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Question: The \(pH\) of \({10^{ - 6}}M{\text{ }}HCl,{\text{ }}{10^{ - 7}}M{\text{ }}HCl\,{\text{and }}{10^{ - ...

The pHpH of 10−6M HCl, 10−7M HCl and 10−8M HCl{10^{ - 6}}M{\text{ }}HCl,{\text{ }}{10^{ - 7}}M{\text{ }}HCl\,{\text{and }}{10^{ - 8}}M{\text{ }}HCl respectively is:
(A) 6,7,86,7,8
(B) 6,6.79,6.986,6.79,6.98
(C) 6,6.79,7.026,6.79,7.02
(D) 6,6.98,86,6.98,8

Explanation

Solution

pHpH is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions are measured to have lower pHpH values than basic or alkaline solutions. The pHpH scale is logarithmic and inversely indicates the concentration of hydrogen ions in solution.

Complete step by step answer: We know that, pH=−log⁡[H+]pH = - \log \left[ {{H^ + }} \right]
So, when [H+]=10−6\left[ {{H^ + }} \right] = {10^{ - 6}} (as HClHCl has 10−6M{10^{ - 6}}M)
We can neglect the concentration of water.
pH=−log⁡[H+]=−log⁡(10−6)=6pH = - \log \left[ {{H^ + }} \right] = - \log \left( {{{10}^{ - 6}}} \right) = 6
Now for, M=10−7M HClM = {10^{ - 7}}M{\text{ }}HCl
We can say that [H+]=10−7\left[ {{H^ + }} \right] = {10^{ - 7}}
Here, we have to consider concentration of water which is 10−7M{10^{ - 7}}M
So, total concentration of H+=2×10−7M{H^ + } = 2 \times {10^{ - 7}}M
Hence, pH=−log⁡[H+]=−log⁡(2×10−7)pH = - \log \left[ {{H^ + }} \right] = - \log \left( {2 \times {{10}^{ - 7}}} \right)
=−log⁡2+7=6.79= - \log 2 + 7 = 6.79
For, 10−8M HCl{10^{ - 8}}M{\text{ }}HCl
[H+]=10−8\left[ {{H^ + }} \right] = {10^{ - 8}}
Here, we have to consider the concentration of water i.e. 10−7M{10^{ - 7}}M
So, the total concentration of H+=10−8+10−7{H^ + } = {10^{ - 8}} + {10^{ - 7}}
=1.1×10−7= 1.1 \times {10^{ - 7}}
Hence, pH=−log⁡[H+]=−log⁡(1.1×10−7)pH = - \log \left[ {{H^ + }} \right] = - \log \left( {1.1 \times {{10}^{ - 7}}} \right)
=6.98= 6.98
We have taken the water’s H+{H^ + } concentration, as you know, pure water undergoes self-ionization to form hydronium ions, H3O+{H_3}{O^ + }, and hydroxide ions, OH−O{H^ - }
2H2O[l]⇌H3O+(aq.)+OH−(aq.)2{H_2}O\left[ l \right] \rightleftharpoons {H_3}{O^ + }\left( {aq.} \right) + O{H^ - }\left( {aq.} \right)
Here, the value of [H3O+]=10−7\left[ {{H_3}{O^ + }} \right] = {10^{ - 7}}
Moreover, we remember that HClHCl is a strong acid and pHpH of an acidic solution can never, ever be higher than 77.
So, the answer to the question is (B) 6,6.79,6.786,6.79,6.78.

Note: The pHpH of 77 is considered neutral. A pHpH less than 77 is acidic, whereas, pHpH greater than 77 is basic. The pHpH scale is logarithmic. It plays a very crucial role in daily life like, if soil will have lesser pHpH than usual range, plants will not be able to grow and produce products. pHpH controls many vital processes in the human body from drinking to digestion of food in the stomach.