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 boiling point of 98.2 $\circ$ C. Determine the vapor pressure of isooctane on a very hot summer day when the temperature is 38 $\circ$ C. A)80.0 torr B)36.7 torr C)67.8 torr D)47.9 torr E)89.3 torr

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 boiling point of isooctane (T1 = 98.2°F = 36.8°C). We are also given the temperature on a very hot summer day (T2 = 38°C). We can use the Clausius-Clapeyron equation to solve for the vapor pressure of isooctane on this day:ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)ln(P2/1 atm) = -(35.8 kJ/mol)/(8.314 J/mol*K) * (1/311 K - 1/309 K)ln(P2) = -1.08P2 = 0.347 atm = 80.0 torrTherefore, the vapor pressure of isooctane on a very hot summer day when the temperature is 38°C is 80.0 torr.

Gasoline Is Primarily a Mixture of Hydrocarbons and Is Sold ∘\circ∘

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