If the exact outer limit of an isolated atom cannot be measured, what criterion can we use to determine atomic radii? What is the difference between a covalent radius and a metallic radius?

The full set of quantum numbers varies depending on the electron being considered in each element or ion, with the numbers consisting of the principal quantum number (n), angular momentum quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system, which in this case are the electrons in various elements or ions.

Answer:

As shown in the attachment

Explanation:

The four possible isomers are as shown in the attachment.

Answer:

8.08 × 10⁻⁴

Explanation:

Let's consider the following reaction.

COCl₂(g) ⇄ CO (g) + Cl₂(g)

The initial concentration of phosgene is:

M = 2.00 mol / 1.00 L = 2.00 M

We can find the final concentrations using an ICE chart.

     COCl₂(g) ⇄ CO (g) + Cl₂(g)

I       2.00            0            0

C        -x             +x           +x

E    2.00 -x          x             x

The equilibrium concentration of Cl₂, x, is 0.0398 mol / 1.00 L = 0.0398 M.

The concentrations at equilibrium are:

[COCl₂] = 2.00 -x = 1.96 M

[CO] = [Cl₂] = 0.0398 M

The equilibrium constant (Keq) is:

Keq = [CO].[Cl₂]/[COCl₂]

Keq = (0.0398)²/1.96

Keq = 8.08 × 10⁻⁴

Answer:

a). [tex]2.25 \times 10^{8}[/tex] m/s

b).  1.23 m/s                                

Explanation:

Given :

Index of refraction for water, [tex]n_{w}[/tex] = 1.33

Index of refraction of diamond, [tex]n_{d}[/tex] = 2.42

We know that,

Refractive index of any material is given by,

[tex]n = \frac{c}{v}[/tex]

where c = sped of light in air

            v = speed of light in any medium

a). Speed of light in water

   [tex]v = \frac{c}{n_{w}}[/tex]

   [tex]v = \frac{3\times 10^{8}}{1.33}[/tex]

   [tex]v = 2.25\times 10^{8}[/tex] m/s

b). Speed of light in diamond

    [tex]v =\frac{c}{n_{d}}[/tex]

   [tex]v =\frac{3\times 10^{8}}{2.42}[/tex]

      = 1.23 m/s

Answer:

Molarity for solution is 1.44 M

Explanation:

Molarity = Mol of solute / 1L of solution

We would need the volume of solution (To be calculated with density)

We would need the moles of solute (To be calculated with  mass and molar mass of solute)

7.41 % by mass means 7.41 g of solute in 100 g of solution

So, moles of solute → 7.41 g / 58.45 g/mol = 0.127 mol

Let's determine the volume by density

Density = Mass / volume

1.14 g/mL = 100 g / Volume

Volume = 100 g / 1.14 g/mL → 87.7 mL

To reach molarity we must have the volume in L

87.7 mL . 1L / 1000 mL = 0.0877 L

Molarity → mol /L = 0.127 mol / 0.0877L → 1.44 M

Answer:

Yes, the 150-mL Erlenmeyer will be large enough to contain the acid.

Explanation:

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. Considering that the density of the phosphoric acid is 1.83 g/mL, we can find the volume occupied by the acid using the following expression.

density = mass / volume

volume = mass / density

volume = 225 g / (1.83 g/mL)

volume = 123 mL

The phosphoric acid occupies 123 mL so the 150-mL Erlenmeyer will be large enough to contain it.

Answer:

1100 millimeters

Explanation:

1 mole of isopentyl alcohol = 22.4L = 22.4×1000 mL = 22,400L

0.050 moles of isopentyl alcohol = 0.050 × 22,400mL = 1120mL = 1100mL (to two significant figures)

Answer:

Lithium and sodium are the most similar because they are both alkali elements located in the same group, and therefore have similar properties.

Nitrogen and oxygen are not the most similar because although they are both non metals elements, are each located in a different group

Explanation:

Li and Na are both alkali elements from group 1 that shares some similities. The both can be obtained by the  water hydrolysis. These are common reactions:

Metal from group 1 + H₂O → Base + H₂

Metal from group 1 + O₂ → oxides

Metal from group 1 + group 17 →  ionic halides

Both form cations with 1+ charge, they can release only 1 e-

N is an element from group 15 and O, from group 16. They are both non metal.

Nitrogen can make a variety of oxides.

They react in water to produce nitric acid:

N₂O₃ + H₂O → 2HNO₃

N₂O₅ + H₂O → 2HNO₃

It has an anion with -3, as oxidation state. (Nitride)

The N with H, makes a well known hidride → ammonia

N₂ + 3H₂ → 2NH₃

The Oxygen also makes a well known hidride → water

2H₂ + O₂ → 2H₂O

Both are covalent hidrides.

