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The vapour pressure of pure liquids A and B are 450 and 700 mm Hg respectively, at 350 K. Find out the composition of the liquid mixture if total vapour pressure is 600 mm Hg. |
XA = 0.4, XB = 0.6 XA = 0.3, XB = 0.7 XA = 0.2, XB = 0.8 XA = 0.5, XB = 0.5 |
XA = 0.4, XB = 0.6 |
The correct answer is option 1. XA = 0.4, XB = 0.6. To find the composition of the liquid mixture (mole fractions of A and B) when the total vapor pressure is 600 mm Hg, we can use Dalton's Law of partial pressures. According to Dalton's Law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Let us denote: \( P_A \) as the partial pressure of component A, \( P_B \) as the partial pressure of component B, \( x_A \) as the mole fraction of component A, \( x_B \) as the mole fraction of component B. Given: Vapor pressure of pure liquid A (\( P^{\circ}_A \)) = 450 mm Hg Vapor pressure of pure liquid B (\( P^{\circ}_B \)) = 700 mm Hg Total vapor pressure of the mixture (\( P_{\text{total}} \)) = 600 mm Hg We can use the equation: \(P_{\text{total}} = P_A + P_B \) Using Raoult's Law, we have: \(P_A = x_A \cdot P^{\circ}_A \) \( P_B = x_B \cdot P^{\circ}_B \) Substituting these equations into the total pressure equation: \(P_{\text{total}} = x_A \cdot P^{\circ}_A + x_B \cdot P^{\circ}_B \) Given that \( P_{\text{total}} = 600 \) mm Hg, \( P^{\circ}_A = 450 \) mm Hg, and \( P^{\circ}_B = 700 \) mm Hg, we can solve for \( x_A \) and \( x_B \). \(600 = x_A \cdot 450 + x_B \cdot 700 \) Now, we can rearrange this equation to solve for \( x_B \): \(600 - 450x_A = 700x_B \) \( x_B = \frac{600 - 450x_A}{700} \) Since \( x_A + x_B = 1 \), we can substitute \( x_B \) from the above equation into \( x_A + x_B = 1 \) and solve for \( x_A \): \(x_A + \frac{600 - 450x_A}{700} = 1 \) \(700x_A + 600 - 450x_A = 700 \) \(250x_A = 100 \) \( x_A = \frac{100}{250} = 0.4 \) Now, we can find \( x_B \): \(x_B = 1 - x_A = 1 - 0.4 = 0.6 \) Therefore, the composition of the liquid mixture is \( x_A = 0.4 \) and \( x_B = 0.6 \). So, the correct option is \(X_A = 0.4, X_B = 0.6\) |