Final answer:
To calculate the pH of the solution, determine the number of moles of HCl and NaOH, calculate the concentration of the resulting solution using the moles, and use the ionization constant of water to find the pH. The resulting pH of the solution is 12.78.
Step-by-step explanation:
To calculate the pH of the solution obtained by mixing hydrochloric acid (HCl) and sodium hydroxide (NaOH), we can first determine the number of moles of each compound. From there, we can calculate the concentration of the resulting solution and use the ionization constant of water to find the pH.
First, let's calculate the number of moles of HCl and NaOH:
Moles of HCl = volume (L) × molarity = (0.4 L) × (0.1 M) = 0.04 moles of HCl
Moles of NaOH = volume (L) × molarity = (0.6 L) × (0.1 M) = 0.06 moles of NaOH
Next, we can determine the concentration of the resulting solution:
Total moles of acid = Moles of HCl - Moles of NaOH = 0.04 - 0.06 = -0.02 moles
Since the moles of NaOH are greater than the moles of HCl, the NaOH is the limiting reagent, and the excess NaOH will remain in the solution.
Therefore, the concentration of the solution is 0.06 moles of NaOH / (0.4 L + 0.6 L) = 0.06 moles / 1 L = 0.06 M
Now, we can use the ionization constant of water (Kw = 1 × 10^-14) to find the concentration of H+ ions in the solution:
Kw = [H+] × [OH-] = (H+) × (OH-)
Since the solution is neutral, [H+] = [OH-], so we can divide Kw by the concentration of OH- to find [H+]:
[H+] = Kw / [OH-] = 1 × 10^-14 / (0.06 M) = 1.67 × 10^-13 M
Finally, we can use the formula for pH to calculate the pH of the solution:
pH = -log[H+] = -log(1.67 × 10^-13) = 12.78