Question

pKa for acetic acid is 4.74. What should be the ratio of concentration of acetic acid and acetate ions to have a solution of pH 5.74?
1 : 10
10 : 1
1 : 1
2 : 1

Answer 1

This question is solved by using the equation of pH for buffer solutions and i.e. known as the Henderson-Hasselbalch equation. This equation is used for the calculation of pH of the buffer solutions. Here we can use the formula of pH for the acidic buffer.

Formula used: $pH\; = \;p{K_a}\; + \;\log \dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}}$ (Henderson-Hasselbalch equation)

Complete Answer:
Here, we can start with the Henderson-Hasselbalch equation. As we have given salt is acetate and acid is acetic acid. According to this we can use the equation.
$pH\; = \;p{K_a}\; + \;\log \dfrac{{\left[ {salt} \right]}}{{\left[ {acid} \right]}}$
Now, we have the values of pH = 5.74 and pKa = 4.74. Then by using this values we can find out the ratio of the concentration of the acetic acid and acetate ion i.e. $\dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}$.
Therefore, putting the above values in our equation we will get;
$5.74\; = \;4.74\; + \;\log \dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}$
$\log \dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}\; = \;5.74\; - \;4.74\; = \;1$
Now, taking the antilog both side of equation we get;
$\dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}\; = \;Anti\log \;1$
We know that Anti log (1) = 10, so the above equation will be equal to,
$\dfrac{{\left[ {C{H_3}CO{O^ - }} \right]}}{{\left[ {C{H_3}COOH} \right]}}\; = 10$

As in the above equation we get the ratio of concentration of the acetate ions to the acetic acid but in question it is asked for the ratio of concentration of the acetic acid to the acetate ions. Hence, we can take the reciprocal of the above equation.
$\dfrac{{\left[ {C{H_3}COOH} \right]}}{{\left[ {C{H_3}CO{O^ - }} \right]}}\; = \;\dfrac{1}{{10}}$
Therefore, we get the ratio of the concentration of the acetic acid to the acetate ion is 1:10.

Hence the correct answer is option (A) 1:10.

Additional information:
Buffer: The buffer solution is the solution which maintains its pH even at the addition of the acid or base. The buffers are of two types 1) Acidic buffer and 2) Basic buffer.
Formula for basic buffer: $pOH\; = \;p{K_b}\; + \;\dfrac{{\left[ {Salt} \right]}}{{\left[ {Base} \right]}}$.

Note: In this question we get the concentration ratio of acid to salt. In this we used the Henderson-Hasselbalch equation of acidic buffer because we have given the acid buffer with its pH and pKa values. When solving this type of question take one thing into mind that which type of buffer is provided to us acid or basic. Because according to that we have to use the formula.