Dichlorodifluoromethane, CCl2F2, one of the chlorofluo- rocarbon refrigerants responsible for destroying part of the Earth's ozone layer, has Pvap = 40.0 mm Hg at -81.6 °C and Pvap = 400 mm Hg at -43.9 °C. What is the normal boiling point of CCl2F2 in °C?

Verified step by step guidance

1. First, we need to understand that the vapor pressure of a substance increases with temperature. The relationship between vapor pressure and temperature can be described by the Clausius-Clapeyron equation: ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1), where P1 and P2 are the vapor pressures at temperatures T1 and T2 respectively, ΔHvap is the heat of vaporization, and R is the ideal gas constant.
2. Next, we need to convert the given temperatures from Celsius to Kelvin, because the Clausius-Clapeyron equation requires temperatures to be in Kelvin. The conversion formula is T(K) = T(°C) + 273.15.
3. Then, we can substitute the given values into the Clausius-Clapeyron equation. We know P1, P2, T1, and T2. We are trying to find the normal boiling point of CCl2F2, which is the temperature at which its vapor pressure equals 1 atmosphere (760 mm Hg). So, we will set P2 to 760 mm Hg and solve for T2.
4. Rearrange the Clausius-Clapeyron equation to solve for T2: T2 = 1 / ((1/T1) - (R/ΔHvap) * ln(P2/P1)).
5. Finally, once we find the value of T2 in Kelvin, we need to convert it back to Celsius using the conversion formula T(°C) = T(K) - 273.15.

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 indicates how readily a substance will evaporate; higher vapor pressure at a specific temperature means the substance is more volatile. Understanding vapor pressure is crucial for determining boiling points, as a liquid boils when its vapor pressure equals the external atmospheric pressure.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. For normal boiling point, this external pressure is defined as 1 atmosphere (760 mm Hg). The boiling point can vary with changes in atmospheric pressure, making it essential to consider the conditions under which the boiling point is measured.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the change in vapor pressure with temperature to the enthalpy of vaporization of a substance. It can be used to estimate the boiling point of a substance at different pressures by plotting the logarithm of vapor pressure against the inverse of temperature. This equation is particularly useful in determining the normal boiling point when given vapor pressures at two different temperatures.