The following table gives the vapor pressure of hexafluorobenzene (C₆F₆) as a function of temperature: (a) By plotting these data in a suitable fashion, determine whether the Clausius–Clapeyron equation (Equation 11.1) is obeyed. If it is obeyed, use your plot to determine ∆H_vap for C₆F₆.

Verified step by step guidance

1. 1. The Clausius-Clapeyron equation is a logarithmic equation that relates the vapor pressure of a substance at a particular temperature to its heat of vaporization. The equation is given as: ln(P) = -ΔHvap/R(1/T) + C, where P is the vapor pressure, ΔHvap is the heat of vaporization, R is the gas constant, T is the temperature in Kelvin, and C is a constant.
2. 2. To determine whether the Clausius-Clapeyron equation is obeyed, plot the natural logarithm of the vapor pressure (ln(P)) against the inverse of the temperature (1/T). If the Clausius-Clapeyron equation is obeyed, the plot should be a straight line.
3. 3. If the plot is a straight line, the Clausius-Clapeyron equation is obeyed. The slope of the line is equal to -ΔHvap/R. Therefore, you can calculate ΔHvap by multiplying the slope by -R.
4. 4. To find the slope, choose two points on the line and use the formula (y2 - y1) / (x2 - x1). Remember that y corresponds to ln(P) and x corresponds to 1/T.
5. 5. Once you have the slope, multiply it by -R to find ΔHvap. Remember to use the appropriate value for R (8.314 J/(mol·K) if your pressure is in atmospheres, or 0.0821 L·atm/(mol·K) if your pressure is in pascals).

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 or solid state into the gas phase. Understanding vapor pressure is crucial for analyzing phase changes and the behavior of substances under varying temperatures.

Clausius–Clapeyron Equation

The Clausius–Clapeyron equation describes the relationship between vapor pressure and temperature for a substance undergoing phase changes. It is expressed as ln(P2/P1) = -ΔH_vap/R(1/T2 - 1/T1), where ΔH_vap is the enthalpy of vaporization, R is the gas constant, and P1 and P2 are the vapor pressures at temperatures T1 and T2. This equation is essential for determining the heat required for vaporization from experimental data.

Enthalpy of Vaporization (ΔH_vap)

The enthalpy of vaporization (ΔH_vap) is the amount of energy required to convert a unit mass of a liquid into vapor at constant temperature and pressure. It is a critical thermodynamic property that indicates the strength of intermolecular forces in a substance. A higher ΔH_vap suggests stronger interactions among molecules, which affects the substance's vapor pressure and boiling point.