The hydrogen ion concentration of a `10^(-8) M HCl` aqueous soultion at `298 K(K_(w)=10^(-14))` is

Options

A. `9.525 xx 10^(-8) M`
B. `1.0 xx 10^(-8) M`
C. `1.0 xx 10^(-6)M`
D. `1.0525 xx 10^(-7)M`

Answer

D

Explanation

From acid , `[H^(+)]-=10^(-8) M`
From `H_(2)O[H^(+)]=[OH^(-)]=x mol L^(-1) `(say)
`[H^(+)]` or `[OH^(-)]cancel(=)10^(-7)` in the presence of acid. Thus in solution `[H^(+)]=(10^(-8) +x)M` and `|OH^(-)|=xM`
But `|H^(+)|" "|OH^(-)|`
`=K_(w)`=K_(w)=|H|^(+)|OH^(-)|=1 xx 10^(-14)`
`:. (10^(-8)+x)(x)=10^(-14)`
or `x^(2)+10^(-8) -10^(-14)=0`
`:. x=-10^(-8) sqrt((106(-16) +4 xx 10^(-14))/(2))`
`=9.51 xx 10^(-8) i.e., OH^(-) =9.51 xx 10^(-8)`
`:. H^(+)=(10^(-14))/((9.51 xx10^(-18)))=1.05 xx 10^(-7)` lt