JEE MAIN - Chemistry (2009 - No. 8)
Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol
of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this
solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mm Hg) of X
and Y in their pure states will be, respectively :
200 and 300
300 and 400
400 and 600
500 and 600
Explanation
$${P_{total}} = P_A^ \circ {X_A} + P_B^ \circ {X_B};$$
$$\,\,\,\,\,\,\,\,$$ $$550 = P_A^ \circ \times {1 \over 4} + P_B^ \circ \times {3 \over 4}$$
$$P_A^ \circ + 3P_B^ \circ = 550 \times 4\,\,...\left( i \right)$$
In second case
$${P_{total}} = P_A^ \circ \times {1 \over 5} + P_B^ \circ \times {4 \over 5}$$
$$P_A^ \circ + 4P_B^ \circ = 560 \times 5\,\,...\left( {ii} \right)$$
Subtract $$(i)$$ from $$(ii)$$
$$\therefore$$ $$\,\,\,\,\,\,\,\,$$ $$P_B^ \circ = 560 \times 5 - 550 \times 4 = 600$$
As $$\,\,\,\,\,\,\,\,$$ $$P_A^ \circ = 400$$
$$\,\,\,\,\,\,\,\,$$ $$550 = P_A^ \circ \times {1 \over 4} + P_B^ \circ \times {3 \over 4}$$
$$P_A^ \circ + 3P_B^ \circ = 550 \times 4\,\,...\left( i \right)$$
In second case
$${P_{total}} = P_A^ \circ \times {1 \over 5} + P_B^ \circ \times {4 \over 5}$$
$$P_A^ \circ + 4P_B^ \circ = 560 \times 5\,\,...\left( {ii} \right)$$
Subtract $$(i)$$ from $$(ii)$$
$$\therefore$$ $$\,\,\,\,\,\,\,\,$$ $$P_B^ \circ = 560 \times 5 - 550 \times 4 = 600$$
As $$\,\,\,\,\,\,\,\,$$ $$P_A^ \circ = 400$$
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