N can have many oxidation's states. O always acts with -2 except for the peroxydes, with -1. O can have a great power of oxidation, that N does not have.

O₂ always acts as a reactant, at combustion reactions.

Lithium and sodium are similar as they are both alkali elements, found in the same group of the periodic table, leading to similar properties. Nitrogen and oxygen, while both nonmetals, are in separate groups, yielding different properties.

a. Lithium and sodium are the most similar because they are both alkali elements located in the same group, and therefore have similar properties. Lithium and sodium both belong to the alkali metals group in the periodic table. They share similar chemical behaviors, as they have only one electron in a valence s subshell outside a filled set of inner shells. This fact influences their reactivity and the compounds they can form.

b. Nitrogen and oxygen are not the most similar because although they are both nonmetal elements, they are each located in a different group. Even though nitrogen and oxygen are close to each other in the periodic table, they do not share the same group, hence they have different properties and different numbers of valence electrons.

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Answer: a) The [tex]K_a[/tex] of acetic acid at [tex]25^0C[/tex] is [tex]1.82\times 10^{-5}[/tex]

b) The percent dissociation for the solution is [tex]4.27\times 10^{-3}[/tex]

Explanation:

[tex]CH_3COOH\rightarrow CH_3COO^-H^+[/tex]

 cM              0             0

[tex]c-c\alpha[/tex]        [tex]c\alpha[/tex]          [tex]c\alpha[/tex]

So dissociation constant will be:

[tex]K_a=\frac{(c\alpha)^{2}}{c-c\alpha}[/tex]

Give c= 0.10 M and [tex]\alpha[/tex] = ?

Also [tex]pH=-log[H^+][/tex]

[tex]2.87=-log[H^+][/tex]  

[tex][H^+]=1.35\times 10^{-3}M[/tex]

[tex][CH_3COO^-]=1.35\times 10^{-3}M[/tex]

[tex][CH_3COOH]=(0.10M-1.35\times 10^{-3}=0.09806M[/tex]

Putting in the values we get:

[tex]K_a=\frac{(1.35\times 10^{-3})^2}{(0.09806)}[/tex]

[tex]K_a=1.82\times 10^{-5}[/tex]

b)  [tex]\alpha=\sqrt\frac{K_a}{c}[/tex]

[tex]\alpha=\sqrt\frac{1.82\times 10^{-5}}{0.10}[/tex]

[tex]\alpha=4.27\times 10^{-5}[/tex]

[tex]\% \alpha=4.27\times 10^{-5}\times 100=4.27\times 10^{-3}[/tex]

The Ka of acetic acid is calculated using the pH and the definition of Ka using an ICE table, then percent dissociation is calculated using the initial concentration and the concentration of H+ found. We first calculate [H+] using the pH, then input those values into the Ka expression to find Ka, then use the formula for percent dissociation to find the percent dissociation.

To solve this problem, we will first calculate the Ka using the known pH and the equilibrium relationship between the pH, Ka and [H+] concentration. Then we will calculate the percent dissociation of the acetic acid.

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Answer:

For a: The number of inner electrons, outer electrons and valence electrons are 28, 7 and 7 respectively.

For b: The number of inner electrons, outer electrons and valence electrons are 54, 1 and 1 respectively.

For c: The number of inner electrons, outer electrons and valence electrons are 23, 1 and 1 respectively.

For d: The number of inner electrons, outer electrons and valence electrons are 36, 2 and 2 respectively.

For e: The number of inner electrons, outer electrons and valence electrons are 2, 7 and 7 respectively.

Explanation:

Outer shell electrons are the electrons which are not tightly held by the electrons. They are called as valence electrons. The electrons present in the highest principle quantum number are known as valence electrons.

Inner shell electrons are the electrons which are tightly held by the electrons. They are called as core electrons.

Inner electrons = Total number of electrons - Valence electrons

Total number of electrons in an atom is equal to the atomic number of the element.

For the given options:

Bromine is the 35th element of the periodic table having electronic configuration of [tex]1s^22s^22p^63s^23p^64s^23d^{10}4p^5[/tex]

Highest principle quantum number is 4

Number of valence electrons = 7

Number of outer electrons = 7

Number of inner electrons = 35 - 7 = 28

Cesium is the 55th element of the periodic table having electronic configuration of [tex]1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^66s^1[/tex]

Highest principle quantum number is 6

Number of valence electrons = 1

Number of outer electrons = 1

Number of inner electrons = 55 - 1 = 54

Chromium is the 24th element of the periodic table having electronic configuration of [tex]1s^22s^22p^63s^23p^64s^13d^{5}[/tex]

