Benzene and toluene form two ideal solution A and B at 313 K. Solution A (total pressure P A ) contains equal mole of toluene and benzene. Solution B contains equal masses of both (total pressure P

Question

Benzene and toluene form two ideal solution A and B at 313 K. Solution A (total pressure P A ​ ) contains equal mole of toluene and benzene. Solution B contains equal masses of both (total pressure P B ​ ). The vapour pressures of pure benzene and pure toluene are 160 and 60 mm Hg , respectively at 313 K . Calculate the value of P A ​ / P B ​ .

TestHub · Accepted Answer

For solution A: Equal moles of benzene and toluene

$X_{B} = X_{T} = 0.5$

$P_{A} = 0.5 (160) + 0.5 (60) = 110 mm H g$

For solution B: Equal masses are taken.

Molar masses: Benzene = 78, Toluene = 92

$X_{b e n ze n e} = \frac{1/78}{1/78 + 1/92} = \frac{92}{170} = 0.541$

$P_{B} = 0.541 (160) + 0.459 (60)$

$P_{B} = 86.56 + 27.54 = 114.1 mm H g$

$\frac{P _{A}}{P _{B}} = \frac{110}{114.1} = 0.964$

$\frac{P _{A}}{P _{B}} = 0.964$

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