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.