Question

Imagine that you are in chemistry lab and need to make 1.00 L of a solution with a pH of 2.60.

You have in front of you

100 mL of 7.00×10−2 M HCl,

100 mL of 5.00×10−2 M NaOH,

and plenty of distilled water.

You start to add HCl to a beaker of water when someone asks you a question. When you return to your dilution, you accidentally grab the wrong cylinder and add some NaOH. Once you realize your error, you assess the situation. You have 82.0 mL of HCl and 88.0 mL of NaOH left in their original containers.

Assuming the final solution will be diluted to 1.00 L , how much more HCl should you add to achieve the desired pH?

Answer 1

For a pH of 2.6, the concentration of protons in the medium should be 10^-pH as pH = -log[H⁺]. This gives [H⁺] = 2.5118x10^-3M.

Next, it can found that the quantity of HCl added was 18mL and that of NaOH was 12mL. Molarity is defined as the no.of moles of a substance in 1L of solution. So, 18mL of 0.07M HCl will contain (0.07mol/L/1000mL)x18mL = 0.00126mol and similarly, 12mL of 0.05M NaOH will contain 0.0006mol. Since there is an excess of acid in the medium, the neutralization by the base proceeds to eliminate only 0.0006mol of acid as the base is the limiting reagent here. Since the acid and base are strong, no salt hydrolysis occurs and thus, the concentration of protons will be the concentration of acid, which is 0.00126 - 0.0006 = 6.6x10^-4mol.

Now, it can be found that the quantity of HCl required for a pH of 2.6 is now the difference between the concentration of protons required to that already present. This arrives as 2.5118x10^-3mol - 6.6x10^-4mol = 1.8518x10^-3mol since the solution is to be made up to 1L making the conversion of molarity to moles direct here.

Backtracking the calculations for finding the no.of moles of HCl in 18mL, we find that there exists 7x10^-5mol of HCl in 1mL of the given solution. So, to obtain 1.8518x10^-3mol, we require 1.8518x10^-3mol/7x10^-5mol/mL = 26.4542mL.

Summarizing, if 26.4542mL of HCl is added to the solution already present and then diluted to 1L, there will be the required 2.5118x10^-3mol/L or 2.5118x10^-3M protons in the medium, giving a pH of 2.6 as required.