.
b)
It is a general concept that TeX₄ ha a bond angle of 90° for axial position and 120° in between equitorial position. This is shown on the fourth uploaded image
Considering TeF₄ and TeCl₄ , F is more electro-negative element Than Cl.This mean that the fluorine would pull strongly the shared electron away from the Te which reduces the electron density near the central Te atom.This would result in decrease bond angle be TeCl₄
So , F(axial) - Te - F(axial) has smaller bond angle than Cl(axial) - Te - Cl(axial)
Considering the equitorial position we see that because of the highly electro - negative fluorine atom, the bond angle decrease much in TeF₄ than in TeCl₄
This means that F(equitorial) - Te - F(equitorial) has smaller bond angle than Cl(equitorial) - Te - Cl(equitorial)
The molecules TeCl4 and TeF4 both have the axial bonds longer than the equatorial bonds due to repulsion. Secondly TeF4 and TeCl4 have axial bond angles less than equatorial bond angles due to their greater electronegativity.
The molecule TeCl4 has a see - saw shape. There are four bonds pairs and one lone pair in the molecule. We have to note that the axial bonds are longer than the equatorial bonds owing to the greater repulsion from the equatorial bonds leading to elongation of bonds.
Looking at the molecules TeF4 and TeCl4, we know that F and Cl are more electronegative than Te hence they pull more on the shared electron pair hence the axial bond angles are smaller than the equatorial bond angles.
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For each set of values, calculate the missing variable using the ideal gas law.
P V T n
Set 1 2.61 atm 1.69 L 36.1 °C n₁
Set 2 302 kPa 2382 mL T₂ 3.23 mol
Set 3 P₃ 0.0250 m³ 288 K 1.08 mol
Set 4 782 torr V₄ 303 K 5.26 mol
Using the Ideal Gas Law, missing variables (n, T, P, or V) are calculable with known values. Each set requires rearranging PV = nRT appropriately and substituting provided values, while ensuring units are consistent, to find the missing quantity.
Explanation:The Ideal Gas Law, PV = nRT, allows us to calculate the missing variable (P, V, T, or n) when the other three are known. The gas constant (R) has values depending on the units used, commonly 0.08206 L.atm/(K•mol) for calculations involving liters, atmospheres, and moles. Let's solve each set:
For Set 1, to find n, rearrange the equation to n = PV/(RT). Using T in Kelvin (36.1°C + 273) and the given values, solve for n.In Set 2, to find T, the equation is rearranged to T = PV/(nR). Remember to convert pressure and volume to appropriate units.For Set 3, P is unknown. Rearrange to P = nRT/V, using the given values with volumes in cubic meters (m³).Lastly, in Set 4 to find V, use V = nRT/P, converting temperature to Kelvin and pressure to atmospheres if necessary.Write a full set of quantum numbers for the following:
(a) The outermost electron in an Li atom
(b) The electron gained when a Br atom becomes a Br⁻ ion
(c) The electron lost when a Cs atom ionizes
(d) The highest energy electron in the ground-state B atom
The quantum numbers serve for experimenting with electron positions within an atom. For each given atom or ion - Li, Br-, Cs, and B - the quantum numbers for the outermost electron exhibit the electron's location in different shells, subshells and spins.
Explanation:The quantum numbers provide a unique address for each electron in an atom, listed as (n, l, ml, ms), where n is the principal quantum number, l is the azimuthal quantum number, ml is the magnetic quantum number, and ms is the spin quantum number.
Li atom: The outermost electron resides in the 2s subshell, so the quantum numbers are (2, 0, 0, ±1/2). Br⁻ ion: Upon gaining an electron, it goes to the 4p subshell. The quantum numbers are (4, 1, -1, -1/2).Cs atom: Before ionization, the outermost electron is in the 6s subshell. The quantum numbers are (6, 0, 0, ±1/2).B atom: For the highest energy electron in the ground-state, it belongs to the 2p subshell. The quantum numbers are (2, 1, 1, ±1/2).Learn more about Quantum Numbers here:https://brainly.com/question/27152536
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For these cases, the quantum numbers have been determined based on electron configurations and orbital positions. The solutions cover Li, Br⁻, Cs, and B electrons specifically.
Quantum numbers are used to describe the position and energy of an electron in an atom. Let's break down the quantum numbers for each of the given scenarios:
(a) The outermost electron in a Li atom:An auto mechanic spills 98.3 of 1.9 sulfuric acid solution from an auto battery. How many milliliters of 1.9 M sodium bicarbonate must be poured on the spill to react completely with the sulfuric acid?
Answer: The volume of sodium bicarbonate needed is 196.6 mL
Explanation:
To calculate the volume of base, we use the equation given by neutralization reaction:
[tex]n_1M_1V_1=n_2M_2V_2[/tex]
where,
[tex]n_1,M_1\text{ and }V_1[/tex] are the n-factor, molarity and volume of acid which is [tex]H_2SO_4[/tex]
[tex]n_2,M_2\text{ and }V_2[/tex] are the n-factor, molarity and volume of base which is [tex]NaHCO_3[/tex]
We are given:
[tex]n_1=2\\M_1=1.9M\\V_1=98.3mL\\n_2=1\\M_2=1.9M\\V_2=?mL[/tex]
Putting values in above equation, we get:
[tex]2\times 1.9\times 98.3=1\times 0.19\times V_2\\\\V_2=\frac{2\times 1.9\times 98.3}{1\times 1.9}=196.6mL[/tex]
Hence, the volume of sodium bicarbonate needed is 196.6 mL
In a laboratory experiment, students synthesized a new compound and found that when 12.37 grams of the compound were dissolved to make 167.6 mL of a benzene solution, the osmotic pressure generated was 6.26 atm at 298 K. The compound was also found to be nonvolatile and a non-electrolyte. What is the molecular weight they determined for this compound?
