This table displays the vapor pressure of nitrogen at several different temperatures. Use the data to determine the heat of vaporization and the normal boiling point of nitrogen. Temperature (K) Pressure (torr) 65 130.5 70 289.5 75 570.8 80 1028 85 1718

Verified step by step guidance

1. <Step 1: Understand the Clausius-Clapeyron Equation.> The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature and is given by: \( \ln P = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T} \right) + C \), where \( P \) is the vapor pressure, \( \Delta H_{vap} \) is the heat of vaporization, \( R \) is the ideal gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, and \( C \) is a constant.
2. <Step 2: Convert the data into a linear form.> To use the Clausius-Clapeyron equation, convert the given temperature and pressure data into a linear form by plotting \( \ln P \) versus \( \frac{1}{T} \). Calculate \( \ln P \) for each pressure value and \( \frac{1}{T} \) for each temperature.
3. <Step 3: Determine the slope of the line.> Plot the calculated \( \ln P \) values against \( \frac{1}{T} \) values. The slope of the resulting line is equal to \( -\frac{\Delta H_{vap}}{R} \). Use linear regression to find the slope of the line.
4. <Step 4: Calculate the heat of vaporization.> Use the slope from the linear regression to calculate the heat of vaporization \( \Delta H_{vap} \) by rearranging the slope formula: \( \Delta H_{vap} = -\text{slope} \times R \).
5. <Step 5: Determine the normal boiling point.> The normal boiling point is the temperature at which the vapor pressure equals 760 torr. Use the linear equation from the plot to solve for \( T \) when \( P = 760 \) torr.

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. As temperature increases, vapor pressure typically increases, indicating that more molecules have enough energy to enter the vapor phase.

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 value is crucial for understanding phase changes and is typically expressed in joules per gram or calories per gram. It can be determined using the Clausius-Clapeyron equation, which relates vapor pressure and temperature.

Normal Boiling Point

The normal boiling point of a substance is the temperature at which its vapor pressure equals the standard atmospheric pressure (1 atm or 760 torr). At this point, the liquid turns into vapor throughout the liquid, not just at the surface. For nitrogen, determining the normal boiling point involves analyzing the vapor pressure data to find the temperature at which the pressure reaches 760 torr.