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Chapter 12: Problem 54

What is the equilibrium vapor pressure of a liquid? How does it change with temperature?

Short Answer

Expert verified
The equilibrium vapor pressure of a liquid is the pressure exerted by the vapor in equilibrium with its liquid phase at a certain temperature. As the temperature increases, the equilibrium vapor pressure increases exponentially as per the Clausius-Clapeyron equation.

Step by step solution

01

Understanding Equilibrium Vapor Pressure

Equilibrium vapor pressure is the pressure at which the gas, or vapor, of a substance is in equilibrium with the liquid or solid form of the substance at a certain temperature. In simple terms, it's the pressure created by the vapor particles when the rate of evaporation equals the rate of condensation in a closed system at a given temperature.
02

Relationship between Vapor Pressure and Temperature

The overall behavior of the vapour pressure in function of temperature can be described by the Clausius-Clapeyron equation, which states that the vapor pressure of a liquid at a specific temperature is proportional to the exponential of the ratio of the heat of vaporization and the product of the ideal gas constant and temperature. Mathematically, it can be represented using the formula: \( P = P_0 \times e^{(-ΔH_{vap}/(R \times T))} \). Here, \( P \) is the equilibrium vapor pressure, \( P_0 \) is a reference pressure, \( ΔH_{vap} \) is the molar heat of vaporization, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature.
03

Deriving the Relation

As the temperature increases, the exponential term in the Clausius-Clapeyron equation becomes larger (since temperature \( T \) is in the denominator), making the overall equilibrium vapor pressure \( P \) to increase. Thus, the equilibrium vapor pressure of a liquid increases exponentially with increasing temperature, demonstrating that more molecules can escape from the liquid to the vapor phase when the temperature is raised.

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Most popular questions from this chapter

A \(1.20-\mathrm{g}\) sample of water is injected into an evacuated \(5.00-\mathrm{L}\) flask at \(65^{\circ} \mathrm{C}\). What percentage of the water will be vapor when the system reaches equi librium? Assume ideal behavior of water vapor an that the volume of liquid water is negligible. The va por pressure of water at \(65^{\circ} \mathrm{C}\) is \(187.5 \mathrm{mmHg}\).

Estimate the molar heat of vaporization of a liquid whose vapor pressure doubles when the temperature is raised from \(85^{\circ} \mathrm{C}\) to \(95^{\circ} \mathrm{C}\).

Define critical temperature. What is the significance of critical temperature in the liquefaction of gases?

Name the kinds of attractive forces that must be overcome to (a) boil liquid ammonia, (b) melt solid phosphorus \(\left(\mathrm{P}_{4}\right),\) (c) dissolve CsI in liquid \(\mathrm{HF},\) (d) melt potassium metal.

Barium metal crystallizes in a body-centered cubic lattice (the Ba atoms are at the lattice points only). The unit cell edge length is \(502 \mathrm{pm},\) and the density of \(\mathrm{Ba}\) is \(3.50 \mathrm{~g} / \mathrm{cm}^{3}\). Using this information, calculate Avogadro's number. (Hint: First calculate the volume occupied by 1 mole of \(\mathrm{Ba}\) atoms in the unit cells. Next calculate the volume occupied by one of the Ba atoms in the unit cell.)
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