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Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 112

A sample of 7.5 L of NH3 gas at 22 _x001F_C and 735 torr is bubbled into a 0.50-L solution of 0.40 M HCl. Assuming that all the NH3 dissolves and that the volume of the solution remains 0.50 L, calculate the pH of the resulting solution.

Verified step by step guidance
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Step 1: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This will be used in the ideal gas law calculation.
Step 2: Use the ideal gas law, PV = nRT, to calculate the number of moles of NH3 gas. Convert the pressure from torr to atm by dividing by 760, and use the volume in liters, the temperature in Kelvin, and R = 0.0821 L·atm/mol·K.
Step 3: Calculate the initial moles of HCl in the solution using the concentration (0.40 M) and the volume of the solution (0.50 L).
Step 4: Determine the limiting reactant by comparing the moles of NH3 and HCl. NH3 reacts with HCl in a 1:1 molar ratio to form NH4Cl.
Step 5: Calculate the concentration of NH4+ in the solution after the reaction. Use this concentration to find the pH by considering the hydrolysis of NH4+ and using the expression for the equilibrium constant, Kb, of NH3.