Question

An acid Solution of pH = $6$ is diluted $1000$ times, and the pH of the final solution becomes

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Solution

pH Abbreviation:The term "pH" can be interpreted as an acronym for "power of hydrogen," or more precisely, “the concentration of hydrogen ions in a liquid.”The mathematical definition of pH is broad and practical. It claims that the pH is equal to the negative logarithmic value of the hydrogen ion (${\mathrm{H}}^{+}$) concentration.$\mathrm{pH}=-\mathrm{log}\left[{\mathrm{H}}^{+}\right]$ Step 1: The given pH and pH after dilution :Given pH = $6$After dilution: $\left[{\mathrm{H}}^{+}\right]$ = $\frac{{10}^{-6}}{{10}^{3}}$ $\left[{\mathrm{H}}^{+}\right]$ = ${10}^{-9}$ Step 2: The total ${\mathrm{H}}^{+}$ ions :Water (${\mathrm{H}}_{2 }\mathrm{O}$)contains $\left[{\mathrm{H}}^{+}\right]$ ionsTotal $\left[{\mathrm{H}}^{+}\right]$$={10}^{-9}+{10}^{-7}$ = ${10}^{-7}\left({10}^{-2}+1\right)$ (Taking,${10}^{-7}$ common) = ${10}^{-7}\left(1.01\right)$Step 3: Taking log :pH = $-\mathrm{log}\left(1.01×{10}^{-7}\right)$ = $7-0.0043$ = $6.9957$Therefore, the pH of the final solution becomes $6.9957$.

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