JEE MAIN - Chemistry (2005 - No. 18)
Benzene and toluene form nearly ideal solutions. At 20 oC, the vapour pressure of
benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of
benzene at 20 oC for a solution containing 78 g of benzene and 46 g of toluene in
torr is
50
25
53.5
37.5
Explicaţie
Given, Vapour pressure of benzene $$ = 75\,\,torr$$
Vapour pressure of toluene $$ = 22\,\,torr$$
mass of benzene in $$=78g$$
hence moles of benzene $$ = {{78} \over {78}} = 1\,mole$$
(mol. wt of benzene $$=78$$)
mass of toluene in solution $$=46g$$
hence moles of toluene $$ = {{46} \over {92}} = 0.5\,\,mole$$
Total moles of benzene and toluene = 1.5 mol
now partial pressure of benzene
$$ = {P^ \circ }_b \times {X_b} = 75 \times {1 \over {1 + 0.5}}$$
$$ = 75 \times {1 \over {1.5}} = 75 \times {2 \over 3} = 50$$ torr
Vapour pressure of toluene $$ = 22\,\,torr$$
mass of benzene in $$=78g$$
hence moles of benzene $$ = {{78} \over {78}} = 1\,mole$$
(mol. wt of benzene $$=78$$)
mass of toluene in solution $$=46g$$
hence moles of toluene $$ = {{46} \over {92}} = 0.5\,\,mole$$
Total moles of benzene and toluene = 1.5 mol
now partial pressure of benzene
$$ = {P^ \circ }_b \times {X_b} = 75 \times {1 \over {1 + 0.5}}$$
$$ = 75 \times {1 \over {1.5}} = 75 \times {2 \over 3} = 50$$ torr