Question

Beta-Pinene(C₁₀H₁₆) and alpha-terpineol(C₁₀H₁₈O) are used in cosmetics to provide a fresh pine scent. At 367K, the pure substances have vapor pressurs of 100.3 torr and 9.8 torr, respectively. What is the composition of the vapor (in terms of mole fractions) above a solution containing equal masses of these compounds at 367K? (Assume ideal behavior).

X_pinene=?

X_terpineol=?

Answer 1

Given :

Temperature : 367K

Vapor pressure of Beta-Pinene(C₁₀H₁₆) = 100.3 torr

Vapor pressure of alpha-terpineol(C₁₀H₁₈O) = 9.8 torr

1. mole fractions for each substance:

A solution has a 1:1 ratio of Beta-Pinene(C₁₀H₁₆): alpha-terpineol(C₁₀H₁₈O)

Beta-Pinene(C₁₀H₁₆): 1/2 = 0.5
alpha-terpineol(C₁₀H₁₈O) : 1/2 = 0.5

2) total pressure above the solution is:

P_total = P°_CP χ_CP + P°_CH χ_CH

x = (100.3) (0.5) + (9.8) (0.5)

x = 50.15 + 4.9

x = 55.05 torr

3) mole fraction of Beta-Pinene(C₁₀H₁₆) in the vapor:

X_{pinene   =} 50.15 torr / 55.05 torr = 0.910

4) mole fraction of alpha-terpineol(C₁₀H₁₈O) in the vapor:

X_{terpineol   =} 4.9 torr / 55.05 torr = 0.0890