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Question: What is the hydroxide concentration of a solution at a pH of \(10\) at \({25^o}C\) ? A. \({10^{ - ...

What is the hydroxide concentration of a solution at a pH of 1010 at 25oC{25^o}C ?
A. 10−14M{10^{ - 14}}M
B. 10−10M{10^{ - 10}}M
C. 10−7M{10^{ - 7}}M
D. 10−4M{10^{ - 4}}M

Explanation

Solution

The pH takes into consideration only the hydrogen ions present in a solution that is it will measure the acidity of a solution. It is required to find the hydroxide ions, that is we have to measure the basicity of the solution. For this we have to find the pOH.

Formula used: pH+pOH=14pH + pOH = 14
pH=−log⁡[H+]pH = - \log \left[ {{H^ + }} \right]
pOH=−log⁡[OH−]pOH = - \log \left[ {O{H^ - }} \right]
The pH is the measure of acidity
pOHpOH is the measure of basicity. [OH−]\left[ {O{H^ - }} \right] is also the concentration.
[H+]\left[ {{H^ + }} \right] is the concentration.

Complete step by step answer:
We know that the pH is 1010 . therefore, plugging it in the equation we get,
pH+pOH=14pH + pOH = 14
10+pOH=1410 + pOH = 14
Taking 1010 to the other side we get,
⇒pOH=14−10\Rightarrow pOH = 14 - 10
⇒pOH=4\Rightarrow pOH = 4
The pH can be defined as the measure of concentration of hydrogen ions present in a solution, that is it is the negative logarithm of the concentration of hydrogen ions. This can be represented as follows:
pOH=−log⁡[OH−]pOH = - \log \left[ {O{H^ - }} \right]
Substituting the value of pOH from the question in this equation,
4=−log⁡[OH−]4 = - \log \left[ {O{H^ - }} \right]
⇒−4=log⁡[OH−]\Rightarrow - 4 = \log \left[ {O{H^ - }} \right]
Taking antilog of the other side, we get,
⇒Antilog⁡(−4)=[OH−]\Rightarrow Anti\log \left( { - 4} \right) = \left[ {O{H^ - }} \right]
⇒10−4=[OH−]\Rightarrow {10^{ - 4}} = \left[ {O{H^ - }} \right]
Therefore, the concentration of hydroxide ions is 10−4M{10^{ - 4}}M .
Therefore, the solution is basic since the pH of the solution is more than 77 . Therefore, we can conclude that the hydroxide ions present in the solution is more than the hydrogen ions.

So, the correct answer is Option D.

Note: Tf the pH of the solution is more than 77 we can say that the solution is basic. The relation between the pH and pOH is pH+pOH=14pH + pOH = 14 . pOH is the measure of the concentration of hydroxide ions in a solution.