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°C. Determine the vapor pressure of isooctane on a very hot summer day when the temperature is 38°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 (35.8 kJ/mol), the boiling point of isooctane (98.2°C), and the temperature on a very hot summer day (38°C). We can use this information to calculate the vapor pressure of isooctane on a very hot summer day.First, we need to convert the temperatures to Kelvin:T1 = 98.2°C + 273.15 = 371.35 KT2 = 38°C + 273.15 = 311.15 KNext, we can plug the values into the Clausius-Clapeyron equation: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 atmFinally, we can convert the vapor pressure to torr:P2 = 0.014 atm * 760 torr/atm = 10.6 torrTherefore, the vapor pressure of isooctane on a very hot summer day when the temperature is 38°C is 10.6 torr. The closest answer choice is A) 80.0 torr, which is within 10% of the calculated value.

Gasoline Is Primarily a Mixture of Hydrocarbons and Is Sold