Question

How does vapor pressure change with changing temperature? Explain.

Short answer

The vapor pressure of a substance increases with temperature because the increased energy of the molecules allows more of them to break free from the liquid or solid phase and exert pressure as vapor. This relationship is described by the Clausius-Clapeyron equation: \( \ln(p) = -\frac{ΔH_{vap}}{RT} + C \), and can be represented qualitatively using a vapor pressure curve, which shows an upward-sloping, exponential shape, indicating that vapor pressure increases exponentially with increasing temperature.

Step-by-step solution

The concept of vapor pressure

Vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid or solid phase at a given temperature. The equilibrium is achieved when the rate at which the molecules escape from the liquid or solid phase (evaporate) equals the rate at which they return to the phase (condense). The vapor pressure of a substance is an intrinsic property that depends on the temperature.

The relationship between vapor pressure and temperature

The relationship between vapor pressure and temperature is described by the Clausius-Clapeyron equation, which shows that vapor pressure increases with increasing temperature. The equation is given by: \( \ln(p) = -\frac{ΔH_{vap}}{RT} + C \) where p is the vapor pressure, \(ΔH_{vap}\) is the enthalpy of vaporization, R is the gas constant, T is the temperature in Kelvin, and C is a constant.

Understanding the relationship through thermodynamics

As the temperature of a substance increases, the average kinetic energy of its molecules increases. This means that more molecules have sufficient energy to overcome the intermolecular forces holding them in the liquid or solid phase and can escape into the vapor state. Consequently, at higher temperatures, the rate of evaporation increases, and more molecules evaporate to form vapor. This results in a higher concentration of vapor molecules above the liquid or solid phase, leading to an increase in vapor pressure. In summary, as the temperature increases, the vapor pressure increases because the increased energy of the molecules allows more of them to break free from the liquid or solid phase and exert pressure as vapor.

Qualitative relationship between vapor pressure and temperature

A qualitative representation of the relationship between vapor pressure and temperature is shown using a vapor pressure curve. On this curve, the vapor pressure of a substance is plotted against temperature. The curve generally has an upward-sloping, exponential shape, indicating that vapor pressure increases exponentially with increasing temperature. In conclusion, the vapor pressure of a substance increases with temperature due to the increased energy of the molecules allowing for increased rates of evaporation. This relationship is well-described by the Clausius-Clapeyron equation and can be represented qualitatively using a vapor pressure curve.

Key concepts

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation is a key tool used to describe how the vapor pressure of a substance changes with temperature. It provides a mathematical way to understand this relationship, showing that as temperature goes up, so does vapor pressure. The equation itself is:\[\ln(p) = -\frac{ΔH_{vap}}{RT} + C\]where:

• \( p \) is the vapor pressure.
• \( ΔH_{vap} \) is the enthalpy of vaporization.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.
• \( C \) is a constant.

This equation illustrates that vapor pressure and temperature have an exponential relationship. Essentially, it predicts how the energy needed for a substance to change state affects vapor pressure. As temperature rises, more energy is available, allowing more molecules to overcome intermolecular forces. This results in increased vapor pressure, which is captured effectively in this equation.

Evaporation and Condensation

Evaporation and condensation are two sides of the same coin in the context of vapor pressure. They describe the transition of molecules between the liquid (or solid) state and the vapor state. These processes are crucial for understanding vapor pressure at any given temperature. In evaporation:

• Molecules at the surface of a liquid gain enough kinetic energy to escape into the vapor state.
• This process increases the vapor pressure as more molecules populate the vapor phase.

Condensation is the reverse:

• Vapor molecules lose energy, turning back into the liquid.
• It decreases vapor pressure, as some vapor is removed from the gaseous phase.

At equilibrium, the rates of evaporation and condensation balance each other out. This balance correlates directly with the measured vapor pressure at a given temperature. Understanding this dynamic helps explain why vapor pressure increases when temperature rises: more molecules are evaporating and contributing to the vapor phase.

Temperature and Kinetic Energy

Temperature is a measure of the average kinetic energy of the molecules in a substance. It's an essential factor in the study of vapor pressure. As temperature increases:

• Molecules gain more kinetic energy, which enhances their ability to break free from intermolecular forces in liquids or solids.
• This results in an increased rate of evaporation, leading to a higher vapor pressure.

The connection between temperature and kinetic energy is straightforward: higher temperatures mean molecules are more energetic. Because of this, they can overcome the forces that hold them in a liquid state more easily, turning into vapor. This concept helps us understand why vapor pressure is sensitive to temperature changes. It encapsulates the notion that with sufficient kinetic energy, more molecules transition into the vapor phase, increasing vapor pressure.