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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Chemistry
Chapter
Solutions

BITSAT 2021 · Chemistry · Solutions

Liquids A and B form an ideal solution in the entire composition...

Liquids A and B form an ideal solution in the entire composition range. At 350K350 \mathrm{ K}, the vapor pressures of pure A and pure B are 7×103Pa7 \times 10^{3} \mathrm{ Pa} and 12×103Pa12 \times 10^{3} \mathrm{ Pa}, respectively. The composition of the vapour is in equilibrium with a solution containing 40 mole percent of A\mathrm{A} at this temperature is:

Options

  1. AxA=0.37;xB=0.63x_{\mathrm{A}}=0.37 ; x_{\mathrm{B}}=0.63
  2. BxA=0.28;xB=0.72x_{\mathrm{A}}=0.28 ; x_{\mathrm{B}}=0.72
  3. CxA=0.4;xB=0.6x_{\mathrm{A}}=0.4 ; x_{\mathrm{B}}=0.6
  4. DxA=0.76;xB=0.24x_{\mathrm{A}}=0.76 ; x_{\mathrm{B}}=0.24

Correct answer

B. xA=0.28;xB=0.72x_{\mathrm{A}}=0.28 ; x_{\mathrm{B}}=0.72

Step-by-step solution

\mathrm{P}_{\mathrm{A}^{{}^{\circ}}=7 \times 10^{3}\mathrm{P}_{\mathrm{B}^{{}^{\circ}}=12 \times 10^{3}x_{\mathrm{A}^{\prime}=0.4 ; x_{\mathrm{B}^{\prime}=1-0.4x_{\mathrm{B}^{\prime}=0.6\mathrm{P}_{\text{total }}=\mathrm{P}_{\mathrm{A}^{{}^{\circ}}}^{x_{\mathrm{A}^{\prime}}+\mathrm{P}_{\mathrm{B}^{{}^{\circ}} x_{\mathrm{B}^{\prime}=7 \times 10^{3} \times 0.4+12 \times 10^{3} \times 0.6=(7 \times 0.4+12 \times 0.6) \times 10^{3}=10^{4}x_{\mathrm{A}}=\frac{\mathrm{P}_{\mathrm{A}^{{}^{\circ}}}^{x^{\prime}} \mathrm{A}}{\mathrm{P}_{\text{total }}}=\frac{7 \times 10^{3} \times 0.4}{10^{4}}\therefore x_{\mathrm{A}}=0.28, x_{\mathrm{B}}=1-0.28=0.72
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