Question

The pH of a mixture of 0.01M $HCl$ and 0.1 M $C{H_3}COOH$ is approximately
a.) 1
b.) 2
c.) 4
d.) 7

Answer 1

Hint: Try to recall that $HCl$ is a strong acid and it dissociates completely when dissolved in water whereas $C{H_3}COOH$ is a weak acid and it dissociates only to a small extent in aqueous solution. Now by using this you can easily find the correct option from the given options.

Complete answer:
It is already known to you that $HCl$ is a strong acid and when dissolved in water dissociates completely thus producing a large number of ${H^ + }$ ions whereas $C{H_3}COOH$ is a weak acid and it dissociate only to a small extent in the aqueous solution giving small amount of ${H^ + }$ ions.
Acetic acid dissociates as: $C{H_3}COOH + {H_2}O \rightleftharpoons {H^ + }(aq) + C{H_3}CO{O^ - }(aq)$
Now, when a strong acid ($HCl$) is mixed with a weak acid, then the high ${H^ + }$ from the strong acid ($HCl$) will force the equilibrium for the dissociation of weak acid ($C{H_3}COOH$) to move strongly to the left.
That is there will be very little ${H^ + }$ in solution coming from the $C{H_3}COOH$ . The ${H^ + }$ in solution will come solely from $HCl$.
Calculation:
$HCl$ completely ionizes as: $HCl + {H_2}O \to {H^ + }(aq) + C{l^ - }(aq)$
$\therefore \left[ {{H^ + }} \right] = {10^{ - 2}}M$ (Given)
So, pH of $HCl$= ${\text{ - lo}}{{\text{g}}_{10}}{\text{ }}\left[ {{H^ + }} \right]$
$\begin{gathered} {\text{ = lo}}{{\text{g}}_{10}}{\text{ }}{\left( {10} \right)^{ - 2}} = - ( - 2){\text{lo}}{{\text{g}}_{10}}\left( {10} \right) = 2 \end{gathered}$

Therefore, from above we can say that option B is the correct option for the given question.

Note: It should be remembered to you that a strong acid has a weak conjugate base and vice versa. For example: ($C{H_3}COOH$) has a strong conjugate base ($C{H_3}CO{O^ - }$).
Also, you should remember that for the same molar concentration of two weak acids or bases, greater the degree of ionization, greater is the strength.