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
220 255.7
230 456.0
235 597.0

Verified step by step guidance

1. insert step 1: Use the Clausius-Clapeyron equation, which relates the vapor pressure and temperature of a substance to its heat of vaporization: \( \ln P = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T} \right) + C \), where \( P \) is the vapor pressure, \( T \) is the temperature in Kelvin, \( \Delta H_{vap} \) is the heat of vaporization, \( R \) is the ideal gas constant (8.314 J/mol·K), and \( C \) is a constant.
2. insert step 2: Convert the given pressures from torr to atm if necessary, or use them directly in the equation as long as the units are consistent.
3. insert step 3: Plot \( \ln P \) versus \( \frac{1}{T} \) using the given data points. The slope of the resulting line will be \( -\frac{\Delta H_{vap}}{R} \).
4. insert step 4: Calculate the slope of the line from the plot. Use the slope to determine \( \Delta H_{vap} \) by rearranging the equation to \( \Delta H_{vap} = -\text{slope} \times R \).
5. insert step 5: To find the normal boiling point, set the vapor pressure \( P \) equal to 760 torr (1 atm) in the Clausius-Clapeyron equation and solve for the temperature \( T \).

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. Understanding vapor pressure is crucial for determining the boiling point of a substance, as the boiling point is reached when the vapor pressure equals the external pressure.

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. This concept is essential for calculating the energy needed for phase changes and is typically expressed in joules per mole. The heat of vaporization can be derived from the Clausius-Clapeyron equation, which relates vapor pressure and temperature.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance. It can be used to calculate the heat of vaporization by plotting the natural logarithm of vapor pressure against the inverse of temperature. This equation is fundamental in thermodynamics and helps in understanding phase transitions and the behavior of substances under varying conditions.