What is the pH of a Weak Acid/Base Mixture?

In summary, the textbook suggests that when you mix acetic acid and NH3, the pH will be neutralized because both Ka values are the same. However, here we are very far from this kind of situation, and the equilibrium is shifted to the products side.
  • #1
cncbmb
16
0

Homework Statement



We have two solutions: One solution that has [tex]0.300[/tex] L of [tex]0.100[/tex] M acetic acid, and the other with [tex]0.100[/tex] L of [tex]0.200[/tex] M [tex]CN^-[/tex].

We mix the two solutions. At equilibrium, what is the pH of the resulting solution?

Homework Equations


For acetic acid, [tex]K_a=1.8*10^{-5}[/tex]
For [tex]CN^-[/tex], [tex]K_b=2.5*10^{-5}[/tex]

The Attempt at a Solution



[tex]CH_3COOH + CN^- <=> CH_3COO- + HCN[/tex]...
The K values aren't useful here since there's no water in the reaction.
We can't assume the reaction goes to completion, in either direction since the acids and bases are weak. Not sure if solution is basic even though the [tex]K_b[/tex] for cyanide anion is greater than the [tex]K_a[/tex] of acetic acid since we have more acetic acid than base.

...
My textbook seems to dodge this issue in its explanation of "the reaction of a weak acid with a weak base." The textbook considers an equilmolar mixture of acetic acid and ammonia and says that the solution in that case would be neutral because the Ka of acetic acid the Kb of NH3 are the same.

Whoa why is the tex so thin?..
 
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  • #2
cncbmb said:
The K values aren't useful here since there's no water in the reaction.

Plenty of water around.

We can't assume the reaction goes to completion, in either direction since the acids and bases are weak.

There is an excess of one reagent... Try to assume that reaction goes to completion (find limiting reagent).
 
  • #3
Why can we assume that the reaction goes to completion?
 
  • #4
In general - we can't. But you have huge excess of one of the reagents, that shifts equilibrium to the products side.

Note that when you mix acetic acid with stoichiometric amount of ammonia, neutralization goes ALMOST to completion with both acid and base neutralized in over 99%. We are just so close to the neutral solution, that tiny equilibrium shift can give a large effect in terms of pH change. However, here we are very far from this kind of situation.

Some reading:
general case of pH calculation
pH of salts
 

What is the pH of a Weak Acid/Base Mixture?

The pH of a weak acid/base mixture depends on several factors, including the concentrations of the acid and base, their equilibrium constants, and their dissociation constants.

How do you calculate the pH of a Weak Acid/Base Mixture?

The pH of a weak acid/base mixture can be calculated using the Henderson-Hasselbalch equation, which takes into account the concentrations of the acid and base, as well as their dissociation constants.

What is the difference between a weak acid/base and a strong acid/base?

A weak acid/base is one that only partially dissociates in water, while a strong acid/base fully dissociates. This means that a weak acid/base will have a lower concentration of ions in solution, resulting in a higher pH compared to a strong acid/base with the same concentration.

Can a weak acid/base mixture have a pH greater than 7?

Yes, a weak acid/base mixture can have a pH greater than 7 if the concentration of the base is higher than the concentration of the acid. This will result in a basic solution with a pH greater than 7.

How does temperature affect the pH of a Weak Acid/Base Mixture?

The pH of a weak acid/base mixture can be affected by temperature, as changes in temperature can alter the equilibrium between the acid and base. In general, an increase in temperature will result in a decrease in pH for an acidic solution and an increase in pH for a basic solution.

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