Question 1

An ice skater exerts a pressure of 3.1 MPa. Calculate the change in the melting point of the ice under the skate, given that the densities of liquid water and ice are 0.998 and 0.920 g cm^-3 respectively and the enthalpy of fusion of water is +6.01 kJ mol^-1.

Accepted Answer

The pressure causes the melting point to decrease due to the higher density of water compared to ice. Using the Clausius-Clapeyron equation, the change in melting point is calculated to be a decrease of approximately 0.22 K.

Question 2

Determine the vapour pressure of diethyl ether, C₄H₁₀O, at a temperature of 298 K, given that the normal boiling temperature is 308 K and enthalpy of vaporization is 25.9 kJ mol^-1.

Accepted Answer

D

Question 3

The normal boiling temperature of trichloromethane, CHCl₃, is 61°C, and the specific enthalpy of vaporization is 250 J g^-1. Determine the vapour pressure at a temperature of 298 K.

Accepted Answer

C

Question 4

The vapour pressure of pyridine, C₅H₅N, is 2.25 kPa at 25°C. Determine the normal boiling temperature of pyridine if the enthalpy of vaporization is 40.3 kJ mol^-1.

Accepted Answer

The normal boiling point is when the vapor pressure equals atmospheric pressure (101.3 kPa). Using the Clausius-Clapeyron equation, we can estimate the boiling point. Given the enthalpy of vaporization and the vapor pressure at 25°C, the calculation shows that the boiling point is approximately 389 K.

Question 5

The vapour pressure of pure 1-propanol is 2792 Pa at 25°C and 11995 Pa at 50°C. Determine the enthalpy of vaporization of 1-propanol.

Accepted Answer

The enthalpy of vaporization can be calculated using the Clausius-Clapeyron equation. By taking the natural logarithm of the ratio of the vapor pressures at two temperatures and rearranging the equation, the enthalpy of vaporization is found to be approximately 46.7 kJ mol^-1.

Question 6

The vapour pressure of pure benzene is 0.146 bar and of pure toluene is 0.185 bar at 298 K. Determine the mole fraction of toluene in an ideal liquid mixture of benzene and toluene for which the total vapour pressure is 0.160 bar at this temperature.

Accepted Answer

Let x be the mole fraction of toluene in the mixture.

According to Raoult's law, the partial pressure of benzene in the mixture is given by:

Pbenzene = xP°benzene

where P°benzene is the vapour pressure of pure benzene.

Similarly, the partial pressure of toluene in the mixture is:

Ptoluene = (1-x)P°toluene

where P°toluene is the vapour pressure of pure toluene.

The total vapour pressure of the mixture is given by:

Ptotal = Pbenzene + Ptoluene

Substituting the given values, we get:

0.160 bar = x(0.146 bar) + (1-x)(0.185 bar)

Solving for x, we get:

x = 0.359 or 35.9%

Therefore, the answer is B.

Question 7

The Henry's law constant for nitrogen dissolved in water at 298 K is 8.68* 10⁹ Pa. Determine the mole fraction of nitrogen in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K.

Accepted Answer

Henry's law states that the partial pressure of a gas in equilibrium with a liquid is proportional to the mole fraction of the gas in the liquid. The Henry's law constant is the proportionality constant.The mole fraction of nitrogen in water can be calculated using the following equation:X_N2 = P_N2 / Hwhere:X_N2 is the mole fraction of nitrogen in waterP_N2 is the partial pressure of nitrogen in airH is the Henry's law constantThe partial pressure of nitrogen in air can be calculated using the following equation:P_N2 = y_N2 * Pwhere:y_N2 is the mole fraction of nitrogen in airP is the total pressure of airThe mole fraction of nitrogen in air is approximately 0.78. The total pressure of air is 1 atm. Therefore, the partial pressure of nitrogen in air is:P_N2 = 0.78 * 1 atm = 0.78 atmThe Henry's law constant for nitrogen dissolved in water at 298 K is 8.68 * 10^9 Pa. Therefore, the mole fraction of nitrogen in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K is:X_N2 = 0.78 atm / (8.68 * 10^9 Pa) = 8.98 * 10^-10The mole fraction of nitrogen in water is approximately 8.98 ppm.

Question 8

What is the osmotic pressure generated at 25°C by a solution of 1.26 g of sucrose, C₁₂H₂₂O₁₁, in 250 cm³ of water?

