pH, Equilibrium and AP Chemistry

The AP Exam looms closer and closer. As I start in earnest working on lots of problems with my face-to-face students, I plan to do the same here. Today, we are looking at a problem from AP Chemistry 2005. pH problems in AP Chemistry, along with a bunch of other topics especially equilibrium and Acids/Bases are among the most feared. Both with and without good reason. Remember, once you have the structure for a problem, the complexity automatically disappears. Here’s a snippet of that problem.

$HC_{3}H_{5}O_{2}_{_{(aq)}}\rightleftharpoons C_{3}H_{5}O_{2}^{-}_{_{(aq)}}+H^{+}_{_{(aq)}}, K_{a} = 1.34\times 10^{-5}$
Propanoic Acid, $HC_{3}H_{5}O_{2}$ , ionizes in water according to the equation above.

a) Write the equilibrium constant for this reaction

b) Calculate the pH of a 0.265 M solution of propanoic acid.

Part (a) is pretty straightforward. If you know how an equilibrium constant is written, you know how to do this!
$K=\frac{[H^{+}][C_{3}H_{5}O_{2}^{-}]}{[HC_{3}H_{5}O_{2}]}$
For (b),

We need to set up an ICE Table (Quick review I = Initial, C= Change, E= Equilibrium)

Now, the equilibrium constant, $K_{a} =\frac{[H^{+}][HC_{3}H_{5}O_{2}^{-}]}{[HC_{3}H_{5}O_{2}]}$ becomes $=\frac{x\cdot x}{0.256-x}$
Plugging in values, $1.34\times 10^{-5}=\frac{x\cdot x}{0.256-x}$
Remember that in weak acids, x is very very small. How do we know that it is a weak acid? By the fact that it has an equilibrium constant. Strong acids are “single arrow” reactions, that means there is no equilibrium or equilibrium constant associated.
So what does this mean? It means that 0.265 – x is approximtely equal to 0.265!! That is incredibly cool, because we just converted a messy quadratic into a LINEAR function.
Let us now solve $1.34\times 10^{-5}=\frac{x\cdot x}{0.256}$ , or $x=1.88\times 10^{-3}$
Time to put on units. $x=1.88\times 10^{-3}$ M. CONTEXT: we are looking for H⁺.
And… we all know that pH = -log [H⁺]. Plugging in, doing the math,
$pH=-log (1.88\times 10^{-3}) = 2.725$

I know that many of you haven’t gotten to buffers yet, so I decided to truncate this problem with sections (a) and (b). This is the time to post questions, even if they are just about significant digits! Good luck, and ask away.

Solving an AP Chemistry problem – pH and Equilibrium

pH, Equilibrium and AP Chemistry

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