You are given 200 mL of a 0.100 M solution of HCl. You add 100 mL of a 0.200 M solution of barium hydroxide, Ba(OH)2, to the HCl solution.
(a) Write the balanced chemical equation for the reaction that occurs, including all phases.
(b) Calculate the concentration (in M) of HCl after the reaction is complete.
(c) Briefly explain why the solution after the reaction is neutral.
Answers:
(a) The balanced chemical equation for the reaction is:
$$2HCl(aq) + Ba(OH)_2(aq) → BaCl_2(aq) + 2H_2O(l)$$
(b) To determine the concentration of HCl after the reaction is complete, we can use the stoichiometry of the balanced chemical equation. Initially, we have 200 mL of a 0.100 M HCl solution, which contains:
Moles of HCl = (0.100 M) × (200 mL) / 1000 = 0.0200 mol
After adding 100 mL of a 0.200 M Ba(OH)2 solution, we have:
Moles of Ba(OH)2 = (0.200 M) × (100 mL) / 1000 = 0.0200 mol
Since the reaction proceeds in a 2:1 mole ratio of HCl to Ba(OH)2, 0.0200 mol of Ba(OH)2 will completely react with 0.0400 mol of HCl. Therefore, after the reaction is complete, we have:
Moles of HCl remaining = 0.0200 mol - 0.0400 mol = -0.0200 mol
Since the total volume of the solution is now 200 mL + 100 mL = 300 mL, the concentration of HCl after the reaction is:
[HCl] = -0.0200 mol / 0.300 L = -0.0667 M
The negative sign indicates that the solution is acidic, but its pH is very close to 7 which means the solution is nearly neutral.
(c) The solution after the reaction is nearly neutral because the reaction between HCl and Ba(OH)2 results in the formation of water (H2O) and barium chloride (BaCl2). Barium chloride is a salt that does not undergo further reaction in water, so it does not contribute to the acidity or basicity of the solution. The remaining hydrogen ions (H+) from the unreacted HCl are neutralized by the hydroxide ions (OH-) from Ba(OH)2. Therefore, the solution is close to neutral, with a pH near 7.