Q: According to the Clausius-Clapeyron equation, what is the relationship between the natural logarithm of vapor pressure ($$\ln P_{\text{vap}}) $$and the inverse of temperature ($$1/T$$)?

$$\ln P_{\text{vap}} is $$linearly proportional to $$1/T$$ with a negative slope.

Q: If you want to calculate the total heat required to convert 1 mole of ice at $$-10^\circC to $$steam at $$110^\circC$$, which of the following expressions correctly represents the sum of all steps?

$$q_{\text{total}} = q_a + q_b + q_c + q_d + q_e$$

Question 1

Which of the following best describes the normal boiling point of a liquid?

Accepted Answer

The temperature at which the vapor pressure of the liquid equals 1 atm.

Question 2

According to the Clausius-Clapeyron equation, what is the relationship between the natural logarithm of vapor pressure ($$\ln P_{	ext{vap}}) $$and the inverse of temperature ($$1/T$$)?

Accepted Answer

$$\ln P_{	ext{vap}} is $$linearly proportional to $$1/T$$ with a negative slope.

Question 3

Given the Clausius-Clapeyron equation in two-point form:

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

If$$ $$P_1 = 760$ mm Hg at T_1$ = 373.1 K $$and $$P_2 = 407$ mm Hg, what is the boiling point T_2$ (in $$^\circ$$C) of water at P_2$? ($$\Delta H_{	ext{vap}} = 40.7$$ kJ/mol, R = 8.314$ J/mol·K)

Accepted Answer

$$83.0^\circC$$

Question 4

Which phase change requires the most energy per mole for water, as seen in the heating curve?

Accepted Answer

Vaporization (liquid to gas)

Question 5

A sample of dichloromethane has a vapor pressure of 21 torr at 240 K and 391 torr at 300 K. Using the Clausius-Clapeyron equation, what is the approximate heat of vaporization ($$\Delta H_{	ext{vap}}) in kJ/$$mol? ($$R = 8.314 J/$$mol·K)

Accepted Answer

$$31.4 kJ/$$mol

Question 6

Which of the following statements about phase changes is TRUE?

Accepted Answer

During a phase change, the temperature of the substance remains constant.

Question 7

What is the correct formula for calculating the amount of heat required to raise the temperature of a substance without a phase change?

Accepted Answer

$$q = m c_m \Delta T$$

Question 8

Which of the following best explains why the plateau at $$100^\circC on $$the heating curve for water represents the boiling of liquid water?

Accepted Answer

The temperature remains constant while energy is used to overcome intermolecular forces and convert liquid to gas.

Question 9

If you want to calculate the total heat required to convert 1 mole of ice at $$-10^\circC to $$steam at $$110^\circC$$, which of the following expressions correctly represents the sum of all steps?

Accepted Answer

$$q_{	ext{total}} = q_a + q_b + q_c + q_d + q_e$$

Question 10

Which of the following is the correct definition of the enthalpy of vaporization ($$\Delta H_{	ext{vap}}$$)?

Accepted Answer

The amount of energy required to overcome intermolecular forces to convert a liquid to a gas.

Question 11

A chemist is studying the vapor pressure of ethanol at different temperatures. If the slope of the $$\ln P_{	ext{vap}} vs$$ $$1/T$$ plot is $$-4000 K$$, what is the enthalpy of vaporization ($$\Delta H_{	ext{vap}}) in kJ/$$mol? ($$R = 8.314 J/$$mol·K)

Accepted Answer

$$33.3 kJ/$$mol

Question 12

Which of the following best describes what happens at the molecular level during the melting of ice at $$0^\circC$$?

Accepted Answer

Intermolecular forces are partially overcome, allowing molecules to move more freely.

Question 13

During which process does the entropy of a substance increase the most?

Accepted Answer

Vaporization (liquid to gas)

Question 14

A student heats 50.0 g of water from $$25^\circC to$$ $$75^\circC. If $$the specific heat capacity of water is $$4.18 J/g$$·$$^\circC$$, how much heat is required?

Accepted Answer

$$10,450 J$$

Question 15

Which of the following is NOT a phase change?

Accepted Answer

Heating water from $$20^\circC to$$ $$50^\circC$$

Question 16

If the enthalpy of fusion ($$\Delta H_{	ext{fus}}) $$for water is $$6.01 kJ/$$mol, how much energy is required to melt $$36.0 g of $$ice at $$0^\circC$$? (Molar mass of water = $$18.0 g/$$mol)

Accepted Answer

$$12.0 kJ$$

Question 17

Which of the following best explains why the boiling point of water decreases at higher altitudes?

Accepted Answer

Atmospheric pressure is lower, so water boils at a lower temperature.

Question 18

Which equation correctly relates the change in Gibbs free energy ($$\Delta G) to $$enthalpy ($$\Delta H) $$and entropy ($$\Delta S) $$during a phase change at equilibrium?

Accepted Answer

$$\Delta G = \Delta H - T \Delta S$$

Phase Changes, Heating Curves, and the Clausius-Clapeyron Equation

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