The **Clausius-Clapeyron Equation** establishes a quantitative relationship between **vapor pressure** and **temperature**.

**Concept:** Understanding the Clasius-Clapeyron Equation

We're going to say by using the Clasius-Clapeyron equation, a quantitative relationship between vapor pressure and temperature can be established. The question here is ln of P2 over P1 equals negative delta H of vaporization. Remember, delta H is enthalpy. Enthalpy of vaporization over R times 1 over T2 minus 1 over T1. We're going to say here that R, since we’re dealing with enthalpy is 8.314 joules over more times K.

Vapor Pressure looks at the equilibrium established between vaporization and condensation. By using the Clasius-Clapeyron equation, the enthalpy of vaporization can be determined.

**Example:** The heat of vaporization (Δ**H _{vap}**) of water is 40.3 kJ/mol at its normal boiling point at 100

A certain substance has a heat of vaporization of 43.09 kJ/mol. At what Kelvin temperature will the vapor pressure be 3.00 times higher than it was at 341 K?

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What is the ΔH°_{vap} of a liquid that has a vapor pressure of 615 torr at 79.8 °C and a boiling point of 96.0 °C at 1 atm?

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Assistance Diethyl ether has a ΔH _{vap} of 29.1 kJ/mol and a vapor pressure of 0.703 atm at 25.0°C. What is its vapor pressure at 79.0°C?

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The vapor pressure of dichloromethane, CH _{2}C_{2}, at 0°C is 134 g. The normal boiling point of dichloromethane is 40°C. Calculate its molar heat of vaporization.

**Express your answer to three significant figures and include the appropriate units.**

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What is the ΔH°_{vap} of a liquid that has a vapor pressure of 622 torr at 79.0°C and a boiling point of 99.8°C at 1 atm?

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A certain substance has a heat of vaporization of 53.47 kJ/mol. At what Kelvin temperature will the vapor pressure be 6.50 times higher than it was at 299 K?

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A certain liquid has a vapor pressure of 92.0 Torr at 23.0°C and 372.0 Torr at 45.0°C.

Calculate the value of ΔH°_{vap} for this liquid.

Calculate the normal boiling point of this liquid.

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A certain substance has a heat of vaporization of 37.11 kJ/mol. At what Kelvin temperature will the vapor pressure be 4.50 times higher than it was at 347 K?

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Enter your answer in the provided box. What is the ΔH° _{vap} of a liquid that has a vapor pressure of 607 torr at 86.5 °C and a boiling point of 93.3 °C at 1 atm?

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A certain liquid has a vapor pressure of 92.0 Torr at 23.0°C and 332.0 Torr at 45.0 C, Calculate the value of ΔHvap for this liquid.

Calculate the normal boiling point of this liquid.

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The formation of methanol is important to the processing of new fuels.

At 298.0 K, Kp = 2.25x10^{4} for the reaction

CO_{(g)} + 2 H_{2(g)} ⇌ CH_{3}OH_{(l) }

If ΔH°_{rxn }= -128 kJ/mol CH_{3}OH, calculate K_{p} at 0°C.

(Enter your answer in scientific notation.)

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The following equation represents the decomposition of a generic diatomic element in its standard state.

1/2 X_{2}_{(g)} → X_{(g) }

Assume that the standard molar Gibbs energy of formation of X(g) is 4.76 kJ mol^{-1} at 2000. K and -65.63 kJ mol^{-1} at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature.

K at 2000. K = _____

K at 3000. K = _____

Assuming that delta H°_{rxn}, is independent of temperature, determine the value of delta H°_{rxn} from these data.

ΔH°_{rxn} = ______ kJ mol^{-1}

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Butane is a common fuel used in cigarette lighters and camping stoves. Normally supplied in metal containers under pressure, the fuel exists as a mixture of liquid and gas, so high temperatures may cause the container to explode. At 25.0°C, the vapor pressure of butane is 2.3 atm. What is the pressure in the container at 135°C ( ΔH°vap = 24.3 kJ/mol)?

