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

Concept #1: Understanding the Clasius-Clapeyron Equation

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

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.

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

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

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

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? ∆Hvap of compound is 25.8 kJ/mol.
A. 319 K
B. 258 K
C. 298 K
D. 416 K

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

The vapor pressure of benzene, C6H6, 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.

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

How much energy is required to vaporize 98.6 g of ethanol (C2H5OH) at its boiling point, if its ΔHvap 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

Which compound has the lowest boiling point?

The vapor pressure of ammonia at several different temperatures is shown below.
Temperature (K)
Pressure (torr)
200
65.3
210
134.3
220
255.7
230
456.0
235
597.0
Use the data to determine the heat of vaporization of ammonia.

The vapor pressure of ammonia at several different temperatures is shown below.
Temperature (K)
Pressure (torr)
200
65.3
210
134.3
220
255.7
230
456.0
235
597.0
Determine the normal boiling point of ammonia.

Liquid nitrogen can be used as a cryogenic substance to obtain
low temperatures. Under atmospheric pressure, liquid nitrogen
boils at 77 K, allowing low temperatures to be reached. However,
if the nitrogen is placed in a sealed, insulated container connected
to a vacuum pump, even lower temperatures can be reached.
Why? If the vacuum pump has sufficient capacity, and is left on
for an extended period of time, the liquid nitrogen will start to
freeze. Explain.

You may want to reference(Page) Section 11.5 while completing this problem.The vapor pressure of a substance is measured over a range of temperatures. A plot of the natural log of the vapor pressure versus the inverse of the temperature (in Kelvin) produces a straight line with a slope of −3.44×103 K .Find the enthalpy of vaporization of the substance.

The following table gives the vapor pressure of hexafluorobenzene (C6 F6 ) as a function of temperature:
Temperature (K
)
Vapor Pressure (torr)
280.0
32.42
300.0
92.47
320.0
225.1
330.0
334.4
340.0
482.9
By plotting these data in a suitable fashion, determine whether the Clausius-Clapeyron equation is obeyed. If it is obeyed, use your plot to determine Hvap for C6 F6.

Suppose the vapor pressure of a substance is measured at two different temperatures.By using the Clausius-Clapeyron equation, large{ln P = -frac {Delta H_{
m vap}}{RT} + C}, derive the relationship between the vapor pressures, P1 and P2, and the absolute temperatures at which they were measured, T1 and T2.

You may want to reference (Pages 503 - 512) Section 11.5 while completing this problem.Propane has a normal boiling point of -42.0oC and a heat of vaporization (Hvap) of 19.04 kJ/mol. What is the vapor pressure of propane at 30.0 oC?

You may want to reference (Pages 503 - 512) Section 11.5 while completing this problem.The vapor pressure of carbon tetrachloride is measured as a function of temperature and the results are tabulated and shown in the table below. Determine the heat of vaporization of carbon tetrachloride from the results.
Temperature
(K)
Pressure
(torr)
255
11.3
265
21.0
275
36.8
285
61.5
295
99.0
300
123.8

What is the Clausius-Clapeyron equation and why is it important?

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 a 136.8°C. What is the heat of vaporization (kJ/mol) of this compound? a. 31.0 KJ/molb. 56.7 KJ/molc. 93.9 KJ/mold. 145 KJ/mole. 188 KJ/mol

What is the vapor pressure (in atm) of a liquid at its normal boiling point? ___________________

The vapor pressure of ammonia at several different temperatures is shown below.a. Use the date to determine the heat of vaporization of ammoniab. Determine the normal boiling point of ammonia.

The normal boiling point of bromine is 58.8°C. Given that the vapor pressure of bromine is 75.0 torr at 2.5°C, calculate the molar enthalpy of vaporization of bromine.a) 3.76 kJ/molb) 2.90 kJ/molc) 29.7 kJ/mold) 3.57 kJ/mole) 31.3 kJ/mol

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?

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?

1) The vapor pressure of dichloromethane, CH 2Cl2, 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 (C4H10), 3,3-dimethylpentane (C7H16), hexane (C6H14), and heptane (C7H16).

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?

