A buffer solution of formic acid (Ka = 1.78 x 10-4) has 3500 times more formate ions than formic acid molecules. What is the pH of this buffer solution?
To find the pH of the buffer solution, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa of the acid and the concentration ratio of the acid and its conjugate base:
pH = pKa + log ([A-] / [HA])
where
pH is the pH of the solution,
pKa is the -log(Ka) of the acid
[A-] is the concentration of the conjugate base (formate ions)
and [HA] is the concentration of the acid (formic acid molecules).
First, we need to find the pKa from the given Ka value:
pKa = -log(Ka) = -log(1.78 x 10^-4) β 3.75
Next, we have the concentration ratio of formate ions to formic acid molecules as 3500. Since [A-] = 3500 * [HA], we can write this ratio as follows:
pH = pKa + log (3500 * [HA] / [HA])
Now, we can cancel out the [HA] from the numerator and denominator, so we have:
pH = 3.75 + log(3500)
Calculating the log of 3500 gives:
log(3500) β 3.54
Finally, add this value to the pKa:
pH = 3.75 + 3.54 β 7.29
So, the pH of this buffer solution is approximately 7.29.