If equal volumes of 0.1 M HCl and 0.2 M TRIS (base form) are mixed together. The pKa of TRIS is 8.30. Which of the following statements about the resulting solution are correct?

(Select all that apply.)

A. The ratio of [conjugate base]/[conjugate acid] is [0.1 M]/[0.05 M].
B. This solution is too basic to be a buffer.
C. The ratio of [conjugate base]/[conjugate acid] is [0.05 M]/[0.05 M].
D. This solution is a good buffer.
E. The majority of TRIS will be in the acid form in the solution.

Explanation:

The sped of sound is given as follows.

            C = [tex]\sqrt{\gamma RT}[/tex]

It is known that for hydrogen,

         R = 4124 J/kg K

         T = 288 k

       [tex]\gamma[/tex] = 1.41

Therefore, calculate the value of [tex]C_{hydrogen}[/tex] as follows.

         [tex]C_{hydrogen} = \sqrt{\gamma RT}[/tex]

                     = [tex]\sqrt{1.41 \times 4124 J/kg K \times 288}[/tex]

                     = 1294.1 m/s

For helium,

         R = 2077 J/kg K

         T = 288 k

       [tex]\gamma[/tex] = 1.66

Therefore, calculate the value of [tex]C_{helium}[/tex] as follows.

         [tex]C_{helium} = \sqrt{\gamma RT}[/tex]

                     = [tex]\sqrt{1.66 \times 2077 J/kg K \times 288}[/tex]

                     = 996.48 m/s

For nitrogen,

         R = 296.8 J/kg K

         T = 288 k

       [tex]\gamma[/tex] = 1.4

Therefore, calculate the value of [tex]C_{hydrogen}[/tex] as follows.

         [tex]C_{hydrogen} = \sqrt{\gamma RT}[/tex]

                     = [tex]\sqrt{1.4 \times 296.8 J/kg K \times 288}[/tex]

                     = 345.93 m/s

So, speed of sound in hydrogen is calculated as follows.

            = [tex]\sqrt{1.41 \times 4124 \times T_{H}}[/tex]

            = [tex]76.26 \sqrt{T_{H}}[/tex]

Speed of sound in helium is as follows.

            = [tex]\sqrt{1.66 \times 2077 \times T_{He}}[/tex]

            = [tex]58.72 \sqrt{T_{He}}[/tex]

For both the speeds to be equal,

       [tex]76.26 \sqrt{T_{H}}[/tex] = [tex]58.72 \sqrt{T_{He}}[/tex]

        [tex]\frac{T_{H}}{T_{He}}[/tex] = 0.593

Therefore, we can conclude that the temperature of hydrogen is 0.593 times the temperature of helium.

Answer:

For a: The edge length of the unit cell is 314 pm

For b: The radius of the molybdenum atom is 135.9 pm

Explanation:

To calculate the edge length for given density of metal, we use the equation:

[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]

where,

[tex]\rho[/tex] = density = [tex]10.28g/cm^3[/tex]

Z = number of atom in unit cell = 2  (BCC)

M = atomic mass of metal (molybdenum) = 95.94 g/mol

[tex]N_{A}[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]

a = edge length of unit cell =?

Putting values in above equation, we get:

[tex]10.28=\frac{2\times 95.94}{6.022\times 10^{23}\times (a)^3}\\\\a^3=\frac{2\times 95.94}{6.022\times 10^{23}\times 10.28}=3.099\times 10^{-23}\\\\a=\sqrt[3]{3.099\times 10^{-23}}=3.14\times 10^{-8}cm=314pm[/tex]

Conversion factor used:  [tex]1cm=10^{10}pm[/tex]  

Hence, the edge length of the unit cell is 314 pm

To calculate the edge length, we use the relation between the radius and edge length for BCC lattice:

[tex]R=\frac{\sqrt{3}a}{4}[/tex]

where,

R = radius of the lattice = ?

a = edge length = 314 pm

Putting values in above equation, we get:

[tex]R=\frac{\sqrt{3}\times 314}{4}=135.9pm[/tex]

Hence, the radius of the molybdenum atom is 135.9 pm

Answer:

1.067

Explanation:

Using the Arrhenius equation relates rate constants to the temperature is:

ln(k2/k1) = −Ea/R * [1/T2−1/T1]

where,

Ea = activation energy in kJ/mol ,

R = universal gas constant, and

T = temperature in K .

T1 = 25 + 273.15

= 298.15 K

T2 = 34 + 273.15

= 307.15 K

k1 = 0.816

Therefore,

k2/k1 = exp(-22.7/0.008314472) * [1/307.15 −1/298.15 ])

= 0.816 * 1.308

k2 = 1.067.

Answer:

The percentage yield of methanol is 78.74%.

Explanation:

[tex]2H_2+CO\rightarrow CH_3OH[/tex]

Theoretical yield of methanol ;

Moles of hydrogen gas = [tex]\frac{5.0 g}{2 g/mol}=2.5 mol[/tex]

Moles of carbon monoxide = [tex]\frac{5.0 g}{28 g/mol}=0.1786 mol[/tex]

According to reaction ,1 mole of CO reacts with 2 moles of hydrogen gas. Then 0.1786 moles of CO will :

[tex]\frac{2}{1}\times 0.1786 mol=0.0893 mol[/tex]

As we can see, that moles of hydrogen gas are in excess and CO are in limiting amount, so amount of methanol will depend upon moles of CO.

