# How would you use the Henderson-Hasselbalch equation to calculate the pH of a buffer solution that is 0.27 M in formic acid (HCO_2H) and 0.50 M in sodium formate (HCO_2Na)?

Aug 11, 2016

That buffer system has a pH of 4.01

#### Explanation:

Before I introduce Henderson-Hasselbalch's equation, we should identify the acid and base. Formate $\left(H C {O}_{2}^{-}\right)$ is the conjugate base of the acid, formic acid, $\left(H C {O}_{2} H\right)$. A conjugate base has one less proton $\left({H}^{+}\right)$than the acid you started with.

Now, we can use this equation:

For this type of question we need a pKa, which is not given in your question. Therefore, I Googled the Ka and it is
(1.8xx10^(-4))

To obtain the pKa from the Ka value, all we have to do is take the
negative logarithm (-log) of the Ka:

$p K a = - \log \left(1.8 \times {10}^{- 4}\right)$ = 3.74

Next, we can obtain the concentration of base and concentration of acid from the question.

[$H C {O}_{2}^{-}$] = .50 M [$H C {O}_{2} H$] =.27 M

We're not really concerned with the sodium cation that attached to the formate ion because it's a spectator ion and it has no effect on the buffer system.

Now, we have all of the information to determine the pH. Let's plug our values into the equation:

$p H = 3.74 + \log \left(\frac{0.50}{0.27}\right)$

$p H = 4.01$