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What is the ΔH°vap of a liquid that has a vapor pressure of 621 torr at 85.2°C and a boiling point of 95.6°C at 1 atm?

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A liquid has a ΔH°vap of 35.5 kJ/mol and a boiling point of 122°C at 1.00 atm. What is its vapor pressure at 113°C?

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A reaction has an equilibrium constant of 8.9x103 at 298 K. At 751 K, the equilibrium constant is 0.43. Find Δ Hrxn for the reaction.

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The vapor pressure of dichloromethane,CH_{2}Cl_{2}, at 0°C is 134mmHg . The normal boiling point of dichloromethane is 40°C.

Calculate its molar heat of vaporization. Express your answer numerically in kilojoules per mole.

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A certain substance has a heat of vaporization of 47.70 kJ/mol. At what kelvin temperature will the vapor pressure be 3.50 times higher than it was at 293K?

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A certain substance has a heat of vaporization of 57.40 kJ/mol. At what Kelvin temperature will the vapor pressure be 3.00 times higher than it was at 317 K?

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The vapor pressure of ammonia at several different temperatures is shown below.

a. Use the date to determine the heat of vaporization of ammonia

b. Determine the normal boiling point of ammonia.

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Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 C.

What is the vapor pressure of ethanol at 15°C?

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Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 °C. What is the vapor pressure of ethanol at 14°C?

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Four alcohols have the formula C_{4}H_{9}OH:

1-butanol, 2-butanol (or sec-butanol), isobutanol (or 2-methyl-1-propanol), and tert-butanol (or 2-methy;-2-propanol).

They are examples of isomers, or compounds that have the same molecular formula but different molecular structures. The below table gives data on the isomers:

Using the Clausius-Clapeyron equation, rank the isomers of butanol in order of decreasing vapor pressure at 25 °C. Does the ranking agree with any conventional wisdom based on the Δ_{vap}H Values or the normal boiling points?

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1) The vapor pressure of dichloromethane, CH _{2}Cl_{2}, at 0°C is 134 mmHg. The normal boiling point of dichloromethane is 40°C. Calculate its molar heat of vaporization.

Express your answer to three significant figures and include the appropriate units.

2) The boiling points for a set of compounds in a homologous series can be qualitatively predicted using intermolecular force strengths. Using their condensed structural formulas, rank the homologous series for a set of alkanes by their boiling point.

Rank from highest to lowest boiling point. To rank items as equivalent, overlap them.

butane (C_{4}H_{10}), 3,3-dimethylpentane (C_{7}H_{16}), hexane (C_{6}H_{14}), and heptane (C_{7}H_{16}).

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Which solids will melt under applied pressure? Check all that apply.

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The vapor pressure of all liquids

1. is the same at 100°C.

2. increase with volume of liquid present.

3. is the same at their freezing points.

4. increases with temperature.

5. decreases with the increasing volume of the container.

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The equilibrium constant of a certain reaction is experimentally determined at 200 K and 250 K and is found to be equal to 1010 and 1016, respectively.What can you say for certain about the reaction?

1. nothing can be said for certain

2. It is endothermic

3. It is exothermic

4. It will become non-spontaneous at higher temperatures

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Useful conversions:

760 torr = 1atm = 760 mm Hg. 1 inch = 2.54cm

Weather trivia: The lowest ever recorded sea-level atmospheric pressure was 25.69 inches of Hg inside of typhoon Tip, on October 12, 1979. If you had been unlucky enough to be inside of it, at sea level, on that date, what would have been the boiling point of water? The enthalpy of vaporization of water is 40.7 kJ/mol.

1. 101.929°C

2. 99.69°C

3. 98.09°C

4. 100.13°C

5. 95.7131°C

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For the decomposition of ammonia to nitrogen and hydrogen, the equilibrium constant is 1.47 x 10^{-6} at 298 K. Calculate the temperature at which K = 0.01. For reaction, Δ*H*° = 92.38 kJ • mol^{-1}.