According to recation 1 mole of CO gives 1 mole of methanol, then 0.1786 moles of CO will give:

[tex]\frac{1}{1}\times 0.1786 mol=0.1786 mol[/tex]

Mass of 0.1786 moles of methanol =

= 0.1786 mol × 32 g/mol = 5.7152 g

Theoretical yield of methanol  = 5.7152 g

Experimental yield of methanol = 4.5 g

Percentage yield of methanol:

To calculate the percentage yield , we use the equation:

[tex]\%\text{ yield}=\frac{\text{Experimental yield}}{\text{Theoretical yield}}\times 100[/tex]

[tex]=\frac{4.5 g}{5.7152 g}\times 100=78.74\%[/tex]

The percentage yield of methanol is 78.74%.

The percent yield of the reaction is approximately 78.53%.

First, we need to write the balanced chemical equation for the reaction between hydrogen [tex](H_2)[/tex] and carbon monoxide (CO) to produce methanol [tex](CH_3OH)[/tex]:

[tex]\[ 2H_2 + CO \rightarrow CH_3OH \][/tex]

From the stoichiometry of the balanced equation, we can see that 2 moles of hydrogen react with 1 mole of carbon monoxide to produce 1 mole of methanol.

Now, we calculate the moles of hydrogen and carbon monoxide that reacted:

Molar mass of hydrogen [tex](H_2)[/tex] = 2 [tex]\times[/tex] 1.008 g/mol = 2.016 g/mol

Moles of hydrogen = mass / molar mass = 5.0 g / 2.016 g/mol = 2.48 moles

Molar mass of carbon monoxide (CO) = 12.01 g/mol + 16.00 g/mol = 28.01 g/mol

Moles of carbon monoxide = mass / molar mass = 5.0 g / 28.01 g/mol = 0.179 moles

Since the reaction requires a 2:1 ratio of hydrogen to carbon monoxide, and we have fewer moles of carbon monoxide, carbon monoxide is the limiting reactant.

The balanced equation tells us that 1 mole of CO produces 1 mole of methanol. Therefore, the theoretical yield of methanol is equal to the moles of CO that reacted:

Theoretical yield in moles = 0.179 moles

Now, we convert the moles of methanol to grams using its molar mass:

Molar mass of methanol [tex](CH_3OH)[/tex] = 12.01 g/mol (C) + 4 \times 1.008 g/mol (H) + 16.00 g/mol (O) = 32.042 g/mol

Theoretical yield in grams = theoretical yield in moles \times molar mass = 0.179 moles \times 32.042 g/mol = 5.73 g

The actual yield of the reaction is given as 4.5 g of methanol.

Now, we can calculate the percent yield:

[tex]\[ \text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Yield} = \left( \frac{4.5 \text{ g}}{5.73 \text{ g}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Yield} \approx 78.53\% \][/tex]

The question is incomplete, here is the complete question:

371. mg of an unknown protein are dissolved in enough solvent to make 5.00 mL of solution. The osmotic pressure of this solution is measured to be 0.118 atm at 25°C. Calculate the molar mass of the protein. Round your answer to 3 significant digits.

Answer: The molar mass of the unknown protein is [tex]1.54\times 10^3g/mol[/tex]

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 = 0.118 atm

i = Van't hoff factor = 1 (for non-electrolytes)

Mass of protein = 371. mg = 0.371 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]0.118atm=1\times \frac{0.371\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 0.371\times 1000\times 0.0821\times 298}{0.118\times 5}=1538.4g/mol=1.54\times 10^3g/mol[/tex]

Hence, the molar mass of the unknown protein is [tex]1.54\times 10^3g/mol[/tex]

Answer:

12.45

Explanation:

There is some info missing. I think this is the original question.

A chemist dissolves 169 mg of pure barium hydroxide in enough water to make up 70 mL of solution. Calculate the pH of the solution. (The temperature of the solution is 25 °C.) Round your answer to 2 significant decimal places.

First, we will calculate the molarity of barium hydroxide.

M = mass / molar mass × liters of solution

M = 0.169 g / 171.34 g/mol × 0.070 L

M = 0.014 M

Barium hydroxide is a strong base that dissociates according to the following equation.

Ba(OH)₂ → Ba²⁺ + 2 OH⁻

The molar ratio of Ba(OH)₂ to OH⁻ is 1:2. The concentration of OH⁻ is 2 × 0.014 M = 0.028 M

The pOH is:

pOH = -log [OH⁻] = - log 0.028 = 1.55

The pH is:

pH = 14 - pOH = 14 - 1.55 = 12.45

Answer:

moles sebacoyl chloride = 2.1 x 10-3 mol

Explanation:

Answer: the volume of the sample decreased

Explanation:

T1 = -98°C = - 98 + 273 = 175K

T2 = -89°C = -89 +273 = 184K

P1 = P

P2 = 110%P = 1.1P

V1 = V

V2 =?

P1V1/T1 = P2V2/T2

PxV/175 = 1.1PxV2/184

175x1.1PxV2 = PVx 184

V2 = (PVx 184) /(175x1.1P)

V2 = 0.96V = 96%V

Therefore, the final volume is 96% of the initial volume. This means that the final volume decreased by 96%

The volume of the sample will increase.  

• Based on the given information,  

• Let us assume that we have constant number of moles of nitrogen gas at -98 degree C, and the initial pressure is P1.  

• It is given that the pressure is increased by 10%, and the temperature is increased to -89 degree C.  

