This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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Here are the solutions to the problems. a) Liquids A and B form an ideal solution. The vapor pressure of pure A is 0.700 atm at the normal boiling point of a solution prepared from 0.250 mole of B and 0.650 mole of A. What is the vapor pressure of pure B at this temperature? Step 1: Identify the given values and the unknown. Given: Vapor pressure of pure A, P_A^ = 0.700 atm Moles of B, n_B = 0.250 mol Moles of A, n_A = 0.650 mol Since the solution is at its normal boiling point, the total vapor pressure, P_total = 1.000 atm. Unknown: Vapor pressure of pure B, P_B^. Step 2: Calculate the mole fractions of A and B in the solution. Total moles, n_total = n_A + n_B n_total = 0.650 mol + 0.250 mol = 0.900 mol Mole fraction of A, X_A = (n_A)/(n_total) X_A = 0.650 mol0.900 mol = 0.7222 Mole fraction of B, X_B = (n_B)/(n_total) X_B = 0.250 mol0.900 mol = 0.2778 Step 3: Apply Raoult's Law for ideal solutions. Raoult's Law states that P_total = X_A P_A^ + X_B P_B^. Substitute the known values into the equation: 1.000 atm = (0.7222)(0.700 atm) + (0.2778) P_B^ 1.000 atm = 0.50554 atm + (0.2778) P_B^ Step 4: Solve for P_B^. 0.2778 P_B^ = 1.000 atm - 0.50554 atm 0.2778 P_B^ = 0.49446 atm P_B^ = 0.49446 atm0.2778 P_B^ = 1.780 atm The vapor pressure of pure B at this temperature is 1.78 atm. b) Acetone and methanol form an ideal solution at 25^. The vapor pressure of pure acetone and pure methanol are 0.342 atm and 0.186 atm respectively. Calculate the mole fraction of methanol in a solution that boils at 25^ and 0.248 atm. Step 1: Identify the given values and the unknown. Given: Vapor pressure of pure acetone, P_acetone^ = 0.342 atm Vapor pressure of pure methanol, P_methanol^ = 0.186 atm Total vapor pressure of the solution, P_total = 0.248 atm Unknown: Mole fraction of methanol, X_methanol. Step 2: Set up the equation using Raoult's Law. Let X_methanol be the mole fraction of methanol. Then the mole fraction of acetone, X_acetone = 1 - X_methanol. Raoult's Law states: P_total = X_acetone P_acetone^ + X_methanol P_methanol^. Substitute the known values into the equation: 0.248 atm = (1 - X_methanol)(0.342 atm) + X_methanol(0.186 atm) Step 3: Solve for X_methanol. 0.248 = 0.342 - 0.342 X_methanol + 0.186 X_methanol 0.248 = 0.342 - (0.342 - 0.186) X_methanol 0.248 = 0.342 - 0.156 X_methanol 0.156 X_methanol = 0.342 - 0.248 0.156 X_methanol = 0.094 X_methanol = (0.094)/(0.156) X_methanol = 0.60256 Rounding to three significant figures: X_methanol = 0.603 The mole fraction of methanol in the solution is 0.603. Send me the next one 📸