Question

How many times more acidic will be the aqueous solution having $2$ pH compared to that having $4$ pH.

Answer 1

For aqueous solution with pH $2$,
pH$=-lo{g}_{10}\left[H^{+}\right]$
$2=-lo{g}_{10}\left[H^{+}\right]$
$\therefore \left[H^{=}\right]=$antilog $(-2.0)$
$\therefore \left[H^{+}\right]=0.01$M
For aqueous solution with pH $4$,
pH$=-lo{g}_{10}\left[H^{+}\right]$
$\therefore -lo{g}_{10}\left[H^{+}\right]=4$
$\therefore lo{g}_{10}\left[H^{+}\right]=-4$
$\therefore \left[H^{+}\right]=0.0001$M
$\frac{\left[H^{+}\right]\text{in aqueous solution having pH 2}}{\left[H^{+}\right]\text{in aqueous solution having pH 4}}=\frac{0.01}{0.0001}=100$
Thus, the aqueous solution with pH $2$ is $100$ times more acidic than the aqueous solution with pH $4$.