Now, the final pressure (P2) will be,  

P1 + P1*10/100 = 1.10 P1

T1 = -98 degree C = -98 + 273 K = 175 K

T2 = -89 degree C = -89 + 273 K = 184 K

At constant no of moles, the ideal gas equation is,  

PV = nRT

Here, n and R are constant, So, P1V1/T1 = P2V2/T2

P1 * V1/T1 / 175 K = 1.10 P1 * V2/184K

V2/V1 = 184/175 * 1.10 = 1.15  

V2 = 1.15 V1

Thus, the volume of sample increase by 1.15 times from the initial volume.

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Answer: aldehyde

Explanation:

the aldehyde group (—CHO) is always at the extreme

Answer: 10 ml of 200 mM [tex]CaCl_2[/tex] is required and 30 ml of water is required.

Explanation:

According to the dilution law,

[tex]C_1V_1=C_2V_2[/tex]

where,

[tex]C_1[/tex] = concentration of stock solution = 200mM

[tex]V_1[/tex] = volume of stock solution = ?

[tex]C_2[/tex] = concentration of resulting solution= 50mM

[tex]V_2[/tex] = volume of another acid solution= 40 ml

[tex]200\times x=50\times 40[/tex]

[tex]x=10ml[/tex]

Thus 10 ml of 200 mM [tex]CaCl_2[/tex] is required and (40-10) ml = 30 ml of water is to be added to make 40 ml of 50mM [tex]CaCl_2[/tex].

Final answer:

To make 40 ml of a 50 mM CaCl2 solution from a 200 mM stock, you need 10 ml of the stock solution and 30 ml of water.

Explanation:

To calculate how much of the 200 mM CaCl2 stock solution you need to dilute to get 40 ml of a 50 mM solution, you can use the dilution formula C1V1 = C2V2, where C1 is the concentration of the stock solution, V1 is the volume of the stock solution needed, C2 is the final concentration, and V2 is the final volume. Plugging in the known values yields (200 mM) × V1 = (50 mM) × (40 ml), solving for V1 gives V1 = (50 mM × 40 ml) / (200 mM) = 10 ml. Therefore, to make 40 ml of a 50 mM CaCl2 solution, you need 10 ml of the 200 mM stock and to dilute it with 30 ml of water.

Answer:

1. Co^2+ 1s2 2s2 2p6 3s2 3p6 3d7

2. N^3- 1s2 2s2 2p6

3. Ca^2+ 1s2 2s2 2p6 3s2 3p6

Explanation:

When Cobalt loses 2 electrons to become Co2+ it loses the electrons which are in 4s2, not the ones in 3d7 because the electrons in 4s2 have a high reactivity. Thus, when electrons are lost from Co atom, they are lost from the 4s orbital first because it is actually higher in energy when both 3d and 4s are filled with electrons.

Answer:

the complete question is found in the attachment

Explanation:

the complete explanation is found in the attachment

A subsidy from the water district to local plant nurseries would lower the cost of production, enabling them to offer more drought-tolerant plants. This would shift the supply curve to the right on a graph, representing an increase in supply. Assuming demand remains steady, this could result in a lower price and increased quantity of plants.

In the economics of supply and demand, a subsidy given to local plant nurseries would likely increase the supply of drought-tolerant plants like purple sage. As the cost of production decreases due to the subsidy, nurseries can afford to produce and sell more plants, shifting the supply curve to the right.

On a graph showing supply and demand curves, you would drag the supply curve to the right to represent this change. This movement should ideally cause a decrease in the price of the plants and increase in quantity, assuming demand stays consistent.

This scenario illustrates the basic economic principle that if you reduce the cost of production (in this case by providing a subsidy), producers are able to supply more of the product, leading to increases in quantity and potential decreases in price. This is an effective tool used often by governments and organizations to influence market dynamics and promote specific goods or services.

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Answer:

Explanation:

a ) Speed of radio waves in space = speed of light in space

= 3 x 10⁸ m /s

Time taken = distance / speed

= 8.1 x 10⁷ x 10³ / 3 x 10⁸ s

= 2.7 x 10² s

= 270 s

b )

Distance = speed x time

= 3 x 10⁸ x 1.2 m

= 3.6 x 10⁸ m

= 3.6 x 10⁵ km

Answer:low lattice energy for the solid and a high hydration energy for its ions

Explanation:

The lattice energy is the energy that holds the ions in the crystal lattice together. This energy must also be supplied for the lattice to disintegrate into its component ions. When this energy is lower than the energy released during the hydration of ions, the lattice easily breaks apart releasing the ions which are now strongly hydrated and the ionic solid is said to be soluble in water. Hence, solubility is favoured by lower lattice energy and higher hydration energy.

Final answer:

The option that favors the solubility of an ionic solid in water is a low lattice energy for the solid and a high hydration energy for its ions.

Explanation:

The correct choice that would most favor the solubility of an ionic solid in water is:

a low lattice energy for the solid and a high hydration energy for its ions

This is because low lattice energy allows for easier breakup of the ionic lattice, while high hydration energy promotes the attachment of water molecules to the ions, increasing solubility.

Answer: The osmotic pressure of the solution is 3.29 atm

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 = ?

i = Van't hoff factor = 1 (for non-electrolytes)

Mass of sucrose = 12.8 grams

Molar mass of sucrose = 342.3 g/mol

Volume of solution = 278 mL

R = Gas constant = [tex]0.082\text{ L atm }mol^{-1}K^{-1}[/tex]

T = temperature of the solution = 298 K

Putting values in above equation, we get:

[tex]\pi=1\times \frac{12.8\times 1000}{342.3\times 278}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 298K\\\\\pi=3.29atm[/tex]

Hence, the osmotic pressure of the solution is 3.29 atm

Statements 1 is correct.

