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

Options

A. `1.0525xx10^(-7)` M
B. `9.525xx10^(-8)` M
C. `1.0xx10^(-8)` M
D. `1.0xx10^(-6)` M

Answer

A

Explanation

`[H^+]_"HCl"=10^(-8)` M
`[H^+]_"total"=[H^+]_"HCl" + [H^+]_"water"`
Let on ionization of water,
`[H^+]=[OH^-]=x`
`therefore [H^+]_"total"=10^(-8)+x`
Now , `[H^+][OH^-]=10^(-14)`
`(10^(-8)+x)(x)=10^(-14)`
`x^2=10^(-8)x -10^(-14)=0`
Soving `x=9.5xx10^(-8)`
`therefore [H^+]_"total"=1xx10^(-8)+9.5xx10^(-8)`
`=10.5xx10^(-8) M` or `1.05xx10^(-7)`M