# Compute pH before/after addition of NaOH?

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In the titration of 50.0 mL of 0.100 M #\beta# -hydroxybutyric acid, #HC_4H_7O_3# , with 0.100 M NaOH, compute pH before addition of NaOH, and after the addition of 25.00 mL and 50.00 mL of NaOH. #pK_a# for #HC_4H_7O_3# is 4.39.

In the titration of 50.0 mL of 0.100 M

Here's what I got.

!! EXTREMLEY LONG ANSWER !!

By definition, the acid dissociation constant will be

In your case, this will be equal to

Since

is very small compared to the initial concentration of the acid, you can use the approximation

This means that you have

You can thus say that

The pH of the initial solution

will be

The initial solution contains

The first solution of sodium hydroxide contains

So, after the first sample of sodium hydroxide is added to the initial solution, the moles of hydroxide anions will be completely consumed. You will be left with

The new volume of the solution will be

Now, notice that the resulting solution contains equal numbers of moles of weak acid and of conjugate base. This means that you're in the buffer region, i.e. the resulting solution contains a buffer.

This is known as the half-equivalence point. Consequently, you will have

and so

The new volume of the solution will be

The concentration of the conjugate base will be equal to

An aqueous solution at room temperature has

and so

By definition, you know that

which, in your case, is

Once again, use the approximation

to get

This means that the resulting solution has

Consequently, you will have

which means that the pH of the solution is

I'll leave the values rounded to three decimal palces, the number of sig figs you have for the concentrations of the two solutions.

Now, does the result make sense?

You are titrating a weak acid with a strong base, so at the equivalence point, the solution will only contain the conjugate base of the acid.

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Before: pH decreases After: pH increases

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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