Explanation:

Pentanal - is an aldehyde have the molecular formula C₅H₁₀O, is soluble in organic solvent and it is derived from Pentane.

3-pentanone is a ketone have the molecular formula C₅H₁₀O.

1,3,5-pentanetriol is an alcohol have the molecular formula C₅H₁₂O₃.

All the 3 molecules have 5 carbon atoms and they don't have equal number of hydrogen atoms.

Pentanal and pentanone, both have carbonyl groups.

3-pentanone is slightly soluble in water, whereas 1,3,5-pentanetriol is mostly soluble in water, since it contains 3-OH groups forms hydrogen bond with water.

All three molecules are derived from Pentane and not from Pentyne.

So statement 1 is correct.

The question is incomplete, here is the complete question:

Consider the following multistep reaction:

C+D⇌CD (fast)

CD+D→CD₂ (slow)

CD₂+D→CD₃ (fast)

C+3D→CD₃

Based on this mechanism, determine the rate law for the overall reaction.

Answer: The rate law for the reaction is [tex]\text{Rate}=k'[C][D]^2[/tex]

Explanation:

Rate law is the expression which is used to express the rate of the reaction in terms of the molar concentration of reactants where each term is raised to the power their stoichiometric coefficient respectively from a balanced chemical equation.

In a mechanism of the reaction, the slow step in the mechanism determines the rate of the reaction.

For the given chemical reaction:

[tex]C+3D\rightarrow CD_3[/tex]

The intermediate reaction of the mechanism follows:

Step 1:  [tex]C+D\rightleftharpoons CD;\text{ (fast)}[/tex]

Step 2:  [tex]CD+D\rightarrow CD_2;\text{(slow)}[/tex]

Step 3:  [tex]CD_2+D\rightarrow CD_3;\text{(fast)}[/tex]

As, step 2 is the slow step. It is the rate determining step

Rate law for the reaction follows:

[tex]\text{Rate}=k[CD][D][/tex]           ......(1)

As, [CD] is not appearing as a reactant in the overall reaction. So, we apply steady state approximation in it.

Applying steady state approximation for CD from step 1, we get:

[tex]K=\frac{[CD]}{[C][D]}[/tex]

[tex][CD]=K[C][D][/tex]

Putting the value of [CD] in equation 1, we get:

[tex]\text{Rate}=k.K[C][D]^2\\\\\text{Rate}=k'[C][D]^2[/tex]  

Hence, the rate law for the reaction is [tex]\text{Rate}=k'[C][D]^2[/tex]

Answer:

[tex]\lambda=2.61\times 10^{-9}\ m[/tex] = 261 nm

Silver is not a good choice.

Explanation:

[tex]E=\frac {h\times c}{\lambda}[/tex]

Where,  

h is Plank's constant having value [tex]6.626\times 10^{-34}\ Js[/tex]

c is the speed of light having value [tex]3\times 10^8\ m/s[/tex]

[tex]\lambda[/tex] is the wavelength of the light

Given that:- Energy = [tex]7.59\times 10^{-19}\ J[/tex]

[tex]7.59\times 10^{-19}=\frac{6.626\times 10^{-34}\times 3\times 10^8}{\lambda}[/tex]

[tex]7.59\times \:10^{26}\times \lambda=1.99\times 10^{20}[/tex]

[tex]\lambda=2.61\times 10^{-9}\ m[/tex] = 261 nm

Visible range has a spectrum of 380 to 740 nm

So, Silver is not a good choice.

The maximum wavelength needed to remove an electron from silver is approximately 262 nm. Silver is not a good choice for a photocell that uses visible light.

To find the maximum wavelength needed to remove an electron from silver, we can use the work function of silver, which is Φ = 4.73 eV. The threshold wavelength for observing the photoelectric effect in silver can be calculated using Equation 6.16, which is λ = hc/Φ. Substituting the given values, we have λ = (1240 eV⋅nm) / (4.73 eV), which gives us a threshold wavelength of approximately 262 nm. Since visible light ranges from 400 to 700 nm, silver is not a good choice for a photocell that uses visible light.

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Explanation:

(a)   The given data is as follows.

           Speed of electron (u) = [tex]5.5 \times 10^{4} m/s[/tex]

According to De Broglie's formula,

                wavelength, [tex]\lambda = \frac{h}{mu}[/tex]

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

              m = mass of electron = [tex]9.11 \times 10^{-31} kg[/tex]

Hence, we will calculate the wavelength as follows.

           [tex]\lambda = \frac{h}{mu}[/tex]

                      = [tex]\frac{6.626 \times 10^{-34}}{9.11 \times 10^{-31}kg \times 5.5 \times 10^{4} m/s}[/tex]

                      = [tex]0.132 \times 10^{-7}[/tex] m

                      = [tex]13.2 \times 10^{-9}[/tex] m

It is known that for any microscope, smallest object that can be observed is equal to [tex]\frac{1}{2}[/tex] the wavelength of of the radiation  smallest object observable with an electron microscope.

Hence,     [tex]\frac{13.2 \times 10^{-9}}{2}[/tex]

                = [tex]6.6 \times 10^{-9}[/tex] m

               = 6.6 nm          (as 1 m = [tex]10^{-9} nm[/tex])

Therefore, the smallest object observable with an electron microscope will be 6.6 nm.

