A trpical aspirin tablet constains 324 mg of aspirin (acetyl salicylic acid `C_(9)H_(8)O_(4)`) a monoprotic acid having `K_(a)=3.0xx10^(-4)` . What is the degree of dissociation of salt and pH of the solution, if two aspirin tables are dissolved to prepare 300 mL solution in water ?

Explanation

Moles of aspirin= `(2xx324xx10^(-3))/(180)=3.6xx10^(-3)`
`:. ["aspirin"]=(3.6xx10^(-3))/(300)xx10^(3)=0.012`
`C_(9)H_(8)O_(4)hArrC_(9)H_(7)O_(4)+H^(+)`
`K_(a)=(Calpha^(2))/((1-alpha))=(0.012xxalpha^(2))/((1-alpha))=3.610^(-3)`
`:. 0.012alpha^(2)+0.0036alpha-0.0036=0`
`alpha=(-0.0036+-sqrt((0.0036)^(2)+4xx0.0036xx0.012))/(2xx0.012)`
`=(-0.0036+-sqrt(1.296xx10^(-5)+17.28xx10^(-5)))/(2xx0.012)`
`=0.42`
`:. [H^(+)]=Calpha=0.42xx0.012=5.04xx10^(-3)`
`:. pH= -log[H^(+)]= -log 5.04xx10^(-3)`
`=2.2976`