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Question: At \({100^0}C\) the \({K_M}\) of the water is 55 times its value at \({25^0}C\).What will be the pH ...

At 1000C{100^0}C the KM{K_M} of the water is 55 times its value at 250C{25^0}C.What will be the pH of the neutral solution? (log⁡(55)=1.74\log (55) = 1.74)
A.6.13
B.7.00
C.7.87
D.5.13

Explanation

Solution

To answer this question, we first need to understand what IS pH. In a water-based solution, pH is the negative log of hydrogen ion concentration. Sren Peter Lauritz Srensen, a Danish biologist, was the first to coin the term "pH" in 1909. pH stands for "potential of hydrogen," with "p" standing for the German word for power, potenz, and H standing for the element symbol for hydrogen.

Complete answer:
As we know that at 250C,KM=1×10−14{25^0}C,{K_M} = 1 \times {10^{ - 14}}
And as given in the question that at 1000C,KM=55×10−14{100^0}C,{K_M} = 55 \times {10^{ - 14}}
So, by using the formula that
[H+]=55×10−14[{H^ + }] = \sqrt {55 \times {{10}^{ - 14}}}
And formula of pH is,
pH=−log⁡[H+]pH = - \log [{H^ + }]
And putting the value of [H+][{H^ + }] concentration
pH=−log⁡[55×10−14]pH = - \log [\sqrt {55 \times {{10}^{ - 14}}} ]
We get
→pH=12[−log⁡(55)+14log⁡(10)]\rightarrow pH = \dfrac{1}{2}[ - \log (55) + 14\log (10)]
→pH=12[−1.74+14]\rightarrow pH = \dfrac{1}{2}[ - 1.74 + 14]
pH=6.13pH = 6.13
So, the final answer is option(A) i.e., 6.13.

Note:
The pH meter is frequently referred to as a "potentiometric pH meter" because it monitors the difference in electrical potential between a pH electrode and a reference electrode. The acidity or pH of the solution is related to the difference in electrical potential.