Gasoline is primarily a mixture of hydrocarbons and is sold with an octane rating that is based on a comparison with the properties of isooctane (C₈H₁₈), which has an enthalpy of vaporization of 35.8 kJ/mol and a normal boiling point of 98.2 $\degree$C.Determine the vapor pressure of isooctane on a very hot day when the temperature is 38.0 $\degree$C.

Question

Quizplus · Accepted Answer

The Clausius-Clapeyron equation can be used to determine the vapor pressure of a liquid at a given temperature. The equation is:ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)where P1 and T1 are the known vapor pressure and temperature, P2 is the unknown vapor pressure, T2 is the unknown temperature, ΔHvap is the enthalpy of vaporization, and R is the ideal gas constant.In this problem, we are given the enthalpy of vaporization of isooctane (ΔHvap = 35.8 kJ/mol) and the normal boiling point of isooctane (T1 = 98.2°C = 371.35 K). We are also given the temperature at which we want to find the vapor pressure (T2 = 38.0°C = 311.15 K).We can plug these values into the Clausius-Clapeyron equation and solve for P2:ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)ln(P2/1 atm) = -(35.8 kJ/mol)/(8.314 J/mol*K) * (1/311.15 K - 1/371.35 K)ln(P2) = -4.30P2 = e^-4.30 = 0.014 atm = 80.6 torrTherefore, the vapor pressure of isooctane on a very hot day when the temperature is 38.0°C is 80.6 torr.

Gasoline Is Primarily a Mixture of Hydrocarbons and Is Sold °\degree°

Gasoline Is Primarily a Mixture of Hydrocarbons and Is Sold $\degree$