Benzene, toluene, ethylbenzene, and xylene (BTEX) are common constituents of gasoline. Vapor pressures of pure liquids are respectively: 0.126, 0.0380, 0.0126, and 0.0117 atm at 25°C. Assuming an equimolar mixture of these liquids obeys Raoult's law, which one of the given will exert maximum partial pressure in the mixture?

Correct option is C

Raoult's Law: The partial pressure of a component in a liquid mixture is given by:
Pi = xi⋅ Pi0
Where:
· Pi ​: Partial pressure of the component.
· xi ​: Mole fraction of the component in the mixture.
· Pi0 : Vapor pressure of the pure component.
Given Data:
· Vapor pressures (Pi0​) of pure components:
· Benzene: 0.126 atm
· Toluene: 0.0380 atm
· Ethylbenzene: 0.0126 atm
· Xylene: 0.0117 atm
In an equimolar mixture (xi=0.25x_i = 0.25xi​=0.25 for each component), the partial pressure is proportional to the pure vapor pressure.
Calculation of Partial Pressures:
Pbenzene = 0.25⋅ 0.126 = 0.0315 atm
Ptoluene​= 0.25 ⋅ 0.0380 = 0.0095 atm
Pethylbenzene= 0.25 ⋅ 0.0126 = 0.00315 atm
Pxylene= 0.25 ⋅ 0.0117 = 0.002925 atm
Observation: Benzene has the highest partial pressure (0.0315 atm) among the components in the mixture.
Key Explanation: 1. Raoult's Law Dependence: The partial pressure of a component depends on its mole fraction and the vapor pressure of the pure component.
2. Benzene's Vapor Pressure: Benzene has the highest vapor pressure among BTEX components, resulting in its maximum partial pressure in the mixture.
3. Equimolar Mixture: Equal mole fractions mean the relative vapor pressures directly determine the partial pressure.
Information Booster: 1. BTEX Compounds:
· Common aromatic hydrocarbons in gasoline.
· Benzene and toluene have relatively higher vapor pressures, contributing significantly to the vapor phase.
2. Raoult's Law Application:
· Assumes ideal behavior in liquid mixtures.
· Useful in predicting the composition of vapor and liquid phases in equilibrium.
3. Vapor Pressure Trends:
· Vapor pressure decreases with increasing molecular weight and intermolecular forces.
· Benzene, being lighter and less polar, has the highest vapor pressure.