Accepted Answer

First, calculate the molarity of the sucrose solution:

1.26 g sucrose / 342.3 g/mol sucrose = 0.00369 mol sucrose
250 cm³ water = 0.25 L water

Molarity = moles of solute / liters of solution

Molarity = 0.00369 mol / 0.25 L = 0.01476 M

Then, use the Van't Hoff equation to calculate the osmotic pressure:

π = iMRT

where:
π = osmotic pressure
i = van't Hoff factor (1 for sucrose)
M = molarity (0.01476 M)
R = gas constant (0.08206 L•atm/mol•K)
T = temperature in Kelvin (25°C + 273.15 = 298.15 K)

π = (1)(0.01476 M)(0.08206 L•atm/mol•K)(298.15 K)
π = 0.0364 atm
π = 36.4 kPa

Therefore, the answer is B.

Question 9

Determine the mass of potassium chloride, KCl, that must be added to water to create an aqueous solution of volume 25 dm³ with an osmotic pressure of 1.0 bar.

Accepted Answer

To solve this problem, we can use the formula for osmotic pressure of an ideal solution:

π = MRT

where π is the osmotic pressure, M is the molarity of the solution, R is the gas constant, and T is the temperature in kelvin.

We can rearrange this formula to solve for the molarity, M:

M = π / RT

We know the volume of the solution is 25 dm3, or 0.025 m3. We also know the osmotic pressure is 1.0 bar. The temperature is not given, so we can assume it is at standard temperature of 273 K.

The molarity of the solution can be found using the formula above:

M = (1.0 bar) / (0.083 L bar/K mol x 273 K)

M = 0.0459 mol/L

Now we can use this molarity to find the mass of KCl needed to make the solution. The molecular weight of KCl is 74.6 g/mol.

mass = moles x molecular weight

mass = 0.0459 mol/L x 25 L x 74.6 g/mol

mass = 75.3 g

Therefore, the answer is D) 75.3 g.

Question 10

Trichloromethane, CHCl₃, and propanone, C₃H₆O, form liquid-vapour mixtures with a maximum-boiling azeotrope. What does this imply about the nature of the interactions between the molecules in the mixture?

Accepted Answer

The fact that trichloromethane and propanone form a maximum-boiling azeotrope implies that there are strong interactions between the molecules in the mixture. This means that it is more difficult for the molecules to escape from the liquid to the vapour phase, leading to a higher boiling point than would be expected based on the boiling points of the individual components.

Question 11

Determine the vapour pressure of n-hexane, C₆H₁₄, at a temperature of 298 K, given that the normal boiling temperature is 342 K and enthalpy of vaporization is 30.9 kJ mol^-1.

Accepted Answer

Using the Clausius-Clapeyron equation, the vapour pressure at 298 K is calculated to be approximately 20.4 kPa.

Question 12

Determine the vapour pressure of toluene, C₇H₈, at a temperature of 350 K, given that the normal boiling temperature is 384 K and enthalpy of vaporization is 37.1 kJ mol^-1.

Accepted Answer

The Clausius-Clapeyron equation can be used to estimate the vapor pressure at a temperature different from the boiling point. Using the given enthalpy of vaporization and normal boiling point, the vapor pressure at 350 K is calculated to be approximately 32.8 kPa.

Question 13

Determine the vapour pressure of acetone, C₃H₆O, at a temperature of 298 K, given that the normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Accepted Answer

The Clausius-Clapeyron equation can be used to estimate the vapour pressure at a different temperature. Using the given normal boiling point and enthalpy of vaporization, the vapour pressure at 298 K is calculated to be approximately 30.8 kPa.

Question 14

Estimate the increase in the vapour pressure of octane, C₈H₁₈, from when the temperature is 298 K to when the temperature is 308 K. The normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Accepted Answer

The answer of Estimate the increase in the vapour pressure...

Question 15

Estimate the change in the vapour pressure of $\alpha$-pinene, C₁₀H₁₆, from when the temperature is 323 K to when the temperature is 273 K. The normal boiling temperature is 430 K and enthalpy of vaporization is 45.4 kJ mol^-1.

Accepted Answer

Using the Clausius-Clapeyron equation, the decrease in vapor pressure can be estimated as approximately 1.44 kPa when the temperature decreases from 323 K to 273 K.

Question 16

The vapour pressure of ethanol, C₂H₆O, is 7.4 kPa at 25°C. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 42.3 kJ mol^-1.

Accepted Answer

The normal boiling point is when the vapor pressure equals atmospheric pressure (101.3 kPa). Using the Clausius-Clapeyron equation, we can estimate the boiling point. Solving for T2 when P2 = 101.3 kPa, we find it to be approximately 352 K.

Question 17

The vapour pressure of methanol, CH₄O, is 27.5 kPa at 308 K. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 37.6 kJ mol^-1.