Highest principle quantum number is 4

Number of valence electrons = 1

Number of outer electrons = 1

Number of inner electrons = 24 - 1 = 23

Strontium is the 38th element of the periodic table having electronic configuration of [tex]1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^2[/tex]

Highest principle quantum number is 5

Number of valence electrons = 2

Number of outer electrons = 2

Number of inner electrons = 38 - 2 = 36

Fluorine is the 9th element of the periodic table having electronic configuration of [tex]1s^22s^22p^5[/tex]

Highest principle quantum number is 2

Number of valence electrons = 7

Number of outer electrons = 7

Number of inner electrons = 9 - 7 = 2

The number of inner, outer, and valence electrons for each element is as follows: Br has 2 inner electrons, 28 outer electrons, and 7 valence electrons; Cs has 2 inner electrons, 118 outer electrons, and 1 valence electron; Cr has 2 inner electrons, 24 outer electrons, and 6 valence electrons; Sr has 2 inner electrons, 36 outer electrons, and 2 valence electrons; F has 2 inner electrons, 7 outer electrons, and 7 valence electrons.

(a) Br has 2 inner electrons, 28 outer electrons, and 7 valence electrons.

(b) Cs has 2 inner electrons, 118 outer electrons, and 1 valence electron.

(c) Cr has 2 inner electrons, 24 outer electrons, and 6 valence electrons.

(d) Sr has 2 inner electrons, 36 outer electrons, and 2 valence electrons.

(e) F has 2 inner electrons, 7 outer electrons, and 7 valence electrons.

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Explanation:

As per the measurements that are made by the student are as follows.

        21.6 cm is equivalent to 8.5 inch

Therefore, 1 cm for the given situation will be equivalent to inch as follows.

              1 cm = [tex]\frac{8.5}{21.6}[/tex] inch

                      = 0.393 inch

Hence, we will calculate the ratio of cm : inch as follows.

               Ratio of cm : inch = [tex]\frac{8.5}{21.6}[/tex]

                                             = 0.39

Thus, we can conclude that the ratio of cm/inch using the students data is 0.39.

In a reaction between hydrogen chloride and oxygen to form water and chlorine gas, using the provided masses and the balanced chemical equation, hydrogen chloride is found to be the limiting reactant, leaving 14.8 g of excess oxygen gas after the reaction.

To solve this problem, we first need to write the balanced chemical equation for the reaction between hydrogen chloride (HCl) and oxygen (O₂) to form water (H₂O) and chlorine gas (Cl₂). The reaction is as follows:

4 HCl(g) + O₂(g) ⇒ 2 H₂O(g) + 2 Cl₂(g)

Using the given masses of reactants, we calculate the molar amounts of HCl and O₂. The molar mass of HCl is approximately 36.5 g/mol and that of O₂ is 32.0 g/mol. Thus:

53.2 g HCl x (1 mol HCl / 36.5 g) = 1.46 mol HCl

26.5 g O₂ x (1 mol O₂ / 32.0 g) = 0.828 mol O₂

According to the balanced equation, it takes 4 moles of HCl to react with 1 mole of O₂. So, we divide the molar amounts by their respective coefficients to find the limiting reactant:

1.46 mol HCl / 4 = 0.365 mol

0.828 mol O₂ / 1 = 0.828 mol

Since 0.365 mol < 0.828 mol, HCl is the limiting reactant. The reaction will consume all of the HCl, leaving some O₂ in excess. To find the amount of excess O₂, we calculate how much O₂ is needed to react with the available HCl:

1.46 mol HCl x (1 mol O₂ / 4 mol HCl) = 0.365 mol O₂ needed

We subtract the O₂ needed from the initial amount to find the excess:

0.828 mol O₂ - 0.365 mol O₂ = 0.463 mol excess O₂

0.463 mol O₂ x 32.0 g/mol = 14.8 g excess O₂

Therefore, the mass of the excess reactant O2 remaining is 14.8 g.

Answer:

Explanation:

a ) period 4 noble gas is krypton

isoelectronic with it are Sr ⁺² and Br⁻

compound is SrBr₂

b ) Period 3 noble gas is Argon

isoelectronic with it are Mg⁺² and O⁻²

compound is MgO

c)  2+ ion is the smallest with a filled d subshell is Zn⁺² , smallest halogen

is F⁻

compound is ZnF₂

d )   ions  from the largest and smallest ionizable atoms in Period 2

Li⁺ and  F⁻

compound is LiF

The compounds resulting from the described ionic interactions are Strontium Sulfide (SrS), Magnesium Oxide (MgO), Iron(II) Fluoride (FeF2), and Beryllium Fluoride (BeF2).

The compound formed by ionic interactions can be determined by considering the properties of the ions given.  