Answer: 288.32g/mol
Explanation:Please see attachment for explanation
What is the standard enthalpy change for the following reaction?
3CH4(g) + 4O3(g) ------> 3CO2(g) + 6H2O(g)
Substance ΔH°f (kJ/mol)
CH4(g) –74.87
O3(g) +142.7
CO2(g) –393.5
H2O(g) –241.8
Answer:
- 2977 kJ
Explanation:
Let's consider the following reaction.
3 CH₄(g) + 4 O₃(g) → 3 CO₂(g) + 6 H₂O(g)
We can find the standard enthalpy change for the reaction (ΔH°r) using the following expression.
ΔH°r = [3 mol × ΔH°f(CO₂(g)) + 6 mol × ΔH°f(H₂O(g))] - [3 mol × ΔH°f(CH₄(g)) + 4 mol × ΔH°f(O₃(g))]
ΔH°r = [3 mol × (-393.5 kJ/mol) + 6 mol × (-241.8 kJ/mol)] - [3 mol × (-74.87 kJ/mol) + 4 mol × (142.7 kJ/mol)]
ΔH°r = - 2977 kJ
Use the periodic table to identify the element with the electron configuration 1s²2s²2p⁴. Write its orbital diagram, and give the quantum numbers of its sixth electron.
The element with the electron configuration 1s²2s²2p⁴ is **oxygen (O)**.
Here's its orbital diagram:
↑ ↑
1s: | |
↓ ↓
↑ ↑
2s: | |
↓ ↓
↑ ↓ ↑ ↓
2p: -----|-----|-----|-----
↓ ↑ ↓ ↑
**Quantum numbers of the sixth electron:**
* Principal quantum number (n): 2 (second energy level)
* Azimuthal quantum number (l): 1 (p orbital)
* Magnetic quantum number (m_l): 0 (p_z orbital)
* Spin quantum number (m_s): +½ or -½ (two possible spin states)
**Explanation:**
- The electron configuration follows the Aufbau principle, filling orbitals from lowest energy to highest energy.
- The first two electrons fill the 1s orbital, the next two fill the 2s orbital, and the sixth electron goes into one of the three 2p orbitals (2p_x, 2p_y, or 2p_z).
- The magnetic quantum number (m_l) specifies the specific 2p orbital, and in this case, it's 0 for the 2p_z orbital.
- The spin quantum number (m_s) represents the electron's spin, which can be either +½ or -½.
During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = - 71 J/K .
What is the entropy change of the system for this process?
ΔSsys =_____ J/K
Answer:
entropy change of the system = +71 J/K
Explanation:
for a reversible process ;
ΔSsurrounding + ΔSsystem = 0 ............(1)
but ΔSsurrounding = - 71 J/K
substitute in equation (1)
ΔSsystem = -ΔSsurrounding
ΔSsystem = -(- 71 J/K)
= +71 J/K
For a reversible process where the surroundings undergo an entropy change of -71 J/K, the entropy change of the system is 71 J/K.
Since the process is reversible, the total entropy change for the universe is zero. This implies that the sum of the entropy changes for the system and the surroundings must be zero.
ΔSuniverse = ΔSsys + ΔSsurr = 0
Given that the entropy change of the surroundings, ΔSsurr, is -71 J/K, we can solve for the entropy change of the system, ΔSsys:
ΔSsys = - ΔSsurr
ΔSsys = - (-71 J/K)
ΔSsys = 71 J/K
Therefore, the entropy change of the system for this process is 71 J/K.
What are the molarity and osmolarity of a 1-liter solution that contains half a mole of calcium chloride? How many molecules of chloride would the solution contain?
Answer:
Molarity = 0.5 M
Osmolarity = 0.5 x 2 = 1 Osmpl.
Molecules of Cl2 = 6.02 x [tex]10^{23}[/tex] / 4= 1.505 x [tex]10^{23}[/tex] no. of molecules
Explanation:
If we add half mole in 1L volume than molarity will obviously be 0.5 M.
The osmolarity is molarity multiplies by number of dissociates of solute that for CaCl2 are 2. So, 2 x 0.5 = 1
Half will be molecules of Ca and half will be of Cl2 for 0.5M.
Final answer:
The molarity of a 1-liter solution with half a mole of calcium chloride is 0.5 M. The osmolarity, considering the dissociation of calcium chloride into three ions, is 1.5 osmol/L. The solution would contain 6.022 x 10²³chloride ions.
Explanation:
The molarity of a solution is defined as the number of moles of a solute per liter of solution. In this case, to calculate the molarity of calcium chloride, CaCl₂, in a 1-liter solution containing half a mole, we simply divide the moles of solute by the volume of the solution in liters:
Molarity (M) = moles of solute / liters of solution
Molarity (M) = 0.5 mol / 1 L = 0.5 M
The osmolarity of a solution is the total concentration of solute particles dissolved in a solution. Since calcium chloride dissociates into three ions (one Ca²⁺ ion and two Cl
- ions), the osmolarity is as follows:
Osmolarity = molarity x number of particles per formula unit
Osmolarity = 0.5 M x 3 = 1.5 osmol/L
For the number of chloride ions in the solution, we must look at the stoichiometry of calcium chloride: each formula unit of CaCl₂ yields two Cl⁻ions. So, we have:
Number of Cl⁻ ions = 0.5 mol CaCl₂ x (2 mol Cl⁻ / 1 mol CaCl₂) x (6.022 x 10²³ ions/mol)
Number of Cl⁻ ions = 1 mol Cl⁻ x 6.022 x 10²³ ions/mol = 6.022 x 10²³ ions