Question

A \(0.4000 \mathrm{M}\) solution of nitric acid is used to titrate \(50.00 \mathrm{~mL}\) of \(0.237 \mathrm{M}\) barium hydroxide. (Assume that volumes are additive.) (a) Write a balanced net ionic equation for the reaction that takes place during titration. (b) What are the species present at the equivalence point? (c) What volume of nitric acid is required to reach the equivalence point? (d) What is the \(\mathrm{pH}\) of the solution before any \(\mathrm{HNO}_{3}\) is added? (e) What is the \(\mathrm{pH}\) of the solution halfway to the equivalence point? (f) What is the \(\mathrm{pH}\) of the solution at the equivalence point?

Short answer

Answer: The balanced net ionic equation for the titration between nitric acid and barium hydroxide is H+ + OH- -> H2O. The pH of the solution halfway to the equivalence point is 7.

Step-by-step solution

Write the balanced equation for the reaction

The equation for the reaction between nitric acid (HNO3) and barium hydroxide (Ba(OH)2) is: HNO3 + Ba(OH)2 -> Ba(NO3)2 + 2H2O Now, we can write the balanced net ionic equation by eliminating spectator ions (the NO3- ions): 2 H+ + 2 OH- -> 2 H2O The balanced net ionic equation is: H+ + OH- -> H2O

Determine the limiting reactant and calculate the moles of each substance at the equivalence point

To determine the limiting reactant, we must first calculate the initial moles of nitric acid and barium hydroxide. Moles of barium hydroxide: mol Ba(OH)2 = (0.237 M) * (50.00 mL/1000) = 0.01185 mol At the equivalence point, moles of H+ from nitric acid should be equal to the moles of OH-. Since there are two moles of H+ per mole of Ba(OH)2, the moles of H+ needed equals: mol H+ = 2 * mol Ba(OH)2 = 2 * 0.01185 = 0.0237 mol

Use stoichiometry to calculate the volume of nitric acid needed to reach the equivalence point

In order to neutralize the barium hydroxide, we need 0.0237 mol of H+. Since the concentration of nitric acid is 0.4000 M, we can find the volume needed as follows: volume HNO3 = (0.0237 mol) / (0.4000 M) = 0.05925 L = 59.25 mL The volume of nitric acid required to reach the equivalence point is 59.25 mL.

Calculate the pH of the solution before any nitric acid is added

Since barium hydroxide is a strong base, it will dissociate completely in water. The concentration of OH- ions can be found by noting that there are two moles of OH- per mole of Ba(OH)2: [OH-] = 2 * 0.237 M = 0.474 M Next, we can calculate the pOH using the relation: pOH = -log10(0.474) Then, we can calculate the pH by using: pH = 14 - pOH

Calculate the pH of the solution halfway to the equivalence point, and at the equivalence point

Halfway to the equivalence point, the moles of H+ and OH- are equal. As the nitric acid is a strong acid and barium hydroxide is a strong base, the resulting solution is neutral, with a pH of 7. At the equivalence point, the amount of H+ ions will be equal to the OH- ions. The reaction forms water leaving a solution of only barium nitrate, which does not affect the pH. At the equivalence point, the pH value of the solution is 7 as well. To summarize the results: a) Balanced net ionic equation: H+ + OH- -> H2O b) Species present at the equivalence point: H2O, Ba2+, and NO3- c) Volume of nitric acid required to reach the equivalence point: 59.25 mL d) pH before any nitric acid is added: 14 -(-log10(0.474)) e) pH halfway to the equivalence point: 7 f) pH at the equivalence point: 7