What is the hydronium-ion concentration of a solution formed by combining 700.mL of 0.19 M HCl with 300.mL of 0.52 M NaOH at 25°C?
HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

Question

Quizplus · Accepted Answer

First, let's write the balanced chemical equation for the reaction:
HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l)

From this equation, we can see that 1 mole of HCl reacts with 1 mole of NaOH to produce 1 mole of water. The balanced equation implies that the hydronium ions (H3O+) and hydroxide ions (OH-) react completely to form water. This is a neutralization reaction, and the concentration of hydronium ions in the final solution depends on the amount of excess acid or base.

To determine the concentration of hydronium ions, we first need to calculate the number of moles of HCl and NaOH that react:
moles HCl = 0.19 M × 0.700 L = 0.133 mol
moles NaOH = 0.52 M × 0.300 L = 0.156 mol

Since the equation is balanced in a 1:1 ratio, we can see that HCl is the limiting reactant, and NaOH is in excess. Therefore, all of the HCl will react with the NaOH, and any excess NaOH will remain.

The number of moles of excess NaOH is:
moles excess NaOH = 0.156 mol - 0.133 mol = 0.023 mol

The total volume of the final solution is 700 mL + 300 mL = 1000 mL = 1 L. Therefore, the total number of moles of NaCl formed is also 0.023 mol.

The hydronium ion concentration can be calculated using the definition of pH:
pH = -log[H3O+]

Since the solution is neutral (equal amounts of acid and base react to form a salt and water), the hydronium ion concentration is equal to the hydroxide ion concentration:
[H3O+] = [OH-]

The hydroxide ion concentration can be calculated from the amount of excess NaOH:
[OH-] = moles OH- / volume of solution = 0.023 mol / 1 L = 0.023 M

Therefore, the hydronium ion concentration is also 0.023 M, and the pH of the solution is:
pH = -log(0.023) = 1.6

To make sure you have selected the correct answer, you can double-check by calculating the concentration of hydroxide ions ([OH-]):
pH + pOH = 14
pOH = 14 - pH = 14 - 1.6 = 12.4
[OH-] = 10^(-pOH) = 10^(-12.4) = 4.3 × 10^(-13) M

This matches Answer B.

What Is the Hydronium-Ion Concentration of a Solution Formed by Combining