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**Problem #1:** What is the pH of a 0.100 M solution of sodium acetate? K_{b} = 5.65 x 10¯^{10}. (I will use NaAc as shorthand)

**Solution:**

1) Here is the chemical reaction (net ionic) for the hydrolysis of NaAc:

Ac¯ + H_{2}O ⇌ HAc + OH¯

2) Here is the K_{b} expression for Ac¯:

[HAc] [OH¯] K _{b}=---------------- [Ac¯]

3) We can then substitute values into the K_{b} expression in the normal manner:

(x) (x) 5.65 x 10¯ ^{10}=---------------- 0.100 - x

4) Ignoring the minus x in the usual manner, we proceed to solve for the hydroxide ion concentration:

x = square root of [(5.65 x 10¯^{10}) (0.100)]x = 7.52 x 10¯

^{6}M = [OH¯]

We then calculate the pH. Since this is a base calculation, we need to do the pOH first:

pOH = - log 7.52 x 10¯^{6}= 5.124pH = 14 - 5.124 = 8.876

**Problem #2**: What is the pH of a 0.0500 M solution of KCN? K_{b} = 2.1 x 10¯^{5}.

**Solution:**

1) Here is the chemical reaction (net ionic) for the hydrolysis of KCN:

CN¯ + H_{2}O ⇌ HCN + OH¯

Here is the K_{b} expression for CN¯:

[HCN] [OH¯] K _{b}=---------------- [CN¯]

2) We can then substitute values into the K_{b} expression in the normal manner:

(x) (x) 2.1 x 10¯ ^{5}=---------------- 0.050 - x

3) Ignoring the minus x in the usual manner, we proceed to sove for the hydroxide ion concentration:

x = square root of [(2.1 x 10¯^{5}) (0.050)]x = 1.025 x 10¯

^{3}M = [OH¯]

4) We then calculate the pH. Since this is a base calculation, we need to do the pOH first:

pOH = - log 1.025 x 10¯^{3}= 2.99pH = 14 - 2.99 = 11.01

I certainly hope that you see that the two calculations are exactly alike, except for the numbers. In fact, when I wrote this tutorial in August 2002, I just copied and pasted the first example and changed the words and numbers. One final point to make: textbooks will often say "find the pH of the cyanide ion, CN¯." What they really mean is a complete chemical substance of which only the CN¯ is chemically relevant to the problem. Please keep in mind that the solution contains a cation (K^{+} in the example above, Na^{+} in the first example.

**Problem #3**: Find the pH of a 0.30 M solution of sodium benzoate, C_{6}H_{5}COONa. The K_{b} for C_{6}H_{5}COO¯ (benzoate ion) is 1.55 x 10¯^{10}.

Go to the answers for the above two problems.

Salts of weak bases are acids. Do them next.

Return to a listing of many types of acid base problems and their solutions