Question

Two weak acids $HA$ and $HB$ have same $pH$ when their concentration ratio is $3:1$. The ratio of the dissociation constants of $HB$ and $HA$ is ________.

Answer 1

pH = $-log\left[H^{+}\right]$

Note: $1=HA;2=HB$

By given conditions,

$p{H}_1=p{H}_2$

$-log\left[C_1{\alpha }_1\right]=-log\left[C_2{\alpha }_2\right]$

$\frac{{\alpha }_2}{{\alpha }_1}=\frac{C_1}{C_2}=3:1$

So the ratio of dissociation constants of HB and HA is

$\frac{K_2}{K_1}=\frac{C_2{\alpha }_2^2}{C_1{\alpha }_1^2}=\frac{3^2}{3}=3$

Thus, the ratio of the dissociation constants of HB and HA is 3