Question

The decrease in % in $\left[H^{+}\right]$ when $pH$ increases by $0.1$ will be $x$ then find the value of $-x/20$ to the nearest integer.

Answer 1

Suppose initial pH is 7. pH increases by 0.1. So final pH is 7.1.

Initial $\left[H^{+}\right]={10}^{-pH}={10}^{-7}$

Final $\left[H^{+}\right]={10}^{-pH}={10}^{-7.1}=7.94\times {10}^{-8}$

Decrease in $\left[H^{+}\right]=\frac{{10}^{-7}-7.94\times {10}^{-8}}{{10}^{-7}}=0.206$

Percent decreases in $\left[H^{+}\right]=100\times 0.206=20.6$

Since it is decrease, a negative sign is introduced.

Percent decreases in $\left[H^{+}\right]=-20.6=x$

$\frac{-x}{20}=\frac{-(-20.6)}{20}\simeq 1$