Ch.12 - Liquids, Solids & Intermolecular Forces

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.12 - Liquids, Solids & Intermolecular Forces

Problem 70

Chapter 12, Problem 70

Benzene has a heat of vaporization of 30.72 kJ/mol and a normal boiling point of 80.1 °C. At what temperature does benzene boil when the external pressure is 445 torr?

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Identify the known values: the heat of vaporization (\(\Delta H_{vap} = 30.72 \text{ kJ/mol}\)), the normal boiling point (\(T_1 = 80.1 \degree C\)), and the normal pressure (\(P_1 = 760 \text{ torr}\)).

Convert the normal boiling point from Celsius to Kelvin: \(T_1 = 80.1 + 273.15\).

Use the Clausius-Clapeyron equation: \(\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)\), where \(P_2 = 445 \text{ torr}\) and \(R = 8.314 \text{ J/mol K}\).

Rearrange the Clausius-Clapeyron equation to solve for \(T_2\): \(T_2 = \left(\frac{1}{T_1} - \frac{R}{\Delta H_{vap}} \ln\left(\frac{P_2}{P_1}\right)\right)^{-1}\).

Substitute the known values into the equation and solve for \(T_2\) in Kelvin, then convert back to Celsius if needed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without a change in temperature. For benzene, this value is 30.72 kJ/mol, indicating the energy needed to vaporize one mole of benzene at its boiling point under standard atmospheric pressure.

Boiling Point and External Pressure

The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure surrounding it. As external pressure increases, the boiling point of the liquid also increases. In this case, the boiling point of benzene will change when the external pressure is adjusted to 445 torr, which is lower than standard atmospheric pressure.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the change in vapor pressure with temperature to the heat of vaporization. It can be used to calculate the new boiling point of a substance when the external pressure changes. This equation is essential for determining how the boiling point of benzene will shift from its normal boiling point of 80.1 °C at a pressure of 445 torr.

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Clausius-Clapeyron Equation

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

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This table displays the vapor pressure of ammonia at several different temperatures. Use the data to determine the heat of vaporization and normal boiling point of ammonia.

Temperature (K) Pressure (torr)

200 65.3

210 134.3

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230 456.0

235 597.0

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