Question

15) What is the hydronium ion concentration [H3O + ] of a 0.125 M hydrocyanic acid solution with Ka = 4.9 × 10-10? The equation for the dissociation of hydrocyanic acid is: HCN(aq) + H2O(l) ⇌ H3O+(aq) + CN- (aq)

Answer 1

The hydronium ion concentration [H₃O⁺]=7.826 x 10⁻⁶

Further explanation

In general, the weak acid ionization reaction  

HA (aq) ---> H⁺ (aq) + A⁻ (aq)  

Ka's value  

$\large {\boxed {\bold {Ka \: = \: \frac {[H ^ +] [A ^ -]} {[HA]}}}}$

Reaction

HCN(aq) + H₂O(l) ⇌ H₃O⁺(aq) + CN⁻ (aq)

0.125

x                                   x               x

0.125-x                         x               x

$\tt Ka=\dfrac{[H_3O^+][CN^-]}{[HCN^-]}$

$\tt 4.9\times 10^{-10}=\dfrac{x^2}{0.125-x}\approx \dfrac{x^2}{0.125}\\\\x^2=6.125\times 10^{-11}\\\\x=7.826\times 10^{-6}$