Question

An acid solution of pH 6 is diluted thousand times. The pH of solution becomes approx ___ ?

Answer 1

$HA+H_{2}O\rightleftharpoons H_3{O}^{+}+A^{-}$
C 0 0
C-x x x
$\Rightarrow K=\frac{x\times x}{(c-x)}\Rightarrow K=\frac{x^2}{c}\Rightarrow K=\frac{(10-6{)}^2}{c}=\frac{1}{c}\times {10}^{-12}-\left(1\right)$
Now, since concentration of HA is very less, we need to consider dissociation of water also,
Dissociation of acid
$HA+H_{2}O\rightleftharpoons H_3{O}^{+}+A^{-}$
$\frac{c}{1000}-x$ x x
$\Rightarrow \frac{x^2}{c}\times 1000=\frac{1}{c}\times {10}^{-12}$
$\Rightarrow x^2={10}^{-15}=0.1\times {10}^{-14}$
$x=\sqrt{0.1}\times {10}^{-7}$
$H_{2}O+H_{2}O\rightleftharpoons H_3{O}^{+}+O{H}^{-}$
x x
$x^2={10}^{-14}$ (Ka for water is ${10}^{-14}$
Total $H^{+}=(\sqrt{0.1}+1)\times {10}^{-7}$
$-log\left(H^{+}\right)=p^H$
$p^H=6.88$.