How Does Temperature Affect Water Vapor Pressure?

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In summary, the Clausius-Clapeyron Equation is a thermodynamic relationship that describes the behavior of two-phase systems, such as vaporization. It is important because it allows us to predict phase changes and understand temperature and pressure relationships. The equation is derived from the first and second laws of thermodynamics and makes assumptions about equilibrium, constant heat of vaporization, ideal gas behavior, and small temperature and pressure changes. It is used in practical applications such as predicting boiling points, studying refrigerants and the water cycle, and designing distillation processes.
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Homework Statement

Determine the vapor pressure of water at 50 degrees C. The molar heat of vaporization of water is 40.7 kJ/mol.

Homework Equations

Clausius-Clapeyron equation.

The Attempt at a Solution

P1 = 760 mm Hg
T1 = 373 K

P2 = ?
T2 = 323 K

ln (P2/760) = ln P2 - ln 760 = -(40700/8.31)(1/323 - 1/373). I'm taking the change in temperature (delta T, or final minus initial temperature, and accordingly I put a negative out in front of the right side of the equation).

ln P2 = 4.6

e^4.6 = P2 = 100 mm Hg (approximately).

Is this correct?

Tables give 92.51 mm Hg, so you are reasonably close.

Thank you :-)!

What is the Clausius-Clapeyron Equation?

The Clausius-Clapeyron Equation is a thermodynamic relationship that describes the behavior of two-phase systems, such as the vaporization of a liquid into a gas. It relates the temperature and pressure of a substance to its enthalpy and entropy.

Why is the Clausius-Clapeyron Equation important?

The Clausius-Clapeyron Equation is important because it allows us to predict the behavior of a substance as it undergoes a phase change, such as boiling or condensation. It also helps us understand the relationship between temperature and pressure in a system.

How is the Clausius-Clapeyron Equation derived?

The Clausius-Clapeyron Equation is derived from the combination of the first and second laws of thermodynamics. It takes into account the change in enthalpy and entropy of a substance during a phase change, as well as the temperature and pressure conditions.

What are the assumptions made in the Clausius-Clapeyron Equation?

The Clausius-Clapeyron Equation assumes that the substance is in equilibrium during the phase change, that the heat of vaporization is constant, and that the vapor behaves as an ideal gas. It also assumes that the temperature and pressure changes are small.

How is the Clausius-Clapeyron Equation used in practical applications?

The Clausius-Clapeyron Equation is used in a variety of practical applications, such as predicting the boiling point of a liquid at different pressures, understanding the behavior of refrigerants in air conditioning systems, and studying the water cycle in Earth's atmosphere. It is also used in the design and operation of distillation processes in chemical engineering.

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