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Offline T

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Acid base concentration question
« on: April 08, 2016, 02:50:04 AM »
An aqueous solution of ammonia has of pH = x, and a solution of hydrochloric acid has pH = y; it is also known that x + y = 14, and x > 11. If equal volumes of these two solutions are mixed together, what would be the concentration of the various ions in the resulting solution in descending order?

A [NH4+] > [Cl–] > [OH–] > [H+]

B [Cl–] > [NH4+] > [H+] > [OH–]

C [NH4+] > [Cl–] > [H+] > [OH–]

D [Cl–] > [NH4+] > [OH–] > [H+]

E [Cl–] = [NH4+] = [OH–] = [H+]

Since x+y = 14 then there are equal amounts of OH- and H+ to start with. To prove this:

x = 14 - y

[H+] of ammonia solution is 10-y
[OH-] of ammonia solution is 10-14/10-y = 10y-14

[H+] of hydrochloric acid solution is 10-x=10y-14

Hence, [OH-] in ammonia = [H+] in hydrochloric acid solution then that means there is a lot more ammonia then hydrochloric acid since ammonia is a weak base. Therefore there the answer is either A or C. However, I cannot decide between those two, can someone give me hints?

Thanks


Offline thetada

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Re: Acid base concentration question
« Reply #1 on: April 08, 2016, 05:24:31 AM »
An aqueous solution of ammonia has of pH = x, and a solution of hydrochloric acid has pH = y; it is also known that x + y = 14, and x > 11. If equal volumes of these two solutions are mixed together, what would be the concentration of the various ions in the resulting solution in descending order?

Since x+y = 14 then there are equal amounts of OH- and H+ to start with. To prove this:

x = 14 - y

[H+] of ammonia solution is 10-y
[OH-] of ammonia solution is 10-14/10-y = 10y-14

[H+] of hydrochloric acid solution is 10-x=10y-14

Is [H+] of ammonia solution not 10-x?

Offline T

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Re: Acid base concentration question
« Reply #2 on: April 08, 2016, 07:25:46 PM »
Yea, sorry. I mixed up the x and y. Thanks

Offline AWK

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Re: Acid base concentration question
« Reply #3 on: April 08, 2016, 08:25:30 PM »
Hint
strong acid, weak base
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Offline Burner

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Re: Acid base concentration question
« Reply #4 on: April 08, 2016, 09:31:54 PM »
[OH-] of ammonia solution is 10-14/10-y = 10y-14

[H+] of hydrochloric acid solution is 10-x=10y-14

I am sorry, but I don't understand these steps. Can someone explain this to me? Thanks.

pH of hydrochloric acid is y. Shouldn't the [H+] of hydrochloric acid solution be 10-y?
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Offline Borek

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Re: Acid base concentration question
« Reply #5 on: April 09, 2016, 03:48:56 AM »
[tex]pH + pOH = 14[/tex]

[tex][H^+] = 10^{-pH}[/tex]

[tex][OH^-] = 10^{-pOH} = 10^{-(14-pH)} = 10^{pH-14}[/tex]

Makes sense now?
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Offline T

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Re: Acid base concentration question
« Reply #6 on: April 09, 2016, 04:26:29 AM »
Hint
strong acid, weak base

Strong acids dissociate more than weak bases. I am finding it really hard to make the link. I think I am missing something very obvious. Going through the steps again:

1) Solution of ammonia has same amount of OH- as H+ in solution of HCl

2) When mixed, before any reacting occurs there is the same amount of OH-, H+, Cl- (since HCl is a strong acid), and ammonium. And there is a lot more ammonia since ammonia is a weak base.

3) The OH- and H+ react to produce water. Since the OH- has been removed, equilibrium makes the ammonia turn into ammonium. But since there is no more HCl (since it dissociated before the reacting) the OH- does not react and stays as OH-. So in the end:
There is a small amount of [H+] (left from the water production reaction)
More [Cl-]
And same amount of [NH4+] and [OH-] from the equilibrium shift in ammonia reaction

What am I missing? Thanks!

Offline thetada

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Re: Acid base concentration question
« Reply #7 on: April 09, 2016, 04:43:33 AM »
I feel like the clue that the original pH of acid was <3 could be useful now. If you estimate the new pH of the mixed solution, you could then estimate ball park figures for the NH4+ and OH-

Offline Burner

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Re: Acid base concentration question
« Reply #8 on: April 09, 2016, 05:33:37 AM »
[tex]pH + pOH = 14[/tex]

[tex][H^+] = 10^{-pH}[/tex]

[tex][OH^-] = 10^{-pOH} = 10^{-(14-pH)} = 10^{pH-14}[/tex]

Makes sense now?

I see, thanks.
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Offline AWK

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Re: Acid base concentration question
« Reply #9 on: April 09, 2016, 09:37:54 AM »
Quote
Strong acids dissociate more than weak bases
strong acid dissociate practically completely
AWK

Offline T

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Re: Acid base concentration question
« Reply #10 on: April 11, 2016, 04:40:37 AM »
I feel like the clue that the original pH of acid was <3 could be useful now. If you estimate the new pH of the mixed solution, you could then estimate ball park figures for the NH4+ and OH-

Is it possible to calculate the pH of the mixed solution without the Ka and Kb? Because you need to account for the equilibrium shift in the NH3+H2::equil:: NH4++OH- reaction.

The only way I can solve this problem is through elimination. I know NH4+ will be the most concentrated so it leaves you with A and C. And I know OH- will be more than H+ because of the equilibrium shift so the answer is A. However, I don't know if [Cl-] > [OH-] or [OH-] > [Cl-], is it possible to do this without the Ka or Kb?

Thanks

Offline thetada

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Re: Acid base concentration question
« Reply #11 on: April 11, 2016, 06:24:22 AM »
Okay, scratch the last suggestion. Try sketching bar graphs illustrating answers to the following 3 qus:

What was the relationship between the concentrations of the four species directly before mixing?
How did that relationship change directly after mixing?
How did it change having established equilibrium?

Offline AWK

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Re: Acid base concentration question
« Reply #12 on: April 12, 2016, 09:06:22 PM »
Quote
What am I missing? Thanks!
And this reasoning is sufficient for choosing answer.
AWK

Offline T

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Re: Acid base concentration question
« Reply #13 on: April 13, 2016, 07:46:24 AM »
Ok, thanks everyone for the *delete me*

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