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Answer:

a) The atomic mass of the potassium is 54.23 amu.

b) The melting point of bromine gas is 6.3°C.

Explanation:

a) Atomic mass of Na =22.99 amu

Atomic mass of Rb = 85.47 amu

Döbereiner triad = Na , K ,Rb

Taking average of  atomic masses of  Na and Rb

Atomic mass of the K = [tex]\frac{22.99 amu+85.47 amu}{2}=54.23 amu[/tex]

The atomic mass of the potassium is 54.23 amu.

b) Melting point of chlorine gas =-101.0°C

Melting point of iodine gas =113.6°C

Döbereiner triad = Cl, Br , I

Melting point of bromine gas :

=[tex]\frac{-101.0^oC +113.6^oC}{2}=6.3^oC[/tex]

The melting point of chlorine gas is 6.3°C.

Answer:

0.827 mol

Explanation:

Sodium bicarbonate (NaHCO₃) reacts with hydrochloric acid (HCl) by the equation:

NaHCO₃ + HCl → CO₂ + NaCl + H₂O

Thus, the stoichiometry between sodium bicarbonate and CO₂ is

1 mol : 1 mol.

The molar mass of sodium bicarbonate is 84.007 g/mol, thus the mass in 1 mol is 84.007 g, and the density of it is 2.2 g/mL, thus the volume in 1 mol is:

V = 84.007/2.2 = 38.185 mL

According to Proust's law, the ratio reaction remains constant so:

38.185 mL of NaHCO₃/1 mol of CO₂ = 31.6 mL of NaHCO₃/n

38.185n = 31.6

n = 31.6/38.185

n = 0.827 mol of CO₂

Answer:

1. Group 1 — 3

2. Transition metals

Explanation:

d-block elements

These elements are also known as transition elements as their positioning and transition of properties lies between s and p block elements.

d-block elements have number of valence electrons equal to their group number, which is equal to the number of electrons in the "valence shell".

For example, Consider a transition metal or d block element Scandium. It's atomic number is 21.

Electronic configuration of Scandium(Sc)- [Ar] 3d¹ 4s²,  it has three electrons in its outermost shell and has a valency of three.

The electron configuration of scandium indicates that the ultimate shell(orbit) of scandium has a complete of electrons. But the electron configuration of scandium within side the Aufbau approach indicates that its ultimate electron([tex]3d^1\\[/tex]) has entered the d-orbital. Thus we can say that scandium has 3 valence electrons.

Therefore, we can say that d block elements have same number of outer electrons and valence electrons.

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Answer : The electron configurations consistent with this fact is, (b) [Kr] 4d¹⁰  

Explanation :

Electronic configuration : It is defined as the representation of electrons around the nucleus of an atom.

Number of electrons in an atom are determined by the electronic configuration.

Paramagnetic compounds : They have unpaired electrons.

Diamagnetic compounds : They have no unpaired electrons that means all are paired.

The given electron configurations of Palladium are:

(a) [Kr] 5s²4d⁸

In this, there are 2 electrons in 's' orbital and 8 electrons in 'd' orbital. From the partial orbital diagrams we conclude that 's' orbital are paired but 'd' orbital are not paired. So, this configuration shows paramagnetic.

(b) [Kr] 4d¹⁰

In this, there are 10 electrons in 'd' orbital. From the partial orbital diagrams we conclude that electrons in 'd' orbital are paired. So, this configuration shows diamagnetic.

(c) [Kr] 5s¹4d⁹

In this, there are 1 electron in 's' orbital and 9 electrons in 'd' orbital. From the partial orbital diagrams we conclude that 's' orbital and 'd' orbital are not paired. So, this configuration shows paramagnetic.

The correct electron configuration for a diamagnetic substance like Palladium (Pd) is [Kr] 4d¹⁰. This is because diamagnetic substances like Palladium need to have all their electron orbitals fully filled, thereby having no unpaired electrons.

The subject of this question is about the electron configuration of Palladium (Pd; Z 46), which is a diamagnetic element. Diamagnetic substances have no unpaired electrons and are not attracted to a magnetic field. Thus, to be consistent with this fact, the electron configuration of Palladium must not have any unpaired electrons.

(a) [Kr] 5s²4d⁸: This configuration would imply there are unpaired electrons in the 4d orbital, which contradicts the fact that Palladium is diamagnetic.

(b) [Kr] 4d¹⁰: This configuration correctly states that all the orbitals are filled, including the 5s orbital before the 4d orbital. Therefore, the correct electron configuration for Palladium, a diamagnetic element, is [Kr] 4d¹⁰.

(c) [Kr] 5s¹4d⁹: The proposed configuration would also suggest an unpaired electron exists in the 4d orbital, which contradicts Palladium being diamagnetic.

