In a solution of $pH = 5$,more acid is added in order to reduce the $pH$ to $2$. The increase in hydrogen ion concentration is $......$ times.

The $pH$ values of $(i) \ 0.1 \ M \ HCl_{(aq)}$,$(ii) \ 0.1 \ M \ KOH$,$(iii)$ tomato juice,and $(iv)$ pure water follow the order.

Water is added to $1.0 \ mL$ of $0.1 \ M$ $HCl$ solution to make the total volume $50 \ mL$. Calculate the $pH$ change of the solution.

Equal volumes of three acid solutions of $pH$ $3$,$4$ and $5$ are mixed in a vessel. What will be the $H^{+}$ ion concentration in the mixture in terms of $\times 10^{-4} \ M$?

$1 \ L$ of $0.02 \ M$ aqueous $HCl$ is mixed with $1 \ L$ of $0.01 \ M$ aqueous $H_2SO_4$ solution. Assuming complete dissociation and no change in the volume upon mixing,the $pH$ of the resultant solution is $(\log_{10} 2 = 0.3)$.

Calculate the $pH$ of the following solutions:
$(a)$ $0.002 \ M \ HNO_3$
$(b)$ $0.06 \ M \ H_2SO_4$