1. 390 K

2. 59 K

3. 117 K

4. 241 K

5. 468 K

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An unknown liquid has a vapor pressure of 88 mmHg at 45 ^{◦}C and 39 mmHg at 25^{◦}C. What is its heat of vaporization?

1. 32 kJ/mol

2. 2000 J/mol

3. 32000 kJ/mol

4. 2000 kJ/mol

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The vapor pressure of benzene, C_{6}H_{6}, is 40.1 mmHg at 1.6 °C. What is its vapor pressure at 60.6 °C? The molar heat of vaporization of benzene is 31.0 kJ/mol.

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At room temperature, a sample of some compound has a vapor pressure of 454 torr. At what temperature will the solution have a vapor pressure of 900 Torr? ∆H_{vap} of compound is 25.8 kJ/mol.

A. 319 K

B. 258 K

C. 298 K

D. 416 K

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A bottle of highly volatile perfume with molecular formula C_{5}H_{8}O_{4}N_{2} spills inside a large infinitely expandable bubble and the bubble expands to its maximum size consistent with the fact that the perfume liquid/vapor equilibrium still exists i.e. the perfume “gas” molecules cause the bubble to expand with no work involved. How many molecules of perfume remain in the liquid phase?

a. not enough information is given to say

b. 22.4 liters

c. none should be left in the liquid phase

d. one mole

e. about one or two molecules

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Which term describes the energy change associated with molecules that have some movement past each other to molecules that have no interactions with other molecules?

A. ΔH_{vap} B. ΔH _{fus} C. ΔH _{cond} D. C _{p}(gas) E. C _{p}(liquid)

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How many of the following would be associated with an increase in the rate of vaporization?

• An increase in temperature

• An increase in the strength of intermolecular forces

• An increase in the amount of surface area

• An increase in vapor pressure

A. none B. one C. two D. three E. four

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Calculate the vapor pressure (mmHg) of potassium at 150°C. The normal boiling point of potassium is 775°C. The heat of vaporization is 81.3 kJ/mol

a) 7.82 x 10 ^{-4} mmHg

b) 0.451 mmHg

c) 237 mmHg

d) 2.81 x 10 ^{-2} mmHg

e) 624 mmHg

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Mercury is a neurotoxic metal with a reasonable high vapor pressure, at least for a metal. The vapor pressure at 25°C is 0.0017 mmHg. But what about the vapor pressure of mercury in a factory where the temperature is 32°C? Will the vapor pressure of mercury be higher or lower in the factory? The enthalpy of vaporization of mercury is 59.11 kJ/mol.

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It was determined that the normal boiling point of a compound was 183.5°C. When the boiling point was measured at 300 mmHg, it was a136.8°C. What is the heat of vaporization (kJ/mol) of this compound?

a. 31.0 KJ/mol

b. 56.7 KJ/mol

c. 93.9 KJ/mol

d. 145 KJ/mol

e. 188 KJ/mol

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Which compound has the lowest boiling point?

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How much energy is required to vaporize 98.6 g of ethanol (C_{2}H_{5}OH) at its boiling point, if its ΔH_{vap} is 40.5 kJ/mol?

A) 86.7 kJ

B) 11.5 kJ

C) 18.9 kJ

D) 52.8 kJ

E) 39.9 kJ

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Which of the following is NOT true about the Clausius-Clapeyron equation?

A) It is a way to measure the heat of vaporization in the laboratory

B) The equation describes an exponential relationship

C) B is a constant based on a particular gas

D) Its graph represents the natural log of the vapor pressure by the inverse of temperature

E) The graphed data is linear

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Which of the following substances would you predict to have the highest ΔH_{vap}?

A) CH_{3}Cl

B) HCl

C) CH_{3}COCH_{3}

D) CH_{3}CH_{2}OH

E) CH_{3}CH_{2}CH_{2}CH_{3}

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