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Answer:

The product is cyclohexanol

Explanation:

Firstly,

A ketone undergo a borohydride reduction reaction to form an alcohol as below,

R-CO-R'  ⇒ R-CO(OH)-R'

        1.56 δ (4H, triplet) - (-CH₂-CH₂-CH-OH) ; triplet as coupling with 2 H,

        1.78 δ (4H, multiplet)  - (-CH₂-CH₂-CH-OH); multiplet as coupling with 2H of CH₂, 1 H of CH

         3.24 δ (1H, quintet); - (-CH₂-CH₂-CH(CH₂-)-OH), coupling with4 H of 2 group of CH₂

         3.58 δ (1H, singlet); - (-CH₂-CH₂-CH(CH₂-)-OH), hydrogen of alcohol group, not tend to coupling with other hydrogen

To calculate the radius of an atom in a body-centered cubic (BCC) structure, we can use the formula: radius (r) = √(3/4) * a/2, where a is the lattice constant.

In a body-centered cubic (BCC) unit cell, the atoms in the corners do not touch each other but contact the atom in the center. The unit cell contains two atoms: one-eighth of an atom at each of the eight corners and one atom in the center. An atom in a BCC structure has a coordination number of eight. To calculate the radius of an atom in a BCC structure, we can use the formula:

Radius (r) = √(3/4) * a/2

where a is the lattice constant. Plugging in the given value of the lattice constant as 409, we can calculate the radius of the atom of metal M in a BCC structure using this formula.

Answer:

Answer in explanation

Explanation:

Argon has 18 electrons. So to get the element in question, we only need to add 18 to the number of the filled electrons.

a. Germanium, atomic number 32

Other group members:

Silicon Si , Carbon C , Tin Sn , Lead Pb and Flerovium Fl

b. Cobalt , atomic number 27

Other group members:

Rhodium Rh , Iridium Ir and Meitnerium Mt

c. Technetium , atomic number 43

Krypton is element 36

Other group members are :

Manganese Mn , Rhenium Re and Bohrium Bh

This is a incomplete question. The complete question is:

It takes 348 kJ/mol to break a carbon-carbon single bond. Calculate the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon. Round your answer to correct number of significant digits

Answer: 344 nm

Explanation:

[tex]E=\frac{Nhc}{\lambda}[/tex]

E= energy  = 348kJ= 348000 J  (1kJ=1000J)

N = avogadro's number = [tex]6.023\times 10^{23}[/tex]

h = Planck's constant = [tex]6.626\times 10^{-34}Js [/tex]

c = speed of light = [tex]3\times 10^8ms^{-1}[/tex]

[tex]348000=\frac{6.023\times 10^{23}\times 6.626\times 10^{-34}\times 3\times 10^8}{\lambda}[/tex]

[tex]\lambda=\frac{6.023\times 10^{23}\times 6.626\times 10^{-34}\times 3\times 10^8}{348000}[/tex]

[tex]\lambda=3.44\times 10^{-7}m=344nm[/tex]    [tex]1nm=10^{-9}m[/tex]

Thus the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon is 344 nm

Answer : The condensed ground-state electron configuration for each is:

(a) [tex][Ar]4s^24p^{1}[/tex]

(b) [tex][Ar]4s^23d^{10}[/tex]

(c) [tex][Ar]4s^23d^{1}[/tex]

Explanation :

Electronic configuration : It is defined as the representation of electrons around the nucleus of an atom.

Number of electrons in an atom are determined by the electronic configuration.

Noble-Gas notation : It is defined as the representation of electron configuration of an element by using the noble gas directly before the element on the periodic table.

(a) The given element is, Ga (Gallium)

As we know that the gallium element belongs to group 13 and the atomic number is, 31

The ground-state electron configuration of Ga is:

[tex]1s^22s^22p^63s^23p^64s^23d^{10}4p^1[/tex]

So, the condensed ground-state electron configuration of Ga in noble gas notation will be:

[tex][Ar]4s^24p^{1}[/tex]

(b) The given element is, Zn (Zinc)

As we know that the zinc element belongs to group 12 and the atomic number is, 30

The ground-state electron configuration of Zn is:

[tex]1s^22s^22p^63s^23p^64s^23d^{10}[/tex]

So, the condensed ground-state electron configuration of Zn in noble gas notation will be:

[tex][Ar]4s^23d^{10}[/tex]

(c) The given element is, Sc (Scandium)

As we know that the scandium element belongs to group 3 and the atomic number is, 21

The ground-state electron configuration of Sc is:

[tex]1s^22s^22p^63s^23p^64s^23d^{1}[/tex]

So, the condensed ground-state electron configuration of Sc in noble gas notation will be:

