A buffer is a mixed solution of a weak acid or base, combined with its conjugate
ID: 793306 • Letter: A
Question
A buffer is a mixed solution of a weak acid or base, combined with its conjugate. Note that this can be understood essentially as a common-ion problem: The conjugate is a common ion added to an equilibrium system of a weak acid or base. The addition of the conjugate shifts the equilibrium of the system to relieve the stress of the added concentration of the common ion. In a solution consisting of a weak acid or base, the equilibrium shift also results in a pH shift of the system.
It is the presence of the common ion in the system that results in buffering behavior, because both added H+ or OH? ions can be neutralized.
Explanation / Answer
The acid disassociation equation is HA --> H + A, where H is H+ the proton and A is A- the anionic conjugate. In this case, A is citrate. (note I omit formal charges to make it look cleaner).
pKa tells us the equilibrium constant for this process:
Ka = [H] [A] / [HA]
The initial concentration of HA (citric acid) is 0.300 M. The initial concentration of H = 0 and A = 0.160 M (because we added a citrate salt).
To find pH, we need to know the final concentration of H, which we'll call x. The other concentrations also change: the final [HA] = 0.300 M - x, and final [A] = 0.160M + x.
Plug in the Ka (-log Ka = pKa) and the final concentrations to get this equation:
10^(-4.77) = [x] [0.160M + x] / [0.300M - x]
Since x is very small, we can estimate that 0.300M - x is approximately 0.300 M, so we'll simplify our calculation by removing that "- x" term. We get:
10^(-4.77) = [x] [0.160M + x] / [0.300M]
This is a quadratic equation, we can simplify to:
x^2 + 0.160 M x - (10^-4.77)(0.16) = 0
Solve this and you find that the final [H] = 0.0000169806343878 or 1.7 x 10^-5.
To find pH, take the -log [H], which should be around pH 5.77
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