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, ΔH° = 92.38 kJ • mol-1.1. 390 K2. 59 K3. 117 K4. 241 K5. 468 K •

Four alcohols have the formula C4H9OH:
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 ΔvapH Values or the normal boiling points?

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?

The vapor pressure of dichloromethane,CH2Cl2, 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.

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)?

Carbon tetrachloride, CCl4, was once used as a dry cleaning solvent, but is no longer used because it is carcinogenic. At 57.8 °C, the vapor pressure of CCl4 is 54.0 kPa, and its enthalpy of vaporization is 33.05 kJ/mol. Use this information to estimate the normal boiling point for CCl4.

A syringe at a temperature of 20 °C is filled with liquid ether in such a way that there is no space for any vapor. If the temperature is kept constant and the plunger is withdrawn to create a volume that can be occupied by vapor, what would be the approximate pressure of the vapor produced?

You may want to reference (Pages 502 - 512) Section 11.5 while completing this problem.Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 oC. What is the vapor pressure of ethanol at 16 oC?

Dry nitrogen gas is bubbled through liquid benzene (C 6H6) at 20.0 ˚C. From 100.0 L of the gaseous mixture of nitrogen and benzene, 24.7 g benzene is condensed by passing the mixture through a trap at a temperature where nitrogen is gaseous and the vapor pressure of benzene is negligible. What is the vapor pressure of benzene at 20.0 ˚C?

Butane (C4H10) has a heat of vaporization of 22.44 kJ/mol and a normal boiling point of -0.4 oC. A 250 mL sealed flask contains 0.65 g of butane at -22 oC. How much butane is present as a liquid?

Butane (C4H10) has a heat of vaporization of 22.44 kJ/mol and a normal boiling point of -0.4 oC. A 250 mL sealed flask contains 0.65 g of butane at -22 oC. If the butane is warmed to 25 oC, how much is present as a liquid?

Acrylic acid (CH2=CHCOOH) is a monomer used to make superabsorbent polymers and various compounds for paint and adhesive production. At 1 atm, it boils at 141.5°C but is prone to polymerization. Its vapor pressure at 25°C is 4.1 mbar. What pressure (in mmHg) is needed to distill the pure acid at 65°C?

The enthalpy of vaporization for acetone is 32.0 kJ/mol. The normal boiling point for acetone is 56.5 ˚C. What is the vapor pressure of acetone at 23.5 ˚C?

You may want to reference (Pages 484 - 521) Chapter 11 while completing this problem.Methylamine has a vapor pressure of 344 torr at -25oC and a boiling point of -6.4oC
. Find ΔHvap for methylamine.

At ordinary temperatures, water is a poor solvent for organic substances. But at high pressure and above 200°C, water develops many properties of organic solvents. Find the minimum pressure needed to maintain water as a liquid at 200.°C (ΔHvap = 40.7 kJ/mol at 100°C and 1.00 atm; assume that this value remains constant with temperature).

Two important characteristics used to evaluate the risk of fire or explosion are a compound’s lower flammable limit (LFL) and flash point. The LFL is the minimum percentage by volume in air that is ignitable. Below that, the mixture is too “lean” to burn. The flash point is the temperature at which the air over a confined liquid becomes ignitable. n-Hexane boils at 68.7°C at 1 atm. At 20.0°C, its vapor pressure is 121 mmHg. The LFL of n-hexane is 1.1%. Calculate the flash point of n-hexane.

You may want to reference (Page) Section 11.5 while completing this problem.Acetic acid has a normal boiling point of 118 oC and a ΔHvap of 23.4 kJ/mol. What is the vapor pressure (in mmHg) of acetic acid at 30 oC?

Pick the one that has the given property. Justify your answer.Greatest heat of vaporization: H 2CO, CH3CH3, CH 4

Pick the one that has the given property. Justify your answer.Smallest enthalpy of fusion: I 2, CsBr, CaO

Methyl salicylate, C8H8O3, the odorous constituent of oil of wintergreen, has a vapor pressure of 1.00 torr at 54.3°C and 10.0 torr at 95.3°C. What is its vapor pressure at 25°C?