[tex][Ar]4s^23d^{1}[/tex]

Answer:

The volume of CO2 is 4.20 L

Explanation:

Step 1: Data given

Pressure = 270 mm Hg =  260 /760 = 0.355263 atm

Temperature : 38.5 °C = 311.65 K

Mass of C4H8 = 0.820 grams

Step 2: The balanced equation

C4H8 + 6O2 → 4CO2 + 4H2O

Step 3: Calculate moles C4H8

Moles C4H8 = mass C4H8 / molar mass C4H8

Moles C4H8 = 0.820 grams / 56.11 g/mol

Moles C4H8 = 0.0146 moles

Step 4: Caalculate moles CO2

For 1 mol C4H8 we need 6 moles O2 to produce 4 moles CO2 and 4 moles H2O

For 0.0146 moles we'll have 4*0.0146 = 0.0584 moles CO2

Step 6: Calculate Volume CO2

p*V = n*R*T

V = (n*R*T) /p

⇒ with V = the volume of CO2 = TO BE DETERMINED

⇒ with n = the moles of CO2 = 0.0584 moles

⇒ with R = the gas constant = 0.08206 L*atm / mol*K

⇒ with T = The temperature = 311.65 K

⇒ with p = the pressure = 0.355263 atm

V = (0.0584 * 0.08206 * 311.65) / 0.355263

V = 4.20 L

The volume of CO2 is 4.20 L

Answer:

For 1: The molarity of [tex]K^+\text{ ions}[/tex] in this solution is 0.0592 M

For 2: The new molarity of [tex]K^+\text{ ions}[/tex] in this solution is [tex]2.07\times 10^{-3}M[/tex]

Explanation:

To calculate the molarity of solution, we use the equation:

[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in L)}}[/tex]

Given mass of KOH = 1.66 g

Molar mass of KOH = 56.1 g/mol

Volume of solution = 500.0 mL

Putting values in above equation, we get:

[tex]\text{Molarity of solution}=\frac{1.66\times 1000}{56.1g/mol\times 500.0}\\\\\text{Molarity of solution}=0.0592M[/tex]

1 mole of KOH produces 1 mole of potassium ions and 1 mole of hydroxide ions

So, molarity of [tex]K^+\text{ ions}=0.0592M[/tex]

Hence, the molarity of [tex]K^+\text{ ions}[/tex] in this solution is 0.0592 M

To calculate the molarity of the diluted solution, we use the equation:

[tex]M_1V_1=M_2V_2[/tex]

where,

[tex]M_1\text{ and }V_1[/tex] are the molarity and volume of the concentrated KOH solution  having [tex]K^+\text{ ions}[/tex]

[tex]M_2\text{ and }V_2[/tex] are the molarity and volume of diluted KOH solution  having [tex]K^+\text{ ions}[/tex]

We are given:

[tex]M_1=0.0592M\\V_1=35.00mL\\M_2=?M\\V_2=1000mL[/tex]

Putting values in above equation, we get:

[tex]0.0592\times 35.00=M_2\times 1000\\\\M_2=\frac{0.0592\times 35.0}{1000}=2.07\times 10^{-3}M[/tex]

Hence, the new molarity of [tex]K^+\text{ ions}[/tex] in this solution is [tex]2.07\times 10^{-3}M[/tex]

Answer : The new molarity of glycerol in the photobacterium cell growth medium is, [tex]6.69\times 10^3\mu M[/tex]

Explanation :

Formula used :

[tex]M_1V_1=M_2V_2[/tex]

where,

[tex]M_1\text{ and }V_1[/tex] are the initial molarity and volume of glycerol.

[tex]M_2\text{ and }V_2[/tex] are the new molarity and volume of glycerol .

We are given:

[tex]M_1=81.3\mu M\\V_1=913mL\\M_2=?\\V_2=11.1mL[/tex]

Putting values in above equation, we get:

[tex]81.3\mu M\times 913mL=M_2\times 11.1mL\\\\M_2=6.69\times 10^3\mu M[/tex]

Hence, the new molarity of glycerol in the photobacterium cell growth medium is, [tex]6.69\times 10^3\mu M[/tex]

Final answer:

The new molarity of glycerol after the evaporation of the solvent from 913 mL to 11.1 mL is 6.69 × 10^6 µM, calculated using the conservation of moles and by adjusting the concentration for the reduced volume.

Explanation:

The molarity of a solution is defined as the number of moles of solute per liter of solution. When the solvent evaporates from a solution and the volume decreases, the molarity of the solute increases because the same amount of solute is now present in a smaller volume of solvent. The original volume of the photobacterium cell growth medium is 913 mL with a glycerol concentration of 81.3 µM (micro molar). The new volume of the cell growth medium after evaporation is 11.1 mL. To find the new molarity, we can use the concept of conservation of moles of solute, which states that the number of moles in the solution before and after evaporation are the same.

