The Ka for acetic acid, HC2H3O2, is 1.8 × 10^-5 . What is the pH of a buffer prepared with 1.0 M HC2H3O2 and 1.0 M C2H3O2^-? HC2H3O2(aq) + H2O(l) ⇔ H3O^+(aq) + C2H3O2^-(aq)

Question

The [latex]K_{a}[/latex] for acetic acid, [latex]HC_{2}H_{3}O_{2}[/latex], is [latex]1.8 imes 10^{-5}[/latex] . What is the pH of a buffer prepared with 1.0 M [latex]HC_{2}H_{3}O_{2}[/latex] and 1.0 M [latex]C_{2}H_{3}O_{2}^{-}[/latex]?

[latex] HC_{2}H_{3}O_{2}(aq) + H_{2}O(l) \xrightleftharpoons[]{} H_{3}O^{+}(aq) + C_{2}H_{3}O_{2}^{-}(aq) [/latex]

Accepted Answer

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM	Given	Need	Connect
	1.0 M [latex]HC_{2}H_{3}O_{2}[/latex], 1.0 M [latex]C_{2}H_{3}O_{2}^{-}[/latex]	PH	[latex] K_{a}[/latex] expression
	Equation
	[latex]HC_{2}H_{3}O_{2}(aq) + H_{2}O(l) \xrightleftharpoons[]{} H_{3}O^{+}(aq) + C_{2}H_{3}O_{2}^{-}(aq)[/latex]

STEP 2 Write the[latex] K_{a}[/latex] expression and rearrange for [latex] H_{3}O^{+}[/latex].

[latex] K_{a} = \frac{\boxed{[H_{3}O^{+}]}[C_{2}H_{3}O_{2}^{-}]}{[HC_{2}H_{3}O_{2}]}[/latex]

[latex] \boxed{[H_{3}O^{+}]} = K_{a} imes \frac{[HC_{2}H_{3}O_{2}]}{[C_{2}H_{3}O_{2}^{-}]} [/latex]

STEP 3 Substitute [HA] and [latex][A^{-}][/latex] into the [latex]K_{a}[/latex] expression.

[latex] \boxed{[H_{3}O^{+}]} = 1.8 imes 10^{-5} imes \frac{[1.0]}{[1.0]}[/latex]

[latex] \boxed{[H_{3}O^{+}]} = 1.8 imes 10^{-5} M[/latex]

STEP 4 Use [latex] [H_{3}O^{+}] [/latex] to calculate pH. Placing the [latex] [H_{3}O^{+}] [/latex] into the pH equation gives the pH of the buffer.

[latex] PH = - \log \boxed{[1.8 imes 10^{-5}]} = 4.74 [/latex]

Question 11.13: The Ka for acetic acid, HC2H3O2, is 1.8 × 10^-5 . What is th...

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