The `pH` of `0.1M` monobasic acid is `4.50`. Calculate the concentration of species, `H^(o+), A^(Θ)`, and `HA` at equilibrium. Also determine the value of `K_(a)` and `pK_(a)` of the monobasic acid.

Explanation

pH=4.5
or -log `[H_3O^+]` =4.5
or log `[H_3O^+]` =-4.5 or 5.5
`therefore [H_3O^+]=3.16xx10^(-5)`
Let the acid, HA ionises as :
`HA(aq)+H_2O(l) hArr H_3O^(+)(aq) +A^(-)(aq)`
`[H_3O^+]=[A^-]=3.16xx10^(-5)` M
`[HA]_"equi"=0.1-3.16xx10^(-5) approx` 0.1 M
`K_a=([H_3O^+][A^-])/"[HA]"`
But `[H_3O^+]=[A^-]`
`K_a=([H_3O^+]^2)/([HA])`
Here [HA]=0.1 mol `L^(-1) , [H_3O^+]=3.16xx10^(-5) mol L^(-1)`
`K_a=((3.16xx10^(-5))^2)/0.1 =1.0xx10^(-8)`
`therefore K_a=1.0xx10^(-8)`
`pK_a=-log (1.0xx10^(-8))`=8