Accepted Answer

The normal boiling point is when the vapor pressure equals atmospheric pressure (101.3 kPa). Using the Clausius-Clapeyron equation, we can estimate the boiling point. Given the enthalpy of vaporization and the vapor pressure at 308 K, the calculation shows that the normal boiling point is approximately 338 K.

Question 18

The vapour pressure of pure cyclohexane is 12.2 kPa at 25°C and 25.1 kPa at 42°C. Determine the enthalpy of vaporization of cyclohexane.

Accepted Answer

Using the Clausius-Clapeyron equation, we can solve for the enthalpy of vaporization ($\Delta H_{vap}$):

$\ln\frac{P_2}{P_1}=\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}ight)$

$P_1 = 12.2 	ext{ kPa}$, $P_2 = 25.1 	ext{ kPa}$, $T_1 = 298	ext{ K}$, $T_2 = 315	ext{ K}$, and $R = 8.314	ext{ J/mol K}$.

Plugging in these values, we get:

$\ln\frac{25.1}{12.2}=\frac{\Delta H_{vap}}{8.314}\left(\frac{1}{298}-\frac{1}{315}ight)$

Solving for $\Delta H_{vap}$, we get:

$\Delta H_{vap} = 33.1 	ext{ kJ/mol}$

Therefore, the best choice is B, which matches this value.

Question 19

The vapour pressure of pure aniline is 1314 Pa at 350 K and 13372 Pa at 400 K. Determine the enthalpy of vaporization of aniline.

Accepted Answer

Using the Clausius-Clapeyron equation:

ln(P2/P1) = (-ΔHvap/R)(1/T2 - 1/T1)

where:
P1 = 1314 Pa (vapour pressure at T1 = 350 K)
P2 = 13372 Pa (vapour pressure at T2 = 400 K)
R = 8.314 J/molK (gas constant)

Rearranging the equation and plugging in the values:

- ln(P1/P2) = (ΔHvap/R)(1/T2 - 1/T1)
- ln(1314/13372) = (ΔHvap/8.314)(1/400 - 1/350)
- -2.970 = ΔHvap/8.314(-0.001429)
- ΔHvap = (-2.970)(8.314)(-700.2)
- ΔHvap = 182.32 kJ/mol

Rounding off to one decimal place, the enthalpy of vaporization of aniline is 53.9 kJ mol^-1. Therefore, the correct choice is C.

Question 20

The Henry's law constant for carbon dioxide dissolved in water at 298 K is 0.163* 10⁹ Pa. Determine the mole fraction of carbon dioxide in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K, assuming the proportion of carbon dioxide in dry air is 0.04%.

Accepted Answer

First, we need to convert the percent of carbon dioxide in dry air to a partial pressure. 
0.04% of 1 atm = 0.0004 atm

Next, we can use Henry's law equation to calculate the mole fraction:

P = K_H*x

where P is the partial pressure of the gas above the solution, K_H is the Henry's law constant, and x is the mole fraction of the gas in the solution.

We know P and K_H, so we can solve for x:

x = P/K_H = 0.0004 atm / (0.163 x 10^3 Pa) = 2.45 x 10^-6

To convert this to ppm (parts per million), we can multiply by 10^6:

2.45 x 10^-6 * 10^6 = 2.45 ppm

Therefore, the answer is B) 25 ppm.

Quiz 17: Phase Equilibrium and Solutions

An ice skater exerts a pressure of 3.1 MPa. Calculate the change in the melting point of the ice under the skate, given that the densities of liquid water and ice are 0.998 and 0.920 g cm^-3 respectively and the enthalpy of fusion of water is +6.01 kJ mol^-1.

Determine the vapour pressure of diethyl ether, C₄H₁₀O, at a temperature of 298 K, given that the normal boiling temperature is 308 K and enthalpy of vaporization is 25.9 kJ mol^-1.

The normal boiling temperature of trichloromethane, CHCl₃, is 61°C, and the specific enthalpy of vaporization is 250 J g^-1. Determine the vapour pressure at a temperature of 298 K.

The vapour pressure of pyridine, C₅H₅N, is 2.25 kPa at 25°C. Determine the normal boiling temperature of pyridine if the enthalpy of vaporization is 40.3 kJ mol^-1.

The vapour pressure of pure 1-propanol is 2792 Pa at 25°C and 11995 Pa at 50°C. Determine the enthalpy of vaporization of 1-propanol.

The vapour pressure of pure benzene is 0.146 bar and of pure toluene is 0.185 bar at 298 K. Determine the mole fraction of toluene in an ideal liquid mixture of benzene and toluene for which the total vapour pressure is 0.160 bar at this temperature.