Methyl salicylate, C8H8O3, the odorous constituent of oil of wintergreen, has a vapor pressure of 1.00 torr at 54.3°C and 10.0 torr at 95.3°C. What is the minimum number of liters of air that must pass over a sample of the compound at 25°C to vaporize 1.0 mg of it?

Mercury (Hg) vapor is toxic and readily absorbed from the lungs. At 20.°C, mercury (ΔHvap = 59.1 kJ/mol) has a vapor pressure of 1.20 x 10−3 torr, which is high enough to be hazardous. To reduce the danger to workers in processing plants, Hg is cooled to lower its vapor pressure. At what temperature would the vapor pressure of Hg be at the safer level of 5.0 x 10−5 torr?

You may want to reference (Pages 503 - 512)Section 11.5 while completing this problem.The vapor pressure of nitrogen at several different temperatures is shown below.Temperature (K) Pressure(torr)65130.570289.575570.8801028851718Use the data to determine the heat of vaporization of nitrogen.

You may want to reference (Pages 503 - 512)Section 11.5 while completing this problem.The vapor pressure of nitrogen at several different temperatures is shown below.Temperature (K) Pressure(torr)65130.570289.575570.8801028851718Determine the normal boiling point of nitrogen.

You may want to reference (Pages 503 - 512)section 11.5 while completing this problem.Benzene has a heat of vaporization of 30.72 kJ/mol and a normal boiling point of 80.1 oC. At what temperature does benzene boil when the external pressure is 450 torr?

The ΔH°f of gaseous dimethyl ether (CH3OCH3) is −185.4 kJ/mol; the vapor pressure is 1.00 atm at −23.7°C and 0.526 atm at −37.8°C. (b) Calculate ΔH°f of liquid dimethyl ether.

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?

A 4.7-L sealed bottle containing 0.33 g of liquid ethanol, C 2H6O, is placed in a refrigerator and reaches equilibrium with its vapor at −11°C. What mass of ethanol is present in the vapor?

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 95.0°C?

A 4.7-L sealed bottle containing 0.33 g of liquid ethanol, C 2H6O, is placed in a refrigerator and reaches equilibrium with its vapor at −11°C. When the container is removed and warmed to room temperature, 20.°C, will all the ethanol vaporize?

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?

A 4.7-L sealed bottle containing 0.33 g of liquid ethanol, C 2H6O, is placed in a refrigerator and reaches equilibrium with its vapor at −11°C. How much liquid ethanol would be present at 0.0°C? The vapor pressure of ethanol is 10. torr at −2.3°C and 40. torr at 19°C.

Carbon disulfide has a vapor pressure of 363 torr at 25 °C and a normal boiling point of 46.3 °C. Find ΔHvap for carbon disulfide.

The vapor pressure for pure water and pure acetone is measured as a function of temperature. In each case, a graph of the log of the vapor pressure versus 1/T is found to be a straight line. The slope of the line for water is -4895 K and the slope of the line for acetone is -3765 K. What is the ΔHvap of water?

Methane (CH4) has a boiling point of −164°C at 1 atm and a vapor pressure of 42.8 atm at −100°C. What is the heat of vaporization of CH4?

The vapor pressure for pure water and pure acetone is measured as a function of temperature. In each case, a graph of the log of the vapor pressure versus 1/T is found to be a straight line. The slope of the line for water is -4895 K and the slope of the line for acetone is -3765 K. What is the ΔHvap of acetone?

The vapor pressure for pure water and pure acetone is measured as a function of temperature. In each case, a graph of the log of the vapor pressure versus 1/T is found to be a straight line. The slope of the line for water is -4895 K and the slope of the line for acetone is -3765 K. Account for the difference of the molecular structure of
the two molecules.

Plot the following data and determine ΔH vap for magnesium and lithium. In which metal is the bonding stronger?

From the following data for liquid nitric acid, determine its heat of vaporization and normal boiling point.

In Breckenridge, Colorado, the typical atmospheric pressure is 520. torr. What is the boiling point of water (ΔHvap = 40.7 kJ/mol) in Breckenridge?