(b)  At [tex]3.0 \times 10^{7} m/s[/tex], the wavelength will be calculated as follows.

              wavelength, [tex]\lambda = \frac{h}{mu}[/tex]

                                  = [tex]\frac{6.626 \times 10^{-34} Js}{9.11 \times 10^{-31} kg \times 3.0 \times 10^{7} m/s}[/tex]

                                  = [tex]24.2 \times 10^{-12}[/tex] m

As, for any microscope, smallest object that can be observed is equal to [tex]\frac{1}{2}[/tex] the wavelength of of the radiation  smallest object observable with an electron microscope.

                = [tex]\frac{24.2 \times 10^{-12}}{2}[/tex]

                = [tex]12.1 \times 10^{-12} m \times 10^{9}nm/m[/tex]

                = 0.0121 nm

Therefore, at [tex]3.0 \times 10^{7} m/s[/tex]  the smallest object observable with an electron microscope is 0.0121 nm.

The smallest object observable with an electron microscope can be calculated using the formula: Size of object = Wavelength of electrons / 2. Plugging in the values and solving for the size of the object gives: Size of object = 3.37 x 10^-12 m. For a speed of 3.0 x 10^7 m/s, the calculation would be: Size of object = 1.22 x 10^-10 m.

The smallest object observable with an electron microscope can be calculated using the formula:

Size of object = Wavelength of electrons / 2

Using the given speed of 5.5 x 10^4 m/s, we can calculate:

Size of object = (h / (m * v)) / 2, where h is Planck's constant and m is the mass of an electron.

Plugging in the values and solving for the size of the object gives:

Size of object = (6.626 x 10^-34 J s / (9.109 x 10^-31 kg * 5.5 x 10^4 m/s)) / 2

Size of object = 3.37 x 10^-12 m

For a speed of 3.0 x 10^7 m/s, the calculation would be:

Size of object = (6.626 x 10^-34 J s / (9.109 x 10^-31 kg * 3.0 x 10^7 m/s)) / 2

Size of object = 1.22 x 10^-10 m

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To determine the final temperature after ice is dropped into water, we analyze the energy transfer phases: ice warming, melting, and temperature equalization, applying specific heat capacities and latent heat of fusion.

To find the final temperature after dropping a cube of ice into water, we must consider the energy exchanges that occur: the ice warming up to 0°C, melting, and the resulting water warming up or cooling down to reach thermal equilibrium with the water already in the glass. For this, we use the concept of specific heat capacity and the latent heat of fusion for water.

The specific heat capacity of ice is about 2.062 J/(g°C), and the specific heat capacity of liquid water is 4.184 J/(g°C). The latent heat of fusion of ice is roughly 334 J/g. By applying the conservation of energy, we equate the heat lost by the warmer substance (water) to the heat gained by the colder substance (ice and the water resulting from melted ice), taking into account phase changes.

However, without numerical calculation in this particular example, the key takeaway is understanding the phases of energy transfer: warming up the ice, melting the ice, and then equalizing the temperature of the mixture. The initial temperatures of the substances and their masses play crucial roles in determining the final temperature.

Answer:

a. glucose

Explanation:

Glucose is the compound that would be most soluble in water because it has regions of hydrogen-oxygen polar bonds, making it hydrophilic. Cholesterol, large proteins, and triglycerides are nonpolar and not very soluble in water.

Water is considered a polar solvent, and as such, substances that dissolve in water are usually polar or ionic compounds. Glucose, a, would be the most soluble in water because it has regions of hydrogen-oxygen polar bonds, making it hydrophilic. Cholesterol, b, is a nonpolar molecule and therefore not very soluble in water. Large proteins, c, can have both polar and nonpolar regions, so their solubility in water depends on the specific protein. Triglycerides, d, are nonpolar and not soluble in water.

Answer:

The new pH after adding HCl is 7.07

Explanation:

The formula for calculating pH of a buffer is

pH = pKa + log([Conjugate base]/[Acid])

Before adding HCl,

         7.55 = 7.55 + log([Conjugate base]/[Acid])

⇔      log([Conjugate base]/[Acid])  = 0

⇔     [Conjugate base] = [Acid] = 1/2 x 0.100 = 0.05 M

⇒ Mole of Conjugate base = Mole of Acid = 0.05 M x 0.12 mL = 0.006 mol

After adding HCl (3.00 mL, 1.00 M)

⇒ Mole of HCl = 0.003 x 1 = 0.003 mol)

New volume solution is 120 m L+ 3 mL = 123 mL

HCl is a strong acid, it will convert the conjugate base to acid form, or we can express

Mole of new Conjugate base = 0.006 - 0.003 = 0.003 mol

                ⇒ Concentration = 0.003/0.123 M

Mole of new Acid form = 0.006 + 0.003 = 0.009 mol

                ⇒ Concentration = 0.009/0.123 M

Use the formula

pH = pKa + log([Conjugate base]/[Acid])

    = 7.55 + log(0.003 / 0.009) = 7.07

To determine the new pH after adding HCl to the TES buffer, we need to consider the Henderson-Hasselbalch equation. Initially, the concentration of TES is 0.100 M and the pH is 7.55. After adding 3.00 mL of 1.00 M HCl, we need to calculate the new concentration of TES and its conjugate base. Using the Henderson-Hasselbalch equation, we can find the new pH by substituting the new concentration of TES, its conjugate base, and the pKa of TES into the equation.

