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NEET CHEMISTRYMedium

Which of the following statements about the composition of the vapour over an ideal 1:11:1 molar mixture of benzene and toluene is correct? Assume that the temperature is constant at 25C25^\circ\text{C}. (Given, vapour pressure data at 25C25^\circ\text{C}, benzene = 12.8 kPa12.8 \text{ kPa}, toluene = 3.85 kPa3.85 \text{ kPa})

A

The vapour will contain a higher percentage of toluene

B

The vapour will contain equal amounts of benzene and toluene

C

Not enough information is given to make a prediction

D

The vapour will contain a higher percentage of benzene

Step-by-Step Solution

According to Raoult's law, the partial vapour pressure of a component in a solution is given by pi=pi0xip_i = p_i^0 x_i. For a 1:11:1 molar mixture, the mole fractions of benzene and toluene in the liquid phase are equal (xbenzene=xtoluene=0.5x_{\text{benzene}} = x_{\text{toluene}} = 0.5). Partial pressure of benzene, pbenzene=12.8 kPa×0.5=6.4 kPap_{\text{benzene}} = 12.8 \text{ kPa} \times 0.5 = 6.4 \text{ kPa}. Partial pressure of toluene, ptoluene=3.85 kPa×0.5=1.925 kPap_{\text{toluene}} = 3.85 \text{ kPa} \times 0.5 = 1.925 \text{ kPa}. Since the partial pressure of benzene is greater than that of toluene in the vapour phase (pbenzene>ptoluenep_{\text{benzene}} > p_{\text{toluene}}), its mole fraction in the vapour phase (yi=piPtotaly_i = \frac{p_i}{P_{\text{total}}}) will also be higher. As a general rule, at equilibrium, the vapour phase is always richer in the component which is more volatile (i.e., has a higher vapour pressure in its pure state). Thus, the vapour will contain a higher percentage of benzene.

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