The temperature inside a pressure cooker is 115 ˚C. Calculate the vapor pressure of water inside the pressure cooker. What would be the temperature inside the pressure cooker if the vapor pressure of water was 3.50 atm?

Carbon tetrachloride, CCl 4, has a vapor pressure of 213 torr at 40. ˚C and 836 torr at 80. ˚C. What is the normal boiling point of CCl4?

Diethyl ether (CH 3CH2OCH2CH3) was one of the first chemicals used as an anesthetic. At 34.6 ˚C, diethyl ether has a vapor pressure of 760. torr, and at 17.9 ˚C, it has a vapor pressure of 400. torr. What is the ΔH of vaporization for diethyl ether?

The following equation represents the decomposition of a generic diatomic element in its standard state.1/2 X2(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

The formation of methanol is important to the processing of new fuels.At 298.0 K, Kp = 2.25x104 for the reactionCO(g) + 2 H2(g) ⇌ CH3OH(l) If ΔH°rxn = -128 kJ/mol CH3OH, calculate Kp at 0°C. (Enter your answer in scientific notation.)

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?

A boiled egg can be cooked at 100.0°C in exactly 5 minutes. At an altitude of around 2000m where the boiling point of water is 93.0°C, it takes exactly 7.5 minutes to cook the egg to the same amount. What is the activation energy for the reaction involved when an egg is boiled?•66 kJ/mol•0.5 kJ/mol•7.9 kJ/mol•>100 kJ/mol•4.5 kJ/mol

Part AThe vapor pressure of a substance is measured over a range of temperatures. A plot of the natural log of the vapor pressure versus the inverse of the temperatures (in Kelvin) produces a straight line with a slope of -3.39 x 103 K. Find the enthalpy of vaporization of the substance. Express your answer using three significant figures.

n-octane, C8H18 boils at 125.7 °C. What is its molar heat of vaporization in kilojoules per mole if its vapor pressure at 20°C is 11 torr?

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.

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.

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.

Enter your answer in the provided box.The vapor pressure of ethanol is 1.00 x 102 mmHg at 34.90 °C. What is its vapor pressure at 56.17 °C? (ΔHvap for ethanol is 39.3 kJ/mol.)

A certain liquid has a vapor pressure of 92.0 Torr at 23.0°C and 203.0 Torr at 45.0°C. Calculate the value of ΔH°vap for this liquid. Calculate the normal boiling point of this liquid.

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?

For a substance with a molar enthalpy of vaporization of 83 kJ/mol, how much must the temperature be lowered from 600 K to decrease the vapor pressure from 800 to 620 torr?

The vapor pressure of liquid aluminum is 400 mm Hg at 2.59 x 103 K. Assuming that its molar heat of vaporization is constant at 252 kJ/mol, the vapor pressure of liquid Al __________ is mm Hg at a temperature of 2.62 x 103 K.

From the following vapor pressure data for acetone, an estimate of the molar heat of vaporization of CH3COCH3 is _______ kJ/mol.

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?

The vapor pressure of liquid silver is 400 mm Hg at 2.33 x 103 K. Assuming that its molar heat of vaporization is constant at 275 kJ/mol, the vapor pressure of liquid Ag is _______ mm Hg at a temperature of 2.30 x 103 K.

The vapor pressure of ethanol is 1.00 x 102 mmHg at 34.90°C. What is its vapor pressure at 64.07°C? (ΔHvap for ethanol is 39.3 kJ/mol.)

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?

Enter your answer in the provided box. 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?

Enter your answer in the provided box. 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?

A certain liquid has a vapor pressure of 92.0 Torr at 23.0°C and 290.0 Torr at 45.0°C. Calculate the value of ΔH°vap for this liquid.

Enter your answer in the provided box. The vapor pressure of ethanol is 100 mmHg at 34.9°C. What is its vapor pressure at 64.5°C? (ΔHvap for ethanol is 39.3 kJ/mol.)

Enter your answer in the provided box.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?

The vapor pressure of dichloromethane, CH 2C2, 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.

The vapor pressure of a liquid doubles when the temperature is raised from 71°C to 8.0 x 101°C. At what temperature will the vapor pressure be five times the value at 71°C?

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