Question

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

Answer 1

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.
• $\mathrm{pH}=-\log \left[{\mathrm{H}}^{+}\right]$

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 $\left[{\mathrm{H}}^{+}\right]$ ions
• Total $\left[{\mathrm{H}}^{+}\right]$$={10}^{-9}+{10}^{-7}$

= ${10}^{-7}\left({10}^{-2}+1\right)$ (Taking,${10}^{-7}$ common)

= ${10}^{-7}(1.01)$

Step 3: Taking log :

• pH = $-\log \left(1.01\times {10}^{-7}\right)$

= $7-0.0043$

= $6.9957$

Therefore, the pH of the final solution becomes $6.9957$.