To determine the new pH after adding HCl to the TES buffer, we need to consider the Henderson-Hasselbalch equation. The equation relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the acid and its conjugate base. In this case, TES acts as the acid and its conjugate base is the salt.

The Henderson-Hasselbalch equation can be written as pH = pKa + log([A-]/[HA]), where [A-]/[HA] is the ratio of the salt to the acid. Initially, the concentration of TES is 0.100 M and the pH is 7.55. After adding 3.00 mL of 1.00 M HCl, we need to calculate the new concentration of TES and its conjugate base.

Using the equation c1V1 = c2V2, where c1 and V1 are the initial concentration and volume of HCl, and c2 and V2 are the final concentration and volume, we can find the new concentration of TES. The initial volume of TES is 120 mL. The final volume is the sum of the initial volume and the volume of HCl added. Calculate the new volume of TES from this information, and then substitute the values into the equation to find the new concentration of TES.

Once we have the new concentration of TES, we can use the Henderson-Hasselbalch equation to find the new pH. Substitute the new concentration of TES and the concentration of its conjugate base into the equation, along with the pKa of TES. Solve for the new pH to determine the answer.

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Answer:

293.99 g

OR

0.293 Kg

Explanation:

Given data:

Lattice energy of Potassium nitrate (KNO3) = -163.8 kcal/mol

Heat of hydration of KNO3 = -155.5 kcal/mol

Heat to absorb by KNO3 = 101kJ

To find:

Mass of KNO3 to dissolve in water = ?

Solution:

Heat of solution = Hydration energy - Lattice energy

                           = -155.5 -(-163.8)

                           = 8.3 kcal/mol

We already know,

1 kcal/mol = 4.184 kJ/mole

Therefore,

= 4.184 kJ/mol x 8.3 kcal/mol

= 34.73 kJ/mol

Now, 34.73 kJ of heat is absorbed when 1 mole of KNO3 is dissolved in water.

For 101 kJ of heat would be

= 101/34.73

= 2.908 moles of KNO3

Molar mass of KNO3 = 101.1 g/mole

Mass of KNO3 = Molar mass x moles

                         = 101.1 g/mole  x  2.908

                         = 293.99 g

                         = 0.293 kg

293.99 g potassium nitrate has to dissolve in water to absorb 101 kJ of heat.     

Final answer:

To absorb 101 kJ of heat, 7.63 grams of potassium nitrate must dissolve in water, calculated based on the lattice energy and heat of hydration provided.

Explanation:

The question asks how much potassium nitrate needs to dissolve in water to absorb 101 kJ of heat, given the lattice energy and heat of hydration for potassium nitrate. First, we convert the given heat into kcal because the energies are provided in kcal/mol: 101 kJ × (1 kcal / 4.184 kJ) = 24.1 kcal. The total heat involved in dissolving potassium nitrate in water can be found by adding the lattice energy to the heat of hydration: -163.8 kcal/mol + (-155.5 kcal/mol) = -319.3 kcal/mol. This value represents the heat released when 1 mole of potassium nitrate dissolves in water.

To find the amount of potassium nitrate that needs to dissolve to absorb 101 kJ (24.1 kcal), we set up a proportion, knowing that -319.3 kcal is released per mole of potassium nitrate dissolved: (1 mole / -319.3 kcal) = (x moles / 24.1 kcal). Solving for x gives x = 24.1 kcal / -319.3 kcal/mol = 0.0755 moles. Finally, to find the mass of potassium nitrate, we multiply the moles by the molar mass of potassium nitrate (KNO3), which is approximately 101.1 g/mol: 0.0755 moles ×101.1 g/mol = 7.63 grams.

Therefore, 7.63 grams of potassium nitrate need to dissolve in water to absorb 101 kJ of heat.

The molarity of the solution when 23.640 g of Mn(ClO4)2 · 6 H2O is added to 200.0 mL of water is 0.3014 M, calculated by dividing the moles of solute by the volume of solution in liters.

To calculate the molarity of a solution when a certain amount of solute is added to a known volume of water, you must first determine the number of moles of solute. For the molarity of the resulting solution when 23.640 g of Mn(ClO4)2 · 6 H2O (molar mass approximately 392.13 g/mol) is dissolved in 200.0 mL of water, the calculation is as follows:

To calculate the moles of Mn(ClO4)2 · 6 H2O: 23.640 g / 392.13 g/mol ≈ 0.06028 mol.

To find molarity (M), which is moles of solute per liter of solution: 0.06028 mol / 0.200 L = 0.3014 M.

To calculate the concentration of the NaOH solution, convert the volume to grams and calculate the moles of NaOH. Then, use the moles and total volume to find the concentration.

To find the concentration of the NaOH solution, we need to calculate the moles of NaOH present in the 3.03 mL volume. First, we convert the volume to grams using the density of the solution: 3.03 mL × 1.53 g/mL = 4.6419 g

Next, we calculate the moles of NaOH:

Moles of NaOH = \dfrac{4.6419 g}{40.00 g/mol} = 0.1160 mol

Finally, we use the moles of NaOH and the total volume of the solution (500 mL) to find the concentration:

Concentration = \dfrac{0.1160 mol}{0.5000 L} = 0.2320 M

Final answer:

The concentration of the diluted NaOH solution after measuring 3.03 mL of a 50% NaOH solution, with a density of 1.53 g/mL, and diluting to 500 mL total volume is 0.1159 M.

