Liquid textA$\text{A}$ and textB$\text{B}$ form an ideal solution. The vapour pressure of pure liquids textA$\text{A}$ and textB$\text{B}$ are 350 and 750text mm Hg$750\text{ mm Hg}$ respectively at the same temperature. If textx_textA$\text{x}_{\text{A}}$ and textx_textB$\text{x}_{\text{B}}$ are the mole fraction of textA$\text{A}$ and textB$\text{B}$ in solution while texty_textA$\text{y}_{\text{A}}$ and texty_textB$\text{y}_{\text{B}}$ are the mole fraction of textA$\text{A}$ and textB$\text{B}$ in vapour phase then:

### Related Formula P_textA = y_textA P_texttotal = x_textA P^0_textA$$P_\text{A} = y_\text{A} P_{\text{total}} = x_\text{A} P^0_\text{A}$$ P_textB = y_textB P_texttotal = x_textB P^0_textB$$P_\text{B} = y_\text{B} P_{\text{total}} = x_\text{B} P^0_\text{B}$$ Dividing both partial pressure formulations yields: fracy_textAy_textB = left(fracP^0_textAP^0_textB ight) cdot fracx_textAx_textB $$\frac{y_\text{A}}{y_\text{B}} = \left(\frac{P^0_\text{A}}{P^0_\text{B}} ight) \cdot \frac{x_\text{A}}{x_\text{B}} $$ ### Core Logic Given pure saturation thresholds: P^0_textA = 350text mm Hg, quad P^0_textB = 750text mm Hg $$P^0_\text{A} = 350\text{ mm Hg}, \quad P^0_\text{B} = 750\text{ mm Hg} $$ Comparing pure component volatility profiles: P^0_textA < P^0_textB implies fracP^0_textAP^0_textB < 1 $$P^0_\text{A} < P^0_\text{B} \implies \frac{P^0_\text{A}}{P^0_\text{B}} < 1 $$ Substituting this inequality into the ratio formula gives: fracy_textAy_textB < 1 cdot fracx_textAx_textB implies fracy_textAy_textB < fracx_textAx_textB $$\frac{y_\text{A}}{y_\text{B}} < 1 \cdot \frac{x_\text{A}}{x_\text{B}} \implies \frac{y_\text{A}}{y_\text{B}} < \frac{x_\text{A}}{x_\text{B}} $$ ### Step 1: Rearranging Ratio Forms Inverting the inequality expression fields safely yields: fracx_textAx_textB > fracy_textAy_textB $$\frac{x_\text{A}}{x_\text{B}} > \frac{y_\text{A}}{y_\text{B}} $$ ### Pattern Recognition Konovalov's Rule Shortcut: The vapour phase is always enriched with the more volatile component. Since component textB$\text{B}$ has a higher pure vapour pressure (750 > 350$750 > 350$), it will be preferentially enriched in the vapour phase, meaning y_textB/y_textA > x_textB/x_textA$y_\text{B}/y_\text{A} > x_\text{B}/x_\text{A}$. Reversing the fractions directly matches option (3). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Solutions