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2. Given below are two statements
Statement I: The changes in $\mathrm{pH}$ with temperature are so small that we often ignore it
Statement II: When the hydrogen ion concentration changes by a factor of 100 , the $\mathrm{pH}$ changes by one unit In the light of above statements, identify the correct answer from the options given below
Options:
Statement I: The changes in $\mathrm{pH}$ with temperature are so small that we often ignore it
Statement II: When the hydrogen ion concentration changes by a factor of 100 , the $\mathrm{pH}$ changes by one unit In the light of above statements, identify the correct answer from the options given below
Solution:
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Verified Answer
The correct answer is:
Statement I is correct but statement II is not correct.
A small change in temperature has little impact on the $\mathrm{pH}$ of a solution as the concentration of the $\mathrm{H}^{+}$ions does not change much.
Thus, statement $\mathrm{I}$ is correct.
$\begin{aligned}
& \mathrm{pH}_1=-\log \left[\mathrm{H}^{+}\right]_1 \text { so if }\left[\mathrm{H}^{+}\right]_2=100\left[\mathrm{H}^{+}\right]_1 \\
& \begin{aligned}
\Rightarrow \mathrm{pH}_2 & =-\log \left[\mathrm{H}^{+}\right]_2=-\log \left(100\left[\mathrm{H}^{+}\right]_1\right) \\
& =-\log (100)+\left[-\log \left[\mathrm{H}^{+}\right]_1\right] \\
& =-2+\mathrm{pH}_1=\mathrm{pH}_1-2
\end{aligned}
\end{aligned}$
Thus, $\mathrm{pH}$ changes by two units.
Therefore, statement II is incorrect.
Thus, statement $\mathrm{I}$ is correct.
$\begin{aligned}
& \mathrm{pH}_1=-\log \left[\mathrm{H}^{+}\right]_1 \text { so if }\left[\mathrm{H}^{+}\right]_2=100\left[\mathrm{H}^{+}\right]_1 \\
& \begin{aligned}
\Rightarrow \mathrm{pH}_2 & =-\log \left[\mathrm{H}^{+}\right]_2=-\log \left(100\left[\mathrm{H}^{+}\right]_1\right) \\
& =-\log (100)+\left[-\log \left[\mathrm{H}^{+}\right]_1\right] \\
& =-2+\mathrm{pH}_1=\mathrm{pH}_1-2
\end{aligned}
\end{aligned}$
Thus, $\mathrm{pH}$ changes by two units.
Therefore, statement II is incorrect.
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