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Question

At 300 K, the vapour pressure of an ideal solution that has 3 mol A and 2 mol B is 600 torr. At the same temperature, if 1.5 mol A & 0.5 mol C (non-volatile) are added to this solution, the vapour pressure of the solution increases by 30 torr. Then, what is the value of PB?

A
940 torr
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B
405 torr
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C
90 torr
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D
45 torr
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Solution

The correct option is C 90 torr
According to Raoult's lawP=PAXA+PBXB600=PA(33+2)+PB(22+3)

3000=3PA+2PB ......(1)

After the addition of 1.5 moles of A and 0.5 mole of C,

630=PA(4.54.5+2+0.5)+PB(24.5+2+0.5)

4.5PA+2PB=4410 .......(2)

Solving equation (1) and (2) we get,
1.5PA=1410PA=940 torr & PB=90 torr

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