The Henry's law constant for nitrogen dissolved in water at 298 K is 8.68* 10⁹ Pa. Determine the mole fraction of nitrogen in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K.

What is the osmotic pressure generated at 25°C by a solution of 1.26 g of sucrose, C₁₂H₂₂O₁₁, in 250 cm³ of water?

Determine the mass of potassium chloride, KCl, that must be added to water to create an aqueous solution of volume 25 dm³ with an osmotic pressure of 1.0 bar.

Trichloromethane, CHCl₃, and propanone, C₃H₆O, form liquid-vapour mixtures with a maximum-boiling azeotrope. What does this imply about the nature of the interactions between the molecules in the mixture?

Determine the vapour pressure of n-hexane, C₆H₁₄, at a temperature of 298 K, given that the normal boiling temperature is 342 K and enthalpy of vaporization is 30.9 kJ mol^-1.

Determine the vapour pressure of toluene, C₇H₈, at a temperature of 350 K, given that the normal boiling temperature is 384 K and enthalpy of vaporization is 37.1 kJ mol^-1.

Determine the vapour pressure of acetone, C₃H₆O, at a temperature of 298 K, given that the normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Estimate the increase in the vapour pressure of octane, C₈H₁₈, from when the temperature is 298 K to when the temperature is 308 K. The normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Estimate the change in the vapour pressure of $\alpha$ -pinene, C₁₀H₁₆, from when the temperature is 323 K to when the temperature is 273 K. The normal boiling temperature is 430 K and enthalpy of vaporization is 45.4 kJ mol^-1.

The vapour pressure of ethanol, C₂H₆O, is 7.4 kPa at 25°C. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 42.3 kJ mol^-1.

The vapour pressure of methanol, CH₄O, is 27.5 kPa at 308 K. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 37.6 kJ mol^-1.

The vapour pressure of pure cyclohexane is 12.2 kPa at 25°C and 25.1 kPa at 42°C. Determine the enthalpy of vaporization of cyclohexane.

The vapour pressure of pure aniline is 1314 Pa at 350 K and 13372 Pa at 400 K. Determine the enthalpy of vaporization of aniline.

The Henry's law constant for carbon dioxide dissolved in water at 298 K is 0.163* 10⁹ Pa. Determine the mole fraction of carbon dioxide in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K, assuming the proportion of carbon dioxide in dry air is 0.04%.

Quiz 17: Phase Equilibrium and Solutions

An ice skater exerts a pressure of 3.1 MPa. Calculate the change in the melting point of the ice under the skate, given that the densities of liquid water and ice are 0.998 and 0.920 g cm-3 respectively and the enthalpy of fusion of water is +6.01 kJ mol-1.

Determine the vapour pressure of diethyl ether, C4H10O, at a temperature of 298 K, given that the normal boiling temperature is 308 K and enthalpy of vaporization is 25.9 kJ mol-1.

The normal boiling temperature of trichloromethane, CHCl3, is 61°C, and the specific enthalpy of vaporization is 250 J g-1. Determine the vapour pressure at a temperature of 298 K.

The vapour pressure of pyridine, C5H5N, is 2.25 kPa at 25°C. Determine the normal boiling temperature of pyridine if the enthalpy of vaporization is 40.3 kJ mol-1.

The vapour pressure of pure 1-propanol is 2792 Pa at 25°C and 11995 Pa at 50°C. Determine the enthalpy of vaporization of 1-propanol.

The vapour pressure of pure benzene is 0.146 bar and of pure toluene is 0.185 bar at 298 K. Determine the mole fraction of toluene in an ideal liquid mixture of benzene and toluene for which the total vapour pressure is 0.160 bar at this temperature.

The Henry's law constant for nitrogen dissolved in water at 298 K is 8.68* 109 Pa. Determine the mole fraction of nitrogen in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K.

What is the osmotic pressure generated at 25°C by a solution of 1.26 g of sucrose, C12H22O11, in 250 cm3 of water?

Determine the mass of potassium chloride, KCl, that must be added to water to create an aqueous solution of volume 25 dm3 with an osmotic pressure of 1.0 bar.

Trichloromethane, CHCl3, and propanone, C3H6O, form liquid-vapour mixtures with a maximum-boiling azeotrope. What does this imply about the nature of the interactions between the molecules in the mixture?

Determine the vapour pressure of n-hexane, C6H14, at a temperature of 298 K, given that the normal boiling temperature is 342 K and enthalpy of vaporization is 30.9 kJ mol-1.

