# Find ph based on given volume and molarity of HCl and NaOH

Hello!
I am trying to crack the following problem:

What is the pH of a solution formed by mixing

125.0 mL of 0.0250 M HCl with 75.0 mL of 0.0500 M

NaOH?

Here is how I am approaching the issue:
both HCl and NaOH are strong acid and base respectively. Hence the concentration of [H3O+] = 0.003125M (this is the amount of moles of HCl in 0.125 L) and [OH-] = 0.00375M
Kw = [H30] x [OH] = 10^(-14)

the difference between [H30] and [OH] = 0.00375 - 0.003125 = 0.000625, which tells me that there are more [OH] in solution; hence it is a basic solution. -log(0.000625) = 3.204
But if I subtract 3.204 from 14 I will get 11.8, but the answer is 11.495

I can get 11.495 if 10(-14) / 0.003125 and take a log. But it can't be right because that would give me pOh not Ph.

I will be grateful for your help!

SteamKing
Staff Emeritus
Homework Helper
Hello!
I am trying to crack the following problem:

What is the pH of a solution formed by mixing

125.0 mL of 0.0250 M HCl with 75.0 mL of 0.0500 M

NaOH?

Here is how I am approaching the issue:
both HCl and NaOH are strong acid and base respectively. Hence the concentration of [H3O+] = 0.003125M (this is the amount of moles of HCl in 0.125 L) and [OH-] = 0.00375M
Kw = [H30] x [OH] = 10^(-14)

the difference between [H30] and [OH] = 0.00375 - 0.003125 = 0.000625, which tells me that there are more [OH] in solution; hence it is a basic solution. -log(0.000625) = 3.204
But if I subtract 3.204 from 14 I will get 11.8, but the answer is 11.495

I can get 11.495 if 10(-14) / 0.003125 and take a log. But it can't be right because that would give me pOh not Ph.

I will be grateful for your help!
Have you considered what happens when some of the HCl is neutralized by the NaOH?

Have you considered what happens when some of the HCl is neutralized by the NaOH?
I am not sure I understand your question correctly. You say "some" of HCl. HCl is a strong acid and NaOH is a strong base, for 1 mole of HCl we need 1 mole of NaOH.

Borek
Mentor
Hence the concentration of [H3O+] = 0.003125M

Please explain where this number comes from.

SteamKing
Staff Emeritus
Homework Helper
I am not sure I understand your question correctly. You say "some" of HCl. HCl is a strong acid and NaOH is a strong base, for 1 mole of HCl we need 1 mole of NaOH.
Yes, but chemicals are stupid. They will react even if precisely correct stoichiometric ratios are not present. The reaction stops when one of the reagents has completely reacted with the other, leaving an excess amount of the second reagent left over.

Please explain where this number comes from.

We have 0.0250 moles of HCl in 1 liter and there are 0.125 liters; hence we have 0.003125 moles of HCl. HCl is a strong acid, hence the concentration of [H3O] is also 0.003125[/QUOTE]

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Yes, but chemicals are stupid. They will react even if precisely correct stoichiometric ratios are not present. The reaction stops when one of the reagents has completely reacted with the other, leaving an excess amount of the second reagent left over.
Ah! Indeed, HCl is a limiting reagent here. I have to think further. Thank you! I will be back if I can't solve it.

Borek
Mentor
0.003125 moles of HCl. HCl is a strong acid, hence the concentration of [H3O] is also 0.003125

No. While your calculation of number of moles is correct, number of moles doesn't equal concentration (unless the volume is exactly 1 L).

No. While your calculation of number of moles is correct, number of moles doesn't equal concentration (unless the volume is exactly 1 L).
maybe the word concentration is wrong, but I mean that there are 0.003125 moles of [H3O]

Borek
Mentor
maybe the word concentration is wrong, but I mean that there are 0.003125 moles of [H3O]

pH is a function of concentration, not number of moles.