Explanation:

To calculate the concentration of the diluted NaOH solution, we need to determine the amount of NaOH in the initial 3.03 mL of 50% solution and then find the molarity after dilution to 500 mL. The density of the solution is given as 1.53 g/mL, so the mass of the 3.03 mL solution is:

mass = volume × density = 3.03 mL × 1.53 g/mL = 4.6359 g

Since the solution is 50% by weight, the mass of NaOH is:

mass of NaOH = 0.50 × 4.6359 g = 2.3180 g

The molar mass of NaOH is approximately 40.00 g/mol, so the number of moles of NaOH in the original solution is:

moles of NaOH = mass / molar mass = 2.3180 g / 40.00 g/mol = 0.05795 mol

After dilution to 500 mL, the molarity (M) is calculated as follows:

Molarity = moles / volume (L) = 0.05795 mol / 0.50 L = 0.1159 M

Therefore, the concentration of the diluted NaOH solution is 0.1159 M.

Answer:

g = 1.11x10⁻⁵Ω.

Explanation:

The membrane conductance (g) can be calculated by dividing membrane current (I) through the driving force (Vm - E) as follows:  

[tex] g_{ion} = \frac{I_{ion}}{V_{m} - E_{ion}} [/tex]

where Vm: is the membrane potential and [tex]E_{ion}[/tex]: is the equilibrium potential for the ion or reversal potential.  

The equilibrium potential for the ion can be calculated using the Nernst equation:

[tex] E_{ion} = \frac{RT}{zF}*Ln(\frac{[ion]_{out}}{[ion]_{ins}}) [/tex]

where R: is the gas constant = 8.314 J/K*mol, F: is the Faraday constant = 96500 C/mol, T: is the temperature (K), z: is the ion's charge, [ion]out and [ion]ins: is the concentration of the ion outside and inside, respectively.    

[tex] E_{ion} = \frac{(8.314 J*K^{-1}*mol^{-1})((15 + 273)K)}{(+1)(96500 C*mol^{-1})}*Ln(\frac{[500mM]}{[70mM]}) = 48.78 mV [/tex]  

Now, we can calculate the  membrane conductance (g) using equation (1):

[tex] g_{ion} = \frac{I_{ion}}{V_{m} - E_{ion}} = \frac{-318*10^{-9} A}{20*10^{-3} V - 48.78*10^{-3} V} = 1.11*10^{-5} \Omega [/tex]

Therefore, the membrane conductance is 1.11x10⁻⁵Ω.

I hope it helps you!        

When 3 mol of phosphine reacts, (3/4) mol of phosphorus and 4.5 mol of hydrogen are produced. The number of moles of phosphine, phosphorus, and hydrogen at any time can be determined using the stoichiometry of the reaction. The time needed for 3 mol of phosphine to react can be found by integrating the given rate equation.

To determine the amount of phosphorus and hydrogen produced when 3 mol of phosphine reacts, we can use the stoichiometry of the reaction. From the balanced equation, we see that for every 4 mol of PH3 that reacts, we get 1 mol of P4 and 6 mol of H2. Therefore, when 3 mol of PH3 reacts, we will produce (3/4) mol of P4 and (3/4) x 6 = 4.5 mol of H2.

Let's denote the number of moles of phosphine as nPH3, the number of moles of phosphorus as nP4, and the number of moles of hydrogen as nH2. At any time t, when 3 mol of phosphine has reacted, the corresponding number of moles of phosphorus and hydrogen can be determined using the stoichiometry of the reaction as mentioned above.

To determine how long it would take for 3 mol of phosphine to have reacted, we can use the given rate equation: dCPH3/dt = -3.715 × 10-6 CPH3. Since we have the initial concentration of phosphine (CPH3) as 5 kmol/m3, we can integrate the rate equation to find the time needed for 3 mol of phosphine to react.

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Final answer:

a) The ratio of lb-mole O2 react/lb-mole NO formed is 1.25. b) The oxygen feed rate corresponding to 40% excess O2 is 175.0 kmol/h. c) Ammonia is the limiting reactant, with the oxygen being in excess by 5.85%. The extent of reaction is 36.17 mol NO produced, with a mass of 1085.73 g.

Explanation:

a. To calculate the ratio (lb-mole O2 react/lb-mole NO formed), we can use the stoichiometry of the reaction. From the balanced equation, we can see that for every 5 moles of O2, we get 4 moles of NO. So, the ratio is 5/4 or 1.25 lb-moles O2 react/lb-mole NO formed.

b. To find the oxygen feed rate corresponding to 40% excess O2, we need to calculate the stoichiometric amount of O2 required and then add 40% of that amount. Since the reaction requires 5 moles of O2 for every 4 moles of NO, the stoichiometric amount of O2 required is (5/4) * 100.0 kmol NH3/h = 125.0 kmol O2/h. Adding 40% of that amount gives 125.0 kmol O2/h + (40/100) * 125.0 kmol O2/h = 175.0 kmol O2/h.