First, we convert the original volume from milliliters to liters:

913 mL = 0.913 L

Then we calculate the moles of glycerol originally in the solution:

moles of glycerol = (81.3 µM) × (0.913 L) = 0.0000813 moles/L × 0.913 L = 7.42449 × [tex]10^{-5}[/tex] moles

Since the amount of glycerol remains the same, and only the volume has changed, we can find the new molarity by dividing the moles of glycerol by the new volume in liters:

New volume in liters: 11.1 mL = 0.0111 L

New molarity = moles of glycerol / new volume
= 7.42449 × [tex]10^{-5}[/tex] moles / 0.0111 L

Performing the calculation gives us:

New molarity = 6.68873 M (rounded to three significant digits). However, this result is not in micro molarity. So to convert this to µM,

1 M = 1,000,000 µM

New molarity in µM = 6.68873 × 1,000,000 µM = 6.69 × 106 µM (or 6,690,000 µM, rounded to three significant digits)

Answer:

We need 21.0 moles of O2

Explanation:

Step 1: Data given

Moles of propanoic acid = 6.0 moles

CH3CH2COOH = propanoic acid

Step 2: The balanced equation

2CH3CH2COOH + 7O2 → 6CO2 + 6H2O

Step 3 :Calculate moles O2

For 2 moles propanoic acid we need 7 moles O2 to produce 6 moles CO2 and 6 moles H2O

For 6.0 moles propanoic acid we need 6.0 * 3.5 = 21 moles O2

We need 21.0 moles of O2

To combust 6 moles of propanoic acid completely, 15 moles of [tex]O_{2}[/tex] are required, based on the balanced chemical equation for the combustion of propanoic acid. 2 [tex]CH_{3} CH_{2} COOH[/tex] + 5 [tex]O_{2}[/tex] → 6 [tex]CO_{2}[/tex] + 4 [tex]H_{2}O[/tex] is the balanced chemical equation.

The question asks for the amount of Oxygen ([tex]O_{2}[/tex]) needed for the complete combustion of propanoic acid ([tex]CH_{3} CH_{2} COOH[/tex]). The combustion of propanoic acid can be represented by a balanced chemical equation:

2 [tex]CH_{3} CH_{2} COOH[/tex] + 5 [tex]O_{2}[/tex] → 6 [tex]CO_{2}[/tex] + 4 [tex]H_{2}O[/tex]

This means that 2 moles of propanoic acid require 5 moles of [tex]O_{2}[/tex] for complete combustion. If we have 6 moles of propanoic acid, a simple stoichiometric calculation would be to multiply the amount of [tex]O_{2}[/tex] required for 2 moles of propanoic acid by 3 (since 6 moles is three times larger than 2 moles), resulting in:

5 moles [tex]O_{2}[/tex]/2 moles [tex]CH_{3} CH_{2} COOH[/tex] × 6 moles [tex]CH_{3} CH_{2} COOH[/tex] = 15 moles [tex]O_{2}[/tex]

Therefore, to combust 6 moles of propanoic acid completely, 15 moles of [tex]O_{2}[/tex] are required.

Here is the complete question

An aqueous solution is saturated with both a solid and a gas at 5 °C. What is likely to happen if the solution is heated to 85 °C ?

View Available Hint(s)

a.) Some gas will bubble out of solution and more solid will dissolve.

b.) Some gas will bubble out of the solution and some solid will precipitate out of the solution.

c.) Some solid will precipitate out of solution.

d.) More gas will dissolve and more of the solid will dissolve.

Answer:

a.) Some gas will bubble out of solution and more solid will dissolve.

Explanation:

Temperature increase usually increases the dissolution of solids in liquids. From the question; Some gas will be bubble out of the solution as the temperature is being increased to 85 °C because that aqueous solution is saturated(i.e equal amount of solute and solvent in the solution) with both  solid and gas at 5 °C, but when the solution is heated to 85 °C, the solution becomes supersaturated( i.e the solute is now more at the given temperature than the solvent).  

Answer:

As the temperature increases, the solubility of the solid increases and the solubility of the gas decreases. When the solution that is saturated between a solid and a gas at 5 ° C and heated to 85 ° C, the gas comes out of the solution first.

Explanation:

A saturated solution is one that has the maximum amount of solute that is dissolved. An unsaturated solution is one that has a low amount of solute compared to the saturated solution. According to Henry's law, the solubility of a gas at a specific temperature is directly proportional to its partial pressure, that is

C ∝ p

C = kp

Where

p is the partial pressure

k ia a proportionality constant

C is the concentration of the gas

Explanation:

The n in Bohr model of the atom is principle quantum number.