I am at my wit's end: if I have 0.003125 moles of [h3o], and based on the fact that HCl is the limiting reagent, I should have used, as I would usually do, -log function to find Ph. But here that would generate incorrect answer. Please, help to understand

pH is a function of concentration, not number of moles.
If HCl is a limiting reagent (because according to stoichiometry there are 1 mole of HCl per 1 mole of NaOH), then the reaction requires 0.003125 moles of HCl and takes only 0.003125 moles of NaOH. Is this correct?

Borek
Mentor
If HCl is a limiting reagent (because according to stoichiometry there are 1 mole of HCl per 1 mole of NaOH), then the reaction requires 0.003125 moles of HCl and takes only 0.003125 moles of NaOH. Is this correct?

Correct so far.

Correct so far.
Thank you.
HCl is a strong acid, and hence will dissociate completely producing 0.003125 moles of [H3O+]. To compute pH I need to find the molarity of H3O. But it's molarity will be the same as HCl? I am truly stuck with this task.

Borek
Mentor
What is the definition of the concentration?

What is the definition of the concentration?
Concentration (like density) = the amount of any given substance in a given volume.

Borek
Mentor
And how do you calculate the concentration? Say, you have 1 mole of substance in 5 liters of the solution, what is the concentration?

And how do you calculate the concentration? Say, you have 1 mole of substance in 5 liters of the solution, what is the concentration?
It will be 1/5. To find the concentration I divide moles by volume.

Borek
Mentor
To find the concentration I divide moles by volume.

So why don't you do the same to solve the initial problem?

So why don't you do the same to solve the initial problem?
Sorry, but I don't see it.
If I have 0.003125 moles of HCL, then I need also 0.003125 moles of NaOH. The molarity of NaOH is 0.0500, so I need 0.0625 liters of NaOH for this reaction.
0.125 l of HCl + 0.0625 L of NaOH gives total 0.1875 liters of solution, in which there are 0.003125 moles of HCl. Therefore, in 1 liter of such solution I should have
0.017 moles of HCl. Is it correct?
If yes, it will be the concentration of [H3O+] in the solution.
Taking -log of this gives me an incorrect answer.

Borek
Mentor
The molarity of NaOH is 0.0500, so I need 0.0625 liters of NaOH for this reaction.

For neutralization - yes. But that's not what the question is about. You are told what was the volume of the NaOH solution.

Previously you were quite close to getting the correct answer - you have correctly calculated amount of excess NaOH, you just forgot to take the final volume into account. Now idea what and why you did this time, but your calculations - while in some respects correct - have nothing to do with the question asked.

For neutralization - yes. But that's not what the question is about. You are told what was the volume of the NaOH solution.

Previously you were quite close to getting the correct answer - you have correctly calculated amount of excess NaOH, you just forgot to take the final volume into account. Now idea what and why you did this time, but your calculations - while in some respects correct - have nothing to do with the question asked.
I understand that it is a very easy exercise, and I have no idea why I am stuck (especially after solving around a hundred exercises after this chapter in texbook). I hope to solve it.
Please, allow me to start again, but from the place where I have found the moles of H3O and OH.
Given:
HCl + NaOH -> H2O + NaCl
Both HCl and NaOH dissociate completely and produce
0.003125 of H3O and 0.003125 of OH plus the excess of 0.000625 moles of OH.

To find pH of the solution I need to find the concentration of H3O in 1 liter of solution, is that correct?
If there is 0.125 liters of HCl of 0.0250M and 0.075 liters of NaOH of 0.050M, then there are 0.00375 moles of OH in 0.075 l of NaOH, but the reaction requires 0.003125 moles of NaOH to react with the same amount of mole of HCl. Therefore I need only 0.0625 liters of NaOH. Therefore, the volume of the final solution if 0.1875, if to dismiss the excess moles of NaOH, which, if I understand correctly, will not take part in the reaction.
Given this volume I have to find the pH I first need to find the concentration of H3O in 1 liter of such solution. Is this correct?

Borek
Mentor
Therefore, the volume of the final solution if 0.1875

No, it is 0.125+0.075 L.