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

Concept #1: Understanding the Clasius-Clapeyron Equation

**Transcript**

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

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Concept #1: Understanding the Clasius-Clapeyron Equation

Example #1: The heat of vaporization (Hvap) of water is 40.3...

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.

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

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?

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?

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).

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?

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.

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?

Methylamine has a vapor pressure of 344 torr at -25oC and a boiling point of -6.4oC
. Find ΔHvap for methylamine.

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.

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?

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?

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?

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?

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?

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?

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?

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?

The following table gives the vapor pressure of hexafluorobenzene (C6 F6 ) as a function of temperature: Temperature (K ) Vapor Pressure (torr)280.032.42300.092.47320.0225.1330.0334.4340.0482.9By 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.

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?

Which solids will melt under applied pressure? Check all that apply.Based on these data,Solid Triple point Normal melting pointA 0.91 atm, 124 °C 108 °C B 0.35 atm, -17 °C 50 °CC 0.0072 atm, 88 °C 89 °Cwhich solids will melt under applied pressure? Check all that apply.a) Ab) Bc) C

Given the data below for cyclohexane,Calculate ΔHvap using all of this data. (For purposes of partial credit only, explain how you arrived at this answer. Be as specific as possible. Incorrect responses with no explanation will receive no partial credit.)

Given the data below for cyclohexane,Predict the normal boiling point of cyclohexane in °C.

1. Consider the following two substances and their vapor pressures at 298 K.Substance Vapor Pressure (mmHg)A 275B 459Based on this information compare the characteristcs of the two substances.weaker intermolecular forcehigher boiling pointhigher heat of vaporizationexist in gaseous phase at 300 K2. The vapor pressure of dichloromethane, CH 2Cl2, at 0°C is 134 mmHg. The normal boiling point of dichloromethane is 40. Calculate its molar heat of vaporization?

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.

The molar enthalpy of vaporization (∆H) of water is 40.7 kJ/mol. What is the vapor pressure of water at 40.°C (R=8.314J/K mol)?A) 11.5 torrB) 311 torrC) 3.58 torrD) 38.6 torrE) 61.4 torr

The vapor pressure of ammonia at several different temperatures is shown below. Temperature (K) Pressure (torr)20065.3210134.3220255.7230456.0235597.0Determine the normal boiling point of ammonia.

If ΔHvap for water is 40.7 kJ/mole, calculate Pvap of water at 37°C.(a) 6.90 torr(b) 12.4 torr(c) 18.7 torr(d) 25.4 torr(e) 52.6 torr

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/mol3. 32000 kJ/mol4. 2000 kJ/mol

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?

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?

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

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?

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. (a) Calculate ΔH°vap of dimethyl ether.

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.

Butane (C4H10) has a heat of vaporization of 22.44 kJ/mol and a normal boiling point of -0.40°C. A 300. mL sealed flask contains 0.620g of butane at -21.0°C. How much liquid butane is present?A. 0.375g B. 0.475g C. 0.245g D. 0.620g E. no liquid left

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)?

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?

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?

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 Δ 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 ΔH°vap for this liquid in kJ/mol.Calculate the normal boiling point of this liquid in °C.

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.

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?

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)25511.326521.027536.828561.529599.0300123.8

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