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### Topic: A problem with pH  (Read 4434 times)

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#### Damiano0707

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##### A problem with pH
« on: March 16, 2018, 01:32:31 PM »
Hello everybody
I can't resolve this problem
You add 23.0mL of HCl 0.150M to a Na2SO3 solution. The final pH is 4.5. What are thr final moles of sulfite in solution?
A 0.00775
B 0.00694
C 0.00433
D 0.00345

I think a buffer solution is created but I can't say anything else.
Thanks to all

#### Borek

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##### Re: A problem with pH
« Reply #1 on: March 16, 2018, 02:22:19 PM »
Treating it like a buffer sounds like a good idea. Do you know the Henderson–Hasselbalch equation? Can you think how to apply it here?

(Actually plugging numbers into the dissociation constant definition is equivalently good approach; hardly surprising when you know where does the HH equation comes from).
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#### Damiano0707

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##### Re: A problem with pH
« Reply #2 on: March 16, 2018, 06:38:43 PM »
Yes I know it. The problem is that I don't know if the reaction is
Na2SO3+HCl--->NaCl+NaHSO3
Or
Na2SO3+2HCl--->2NaCl+H2SO3
In the first case I have SO32-/HSO32- and I could apply the equation. But there is still another problem. What are the moles of HCl that react?
In the second case I have SO32-/H2SO3 and I don't think I could apply the equation.

#### Borek

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##### Re: A problem with pH
« Reply #3 on: March 16, 2018, 07:13:14 PM »
What are pKa values of sulfuorus acid? What does the pH tell you - which pair of acid/conjugate base dominates the solution?
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#### Damiano0707

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##### Re: A problem with pH
« Reply #4 on: March 16, 2018, 07:36:01 PM »
What do you mean? Do you want to say in an acid base reaction weaker acids and bases are created? But HCl is a strong acid so either H2SO3 or NaHSOè can be created

#### Damiano0707

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##### Re: A problem with pH
« Reply #5 on: March 16, 2018, 07:38:06 PM »
Wait a second... The pKa1 is much lower tanh pKa2 so SO32-/HSO3- dominates.

#### Damiano0707

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##### Re: A problem with pH
« Reply #6 on: March 16, 2018, 07:43:52 PM »
I can't resolve the problem anyway

nb=ka2*na/[H+]=6.76*10^-6 It's not a result

I considered that the moles oh HCl are the same of NaHSO3.

#### XeLa.

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##### Re: A problem with pH
« Reply #7 on: March 16, 2018, 09:43:17 PM »
Okay, you need to make one important assumption when tackling this problem, which is you need to assume that HCl reacts with an excess of sodium sulfite solution.

If this is the case, what can we say about the equilbrium, and how will we set up HH equation?

EDIT: It looks like you made it above:

I considered that the moles oh HCl are the same of NaHSO3.

That's good, what happens next?

#### Damiano0707

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##### Re: A problem with pH
« Reply #8 on: March 16, 2018, 10:40:19 PM »
As I said jI used the equation

nb = ka*na/[H+] = 6.76*10^-6
nb: number of moles of SO32-
ka: costant of equilibrium HSO3-=SO32-+H+
na: number of moles of HCl
[H+]: concentration given from pH

But the result is not among those one given in the problem. Why isn't correct?

#### Borek

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##### Re: A problem with pH
« Reply #9 on: March 17, 2018, 05:23:22 AM »
What are both pKa values, and please write both equilibrium expressions for them.
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#### Borek

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##### Re: A problem with pH
« Reply #10 on: March 17, 2018, 05:24:37 AM »
Wait a second... The pKa1 is much lower tanh pKa2 so SO32-/HSO3- dominates.

No. Which one dominates depends on what is the pH. You would be right in the case of just dissociation, but here pH is forced on the system.
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#### Damiano0707

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##### Re: A problem with pH
« Reply #11 on: March 17, 2018, 03:09:13 PM »
The equilibriums are
HSO3-=SO32-+H+         pKa2=7.21
H2SO3=HSO3-+H+       pKa1=1.92

So I think the first equilibrium dominates because its pKa2 is nearer to pH but the calculus doesn't change and I don't get how to achieve the result

#### Borek

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##### Re: A problem with pH
« Reply #12 on: March 17, 2018, 03:18:30 PM »
$$K_a = \frac {[H^+][A^-]}{[HA]}$$

rearranged:

$$\frac {[A^-]}{[HA]} = \frac {K_a}{[H^+]}$$

You know everything on the right, try to use it to estimate relative amounts of H2SO3/HSO3-/SO32- - is there much H2SO3 present?
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#### Damiano0707

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##### Re: A problem with pH
« Reply #13 on: March 17, 2018, 03:59:44 PM »

[SO2-]/[HSO3-]=1.96*10^-3

But

[HSO3-]/[H2SO3]=ka1/[[H+]=379

[H2SO3] can be trascurated, but I don't get how I can continue. Do I have to consider that the moles of HCl are the same of HSO3-?

#### Borek

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##### Re: A problem with pH
« Reply #14 on: March 17, 2018, 05:26:28 PM »
Sigh, this question is a bit tricky, but actually much simpler than I thought (still, we got there thank's to the systematic approach).

Note, that from the numbers you have listed it is obvious that the solution contains mostly HSO3-. That means we are neither close to the pH=pKa1 nor pH=pKa2 (at which points there is a 50/50 ratio of the acid and conjugate base).

Do you know how to calculate pH of an amphiprotic salt solution?
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