Question

If this solution were diluted to $10$ times its volume, what would be the $pH$? (write the value to the nearest integer)

Answer 1

On diluting the solution $10$ times,
$\left[HCOOH\right]=0.005,\left[HCOONa\right]=0.006$
$HCOOH\rightleftharpoons H^{+}+HCO{O}^{-}$
$0.005$ 0 0 (Initially)
$0.005(1-\alpha )$ $0.005\alpha$ $0.005\alpha +0.006$ (At equilibrium)
$K_a=1.8\times {10}^{-4}=\frac{(0.005\alpha +0.006)\left(0.005\alpha \right)}{0.005(1-\alpha )}$
$\frac{0.005{\alpha }^2+0.006\alpha }{1-\alpha }=1.8\times {10}^{-4}$
$\Rightarrow 27.77{\alpha }^2+34.33\alpha -1=0$
$\alpha =0.0285$
$\left[H^{+}\right]=0.005\alpha =1.425\times {10}^{-4}$
$pH=3.846$

Hence, the answer to nearest integer is $4$.