JEE Main · 2019 · Shift-ImediumSOL-117

Liquid M and liquid N form an ideal solution. The vapour pressures of pure liquids M and N are 450 and 700 mmHg,…

Solutions · Class 12 · JEE Main Previous Year Question

Question

Liquid M and liquid N form an ideal solution. The vapour pressures of pure liquids M and N are 450 and 700 mmHg, respectively, at the same temperature. Then correct statement is:

(xMx_M = Mole fraction of 'M' in solution; xNx_N = Mole fraction of 'N' in solution; yMy_M = Mole fraction of 'M' in vapour phase; yNy_N = Mole fraction of 'N' in vapour phase;)

Options
  1. a

    xMxN>yMyN\frac{x_M}{x_N} > \frac{y_M}{y_N}

  2. b

    xMxN=yMyN\frac{x_M}{x_N} = \frac{y_M}{y_N}

  3. c

    xMxN<yMyN\frac{x_M}{x_N} < \frac{y_M}{y_N}

  4. d

    (xMyM)<(xNyN)(x_M - y_M) < (x_N - y_N)

Correct Answera

xMxN>yMyN\frac{x_M}{x_N} > \frac{y_M}{y_N}

Detailed Solution

Strategy:\n> For an ideal solution, the vapour is enriched in the more volatile component (Konovalov's Rule). Relate the liquid phase ratios to the vapour phase ratios using pure state vapour pressures.\n\nStep 1: Identify the more volatile component\nPN=700textmmHgP_N^\circ = 700\\text{ mm Hg} and PM=450textmmHgP_M^\circ = 450\\text{ mm Hg}.\nN is more volatile.\n\nStep 2: Relate the ratios\nyM=fracxMPMPtexttotal,yN=fracxNPNPtexttotaly_M = \\frac{x_M P_M^\circ}{P_{\\text{total}}}, \quad y_N = \\frac{x_N P_N^\circ}{P_{\\text{total}}}\nDividing the two:\nfracyMyN=fracxMxNfracPMPN\\frac{y_M}{y_N} = \\frac{x_M}{x_N} \cdot \\frac{P_M^\circ}{P_N^\circ}\n\nStep 3: Analyze the inequality\nSince PM/PN=450/700<1P_M^\circ / P_N^\circ = 450 / 700 < 1:\nfracyMyN<fracxMxN    fracxMxN>fracyMyN\\frac{y_M}{y_N} < \\frac{x_M}{x_N} \implies \\frac{x_M}{x_N} > \\frac{y_M}{y_N}\n\ntextAnswer:(1)\boxed{\\text{Answer: (1)}}

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Liquid M and liquid N form an ideal solution. The vapour pressures of pure liquids M and N are 450… (JEE Main 2019) | Canvas Classes