The Rydberg n integer stats represent electron orbits at various integral distances from the atom in Bohr's conceptualization of the atom. Subsequent models discovered that the values for n1 and n2 match the two orbitals ' principle quantum numbers.

Final answer:

The Rydberg equation and the Bohr model are related through the principal quantum number n. In the Rydberg equation, n1 and n2 represent initial and final energy levels during an electron transition, similar to the energy levels denoted by n in the Bohr model of the atom. This relationship explains the emission spectra of atoms such as hydrogen.

Explanation:

The Rydberg equation relates to the Bohr model through the quantum number n. In the Rydberg equation, n1 corresponds to the lower energy level (or orbit) from which an electron transitions to a higher energy level designated by n2 where n2 > n1. The principle quantum number n in the Bohr model signifies distinct energy levels or orbits in which electrons can reside around the nucleus, with the lowest energy state starting at n=1 and increasing integers signifying higher energy states.

When an electron jumps between energy levels, light is emitted, and the wavelength of this light can be calculated using the Rydberg formula, which includes the Rydberg constant and the initial and final principal quantum numbers. For the hydrogen atom, transitions to the ground state (n = 1) produce the Lyman series in the ultraviolet band, while transitions to the first excited state (nf = 2) result in the Balmer series in the visible band, and so on for higher energy levels.

Answer:

less than

Explanation:

The absorbance of a solution is a function of the concentration (amount) of a substance in the solution. Mathematically, if the concentration is increased, the absorbance of the solution will also increase and if the concentration is decreased, the absorbance will decrease. There will be a decrease in the value of the absorbance because the calculated and predicted masses are not the same.

Final answer:

The absorbance of a solution made from a solid may be greater or less than that of an unknown solution, depending on their respective concentrations and properties.

Explanation:

When comparing the absorbance of a solution made from a solid to that of an unknown solution, we need to consider the concentration or the size of the container. A solution made from a solid may have a higher absorbance because it contains a higher concentration of molecules that can interact with light. On the other hand, the absorbance of the unknown solution will depend on its specific properties. Therefore, whether the absorbance of the solution made from a solid is greater, less than, or the same as the absorbance of the unknown solution cannot be determined without further information.

Answer: The enthalpy change is 34.3 kJ

Explanation:

The conversions involved in this process are :

[tex](1):H_2O(s)(-18^0C)\rightarrow H_2O(s)(0^0C)\\\\(2):H_2O(s)(0^0C)\rightarrow H_2O(l)(0^0C)\\\\(3):H_2O(l)(0^0C)\rightarrow H_2O(l)(25^0C)[/tex]

Now we have to calculate the enthalpy change.

[tex]\Delta H=[m\times c_{s}\times (T_{final}-T_{initial})]+n\times \Delta H_{fusion}+[m\times c_{l}\times (T_{final}-T_{initial})][/tex]

where,

[tex]\Delta H[/tex] = enthalpy change = ?

m = mass of water = 72.0  g

[tex]c_{s}[/tex] = specific heat of ice = [tex]2.09J/g^0C[/tex]

[tex]c_{l}[/tex] = specific heat of liquid water = [tex]4.184J/g^0C[/tex]

n = number of moles of water = [tex]\frac{\text{Mass of water}}{\text{Molar mass of water}}=\frac{72.0g}{18g/mole}=4.00moles[/tex]

[tex]\Delta H_{fusion}[/tex] = enthalpy change for fusion = 6010 J/mole

Now put all the given values in the above expression, we get

[tex]\Delta H=[72.0g\times 2.09J/g^0C\times (0-(-18)^0C]+4.00mole\times 6010J/mole+[72.0g\times 4.184J/g^)C\times (25-0)^0C][/tex][tex]\Delta H=34279.8J=34.3kJ[/tex]        (1 KJ = 1000 J)

Therefore, the enthalpy change is 34.3 kJ

Final answer:

The total amount of heat energy required to convert 72.0 g of ice at − 18.0 °C to water at 25.0 °C is 34.2 kJ. This includes heating the ice to 0 °C, melting it, and then heating the water to 25.0 °C.

Explanation:

To calculate the amount of heat energy required in kilojoules to convert 72.0 g of ice at − 18.0 °C to water at 25.0 °C, we must consider three stages of the process: heating the ice to 0 °C, melting the ice, and then heating the resulting water to 25.0 °C.

The total energy Qtotal is the sum of Q1, Q2, and Q3, which is 2664 J + 23976 J + 7566 J = 34206 J.

To convert this value to kilojoules, we divide by 1,000: 34206 J / 1000 = 34.206 kJ. Therefore, the answer to three significant figures is 34.2 kJ.