c. To determine the limiting reactant, we need to compare the amounts of ammonia and oxygen given. The molecular weight of ammonia (NH3) is 17 g/mol and oxygen (O2) is 32 g/mol. So, the mass of 50.0 kg of ammonia is 50.0 kg * (1000 g/kg) / (17 g/mol) = 2941.18 mol. The mass of 100.0 kg of oxygen is 100.0 kg * (1000 g/kg) / (32 g/mol) = 3125.0 mol. Comparing these amounts, we can see that ammonia is the limiting reactant as there is less of it. The percentage by which the other reactant (oxygen) is in excess can be calculated as [(3125.0 mol - 2941.18 mol) / 3125.0 mol] * 100 = 5.85 %. The extent of reaction and mass of NO produced can be determined using the stoichiometry of the reaction. From the balanced equation, we can see that for every 4 moles of NO produced, 5 moles of O2 are consumed. So, the extent of reaction is (3125.0 mol - 2941.18 mol) / 5 = 36.17 mol NO produced. The mass of NO produced can be calculated as 36.17 mol * (30.01 g/mol) = 1085.73 g.

a) Ratio (lb-mole O2 react/lb-mole NO formed) is 1.25 lb-mole O₂ / lb-mole NO.

b) Oxygen feed rate is 175.0 kmol O₂/h.

c) Limiting reactant is NH₃; Percentage excess of O₂ is 10.1%; Extent of reaction is 2.94 kmol NH₃; Mass of NO produced is 88.23 kg

a. Calculate the ratio (lb-mole O₂ react/lb-mole NO formed).

b. If ammonia is fed to a continuous reactor at a rate of 100.0 kmol NH₃/h, what oxygen feed rate (kmol/h) would correspond to 40.0% excess O₂?

c. If 50.0 kg of ammonia and 100.0 kg of oxygen are fed to a batch reactor, determine the limiting reactant, the percentage by which the other reactant is in excess, and the extent of reaction and mass of NO produced (kg) if the reaction proceeds to completion.

Answer:

a) Yes, these bands of signals overlap.

b) FM has broader transmission band.

Explanation:

a) Frequency range of TV channels = 59.5 to 215.8 MHz

Wavelength range of FM radio = 2.78 m to 3.41 m

Frequency of the wave = [tex]\nu [/tex]

Wavelength of the wave = [tex]\lambda [/tex]

Speed of light = c = [tex]3\times 10^8 m/s[/tex]

[tex]\nu =\frac{c}{\lambda }[/tex]

Frequency of wave with, [tex]\lambda = 2.78 m[/tex]

[tex]\nu =\frac{3\times 10^8 m/s}{2.78 m}=1.079\times 10^8 Hz[/tex]

[tex]1.079\times 10^8 Hz=1.079\times 10^8\times 10^{-6} MHz=107.9 MHz[/tex]

Frequency of wave with, [tex]\lambda = 3.41m[/tex]

[tex]\nu =\frac{3\times 10^8 m/s}{3.41 m}=8.798\times 10^7 Hz[/tex]

[tex]8.798\times 10^7 Hz=8.798\times 10^7\times 10^{-6} MHz=87.98 MHz[/tex]

Frequency range of FM = 87.89 to 107.9 MHz

Frequency range of TV channels = 59.5 to 215.8 MHz

Yes, these bands of signals overlap.

b)  

Frequency range of AM = 550 to 1600 kHz

1 kHz = 0.001 MHz

550 to 1600 kHz = [tex]550\times 0.001 MHz[/tex] to [tex]1600\times 0.001 MHz[/tex]

= 0.55 MHz to 1.6 MHz

Frequency range of AM = 0.55 to 1.6 MHz

Frequency range of FM = 87.89 to 107.9 MHz

FM has broader transmission band.

Explanation:

a) IE1 of Germenium.  ionization energy decreases down the group.

b) Here IE2 of Ga is higher because second valence electron of gallium is in s orbital whereas second valence electron of germenium is in p orbital.

c) IE3 of Ge is higher as this follows the trend.

d)IE4 of Ga is higher because the 4th valence electron of Ga is a core electron and the for Ge it is in s orbital and it takes higher energy to break a core electron than the orbital ones.

When comparing Ga and Ge, IE₁ and IE₂ of Ga are lower due to being earlier in the periodic table, but IE₄ of Ga is expected to be higher as it involves removing an electron from a full orbital. IE₃ for both may be similar due to both elements having three valence electrons. The correct answer is d) IE₄ of Ga or IE₄ of Ge.

The subject in question involves comparing first and successive ionization energies (IE) for elements in the periodic table, particularly gallium (Ga) and germanium (Ge). Ionization energy refers to the energy required to remove an electron from a gaseous atom or ion.

As general rules, (a) the first IE tends to increase across a period as the nuclear charge increases, and (b) IE increases for successive ionizations as the atom or ion becomes progressively more positively charged.

(a) IE₁ of Ga would be lower than IE₁ of Ge because Ga is to the left of Ge in the periodic table, and thus Ge has a higher nuclear charge and a stronger attraction to its valence electron.

(b) IE₂ of Ga would also be lower than IE₂ of Ge because the additional electron from Ga would come from the same valence shell as the first electron, while Ge's second ionization would remove an electron that experiences a stronger nuclear charge.

(c) As both Ga and Ge have three valence electrons, the IE₃ of Ga and Ge will both involve removing an electron from a similarly charged ion, but because Ga has a higher energy 4p subshell, its IE₃ might be slightly lower than Ge's, which is removing an electron from the 4s subshell (which after removing two electrons is now full and lower in energy).

(d) At the IE₄ level, we see a large jump in ionization energy for both elements as electrons are being removed from an energy level closer to the nucleus; however, IE₄ of Ga will generally be higher than IE₄ of Ge due to  of an electron from a full orbital in Ga, which has higher energy compared to the removal from a half-filled orbital in Ge.

These comparisons are based on the understanding that ionization energies increase both with increasing positive charge and with the removal of electrons closer to the nucleus.