Question

${\text{p}}{{\text{K}}_{\text{a}}}$ for acetic acid is 4.74. What should be the ratio of concentration of acetic acid and acetate ions to have a solution with pH 5.74?
a) 1:10
b) 10:1
c) 1:1
d) 2:1

Answer 1

Hint: We can use the Henderson-Hasselbalch equation for solving this problem. The Henderson-Hasselbalch equation is $pH = p{K_a} + {\log _{10}}\left( {\dfrac{{\left[ {Base} \right]}}{{\left[ {Acid} \right]}}} \right)$ can be used to estimate the pH of a buffer solution.

Complete step by step answer:
The dissociation reaction of acetic acid and acetate ions is:
$C{H_3}COOH \to C{H_3}CO{O^ - } + {H^ + }$

To calculate the concentration of acetic acid and acetate ion, we use the Henderson-Hasselbalch equation:
$pH = p{K_a} + {\log _{10}}\left( {\dfrac{{\left[ {Base} \right]}}{{\left[ {Acid} \right]}}} \right)$

Now we can put all the given values in the equation, we get:
$5.74 = 4.74 + \log \dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}$

$\left( {\dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}}} \right) = anti\log \left( 1 \right) = {10^1}$

$\left( {\dfrac{{\left[ {Acid} \right]}}{{\left[ {salt} \right]}}} \right) = \dfrac{1}{{10}}$
So, the ratio of concentration of acetic acid and acetate ions is found to be 1:10.
Therefore, the correct option is (a).

Additional Information:
In 1908, Lawrence Joseph Henderson derived an equation to calculate the pH of a buffer solution. In 1917, Karl Albert Hasselbalch re-expressed that formula in logarithmic terms, resulting in the Henderson-Hasselbalch equation.
A simple buffer solution consists of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate. The Henderson-Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant ${{\text{K}}_{\text{a}}}$, and the concentration of the species in solution.

Note: Please note that the Henderson-Hasselbalch equation is only applicable for buffer solutions. To derive this equation, a number of simplifying assumptions have to be made. The mixture has the ability to resist changes in pH when a small amount of acid or base is added, which is the defining property of a buffer solution.