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

The pHpHof 0.05M0.05Macetic acid (Ka=2×10−5)({K_a} = 2 \times {10^{ - 5}})is:
(A) 22
(B) 1111
(C) 10−3{10^{ - 3}}
(D) 33

Explanation

Solution

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

Complete Step by step answer: It is given in the question that,
The concentration of acetic acid is 0.05M0.05M
Ka=2×10−5{K_a} = 2 \times {10^{ - 5}}
We can use a formula,
[H+]=CKa[{H^ + }] = \sqrt {C{K_a}}
Where,
[H+][{H^ + }] is the concentration of H+{H^ + } ion
CC is concentration of acetic acid
Ka{K_a} is the solubility of acetic acid.
By substituting the given values in the above equation, we get
[H+]=0.05×2×10−5[{H^ + }] = \sqrt {0.05 \times 2 \times {{10}^{ - 5}}}
Simplifying it, we get
⇒[H+]=0.1×10−5\Rightarrow [{H^ + }] = \sqrt {0.1 \times {{10}^{ - 5}}}
⇒[H+]=10−6\Rightarrow [{H^ + }] = \sqrt {{{10}^{ - 6}}}
⇒[H+]=10−3\Rightarrow [{H^ + }] = {10^{ - 3}}
⇒[H+]=0.001\Rightarrow [{H^ + }] = 0.001
Now, we can apply the formula of pHpH as
pH=−log⁡[H+]pH = - \log [{H^ + }]
Where,
[H+]\left[ {{H^ + }} \right] is the concentration of H+{H^ + } ion.
By substituting the value of [H+]\left[ {{H^ + }} \right] in the above formula, we get
pH=−log⁡(0.001)pH = - \log (0.001)
⇒pH=−log⁡(10−3)\Rightarrow pH = - \log ({10^{ - 3}})
Now, since, log⁡mn=nlog⁡m\log {m^n} = n\log m and since, the base of log in the formula of pHpH is 1010. We can write,
⇒pH=3log⁡10(10)\Rightarrow pH = 3{\log _{10}}(10)
Since, log⁡aa=1{\log _a}a = 1, we can write
pH=3×1pH = 3 \times 1
Thus, the value of pHpH of 0.05M0.05M acetic acid is 33

Therefore, from the above explanation the correct option is (D) 3.3.

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 pHpH scale ranges from 0−140 - 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 0−70 - 7. And bases have pH values from 7−147 - 14. Extreme difference to pH values, above or below 7 is dangerous for human life.