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Valeric acid, HC5H9O2 (Ka = 1.5 ✕ 10−5), is used in the manufacture of magnesium valerate, a nerve-calming agent. What is the hydronium ion concentration (in M) in a 0.737 M solution of HC5H9O2? (Assume Kw = 1.01 ✕ 10−14.)

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Answer:

[tex][H^+]=0.00332M[/tex]

Explanation:

Hello,

In this case, considering the dissociation of valeric acid as:

[tex]HC_5H_9O_2 \rightleftharpoons C_5H_9O_2 ^-+H^+[/tex]

Its corresponding law of mass action is:

[tex]Ka=\frac{[H^+][C_5H_9O_2^-]}{[HC_5H_9O_2]}[/tex]

Now, by means of the change [tex]x[/tex] due to dissociation, it becomes:

[tex]Ka=\frac{(x)(x)}{0.737-x}=1.5x10^{-5}[/tex]

Solving for [tex]x[/tex] we obtain:

[tex]x=0.00332M[/tex]

Thus, since the concentration of hydronium equals [tex]x[/tex], the answer is:

[tex][H^+]=x=0.00332M[/tex]

Best regards.