The value of X_A for which (Y_A − X_A) is minimum — Solutions and Colligative Properties Chemistry Question

💡 Solution & Explanation

Y_A = X_A × P_A° / (X_A(P_A° − P_B°) + P_B°). Setting d(Y_A − X_A)/dX_A = 0 gives P_A°P_B° / (X_A(P_A° − P_B°) + P_B°)² = 1 → X_A(P_A° − P_B°) + P_B° = √(P_A°P_B°) → X_A = (√(P_A°P_B°) − P_B°) / (P_A° − P_B°).