Question

The $pH$of $0.05M$acetic acid $({K_a} = 2 \times {10^{ - 5}})$is:
(A) \[2\]
(B) \[11\]
(C) ${10^{ - 3}}$
(D) $3$

Answer 1

Hint: $pH$is a scale used to specify the acidity or basically of an aqueous solution. Find out the concentration of ${H^ + }$ ion in acetic acid using its molarity. Then use the formula of $pH$ to solve the question.

Complete Step by step answer:It is given in the question that,
The concentration of acetic acid is $0.05M$
${K_a} = 2 \times {10^{ - 5}}$
We can use a formula,
$[{H^ + }] = \sqrt {C{K_a}} $
Where,
$[{H^ + }]$ is the concentration of ${H^ + }$ ion
$C$ is concentration of acetic acid
${K_a}$ is the solubility of acetic acid.
By substituting the given values in the above equation, we get
$[{H^ + }] = \sqrt {0.05 \times 2 \times {{10}^{ - 5}}} $
Simplifying it, we get
$ \Rightarrow [{H^ + }] = \sqrt {0.1 \times {{10}^{ - 5}}} $
$ \Rightarrow [{H^ + }] = \sqrt {{{10}^{ - 6}}} $
$ \Rightarrow [{H^ + }] = {10^{ - 3}}$
$ \Rightarrow [{H^ + }] = 0.001$
Now, we can apply the formula of $pH$ as
$pH = - \log [{H^ + }]$
Where,
$\left[ {{H^ + }} \right]$ is the concentration of ${H^ + }$ ion.
By substituting the value of $\left[ {{H^ + }} \right]$ in the above formula, we get
$pH = - \log (0.001)$
$ \Rightarrow pH = - \log ({10^{ - 3}})$
Now, since, $\log {m^n} = n\log m$ and since, the base of log in the formula of $pH$ is $10$. We can write,
$ \Rightarrow pH = 3{\log _{10}}(10)$
Since, ${\log _a}a = 1$, we can write
$pH = 3 \times 1$
Thus, the value of $pH$ of $0.05M$ acetic acid is $3$

Therefore, from the above explanation the correct option is (D) $3.$

Note: This is a simple question of substituting the given values in the formula. You need to know the formula of finding pH to solve this question. Properties of logarithm are also important for this question. You can use the log table to find the values. But knowing the properties of logarithms, saves time.
The $pH$ scale ranges from $0 - 14$. Nearly all compounds fall in this pH range. But it is possible that some compounds might go below 0 or above 14. Acids have pH values from $0 - 7$. And bases have pH values from $7 - 14$. Extreme difference to pH values, above or below 7 is dangerous for human life.