Question

The vapour pressure of ethanol and methanol are $44.5mm$ $Hg$ and $88.7mm$ $Hg$ respectively. An ideal solution is formed at the same temperature by mixing $60g$ of ethanol with $40g$ of methanol. The total vapour pressure of the solution and the mole fraction of methanol in the vapour are respectively:

• A. $43.46mm$ and $0.51$
• B. $66.13mm$ and $0.657$
• C. $66.15mm$ and $0.791$
• D. $70.59mm$ and $0.657$

Answer 1

Answer: (B)

$66.13mm$ and $0.657$

Molar mass of ethyl alcohol $C_2{H}_{5}OH=46$

No of moles of ethyl alcohol $=60/46=1.304$

Molar mass of methyl alcohol $C{H}_{3}OH=32$

No of moles of methyl alcohol $=40/32=1.25$

Mole fraction $\left(X_A\right)$ of $C_2{H}_{5}OH=1.304/1.304+1.25=0.5107$

Mole fraction $\left(X_B\right)$ of $C{H}_{3}OH=1.25/1.304+1.25=0.489$

Partial pressure of $C_2{H}_{5}OH=X_A{P}_B^{\circ }=0.5107\times 44.5$

$=22.73mmHg$

Partial pressure of $C{H}_{3}OH=X_B{P}^{{}^{\circ }}B=0.4893\times 88.7$

$=43.73mmHg$

Total vapour pressure $=22.73+43.73=66.13$ mm Hg

Mole fraction of methyl alcohol in vapour phase$=43.40/66.13=0.6563$

Option (B) is correct.