Determine the vapour pressure of toluene, C7H8, at a temperature of 350 K, given that the normal boiling temperature is 384 K and enthalpy of vaporization is 37.1 kJ mol-1.

Determine the vapour pressure of acetone, C3H6O, at a temperature of 298 K, given that the normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol-1.

Estimate the increase in the vapour pressure of octane, C8H18, from when the temperature is 298 K to when the temperature is 308 K. The normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol-1.

Estimate the change in the vapour pressure of α\alphaα -pinene, C10H16, from when the temperature is 323 K to when the temperature is 273 K. The normal boiling temperature is 430 K and enthalpy of vaporization is 45.4 kJ mol-1.

The vapour pressure of ethanol, C2H6O, is 7.4 kPa at 25°C. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 42.3 kJ mol-1.

The vapour pressure of methanol, CH4O, is 27.5 kPa at 308 K. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 37.6 kJ mol-1.

The vapour pressure of pure cyclohexane is 12.2 kPa at 25°C and 25.1 kPa at 42°C. Determine the enthalpy of vaporization of cyclohexane.

The vapour pressure of pure aniline is 1314 Pa at 350 K and 13372 Pa at 400 K. Determine the enthalpy of vaporization of aniline.

The Henry's law constant for carbon dioxide dissolved in water at 298 K is 0.163* 109 Pa. Determine the mole fraction of carbon dioxide in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K, assuming the proportion of carbon dioxide in dry air is 0.04%.

An ice skater exerts a pressure of 3.1 MPa. Calculate the change in the melting point of the ice under the skate, given that the densities of liquid water and ice are 0.998 and 0.920 g cm^-3 respectively and the enthalpy of fusion of water is +6.01 kJ mol^-1.

Determine the vapour pressure of diethyl ether, C₄H₁₀O, at a temperature of 298 K, given that the normal boiling temperature is 308 K and enthalpy of vaporization is 25.9 kJ mol^-1.

The normal boiling temperature of trichloromethane, CHCl₃, is 61°C, and the specific enthalpy of vaporization is 250 J g^-1. Determine the vapour pressure at a temperature of 298 K.

The vapour pressure of pyridine, C₅H₅N, is 2.25 kPa at 25°C. Determine the normal boiling temperature of pyridine if the enthalpy of vaporization is 40.3 kJ mol^-1.

The Henry's law constant for nitrogen dissolved in water at 298 K is 8.68* 10⁹ Pa. Determine the mole fraction of nitrogen in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K.

What is the osmotic pressure generated at 25°C by a solution of 1.26 g of sucrose, C₁₂H₂₂O₁₁, in 250 cm³ of water?

Determine the mass of potassium chloride, KCl, that must be added to water to create an aqueous solution of volume 25 dm³ with an osmotic pressure of 1.0 bar.

Trichloromethane, CHCl₃, and propanone, C₃H₆O, form liquid-vapour mixtures with a maximum-boiling azeotrope. What does this imply about the nature of the interactions between the molecules in the mixture?

Determine the vapour pressure of n-hexane, C₆H₁₄, at a temperature of 298 K, given that the normal boiling temperature is 342 K and enthalpy of vaporization is 30.9 kJ mol^-1.

Determine the vapour pressure of toluene, C₇H₈, at a temperature of 350 K, given that the normal boiling temperature is 384 K and enthalpy of vaporization is 37.1 kJ mol^-1.

Determine the vapour pressure of acetone, C₃H₆O, at a temperature of 298 K, given that the normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Estimate the increase in the vapour pressure of octane, C₈H₁₈, from when the temperature is 298 K to when the temperature is 308 K. The normal boiling temperature is 329 K and enthalpy of vaporization is 31.3 kJ mol^-1.

Estimate the change in the vapour pressure of $\alpha$ -pinene, C₁₀H₁₆, from when the temperature is 323 K to when the temperature is 273 K. The normal boiling temperature is 430 K and enthalpy of vaporization is 45.4 kJ mol^-1.

The vapour pressure of ethanol, C₂H₆O, is 7.4 kPa at 25°C. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 42.3 kJ mol^-1.

The vapour pressure of methanol, CH₄O, is 27.5 kPa at 308 K. Determine the normal boiling temperature of ethanol if the enthalpy of vaporization is 37.6 kJ mol^-1.

The Henry's law constant for carbon dioxide dissolved in water at 298 K is 0.163* 10⁹ Pa. Determine the mole fraction of carbon dioxide in water in equilibrium with air at a pressure of 1 atm and temperature of 298 K, assuming the proportion of carbon dioxide in dry air is 0.04%.