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The hydrogen ion concentration of a 10^(...

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

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 `

Text Solution

Verified by Experts

The correct Answer is:
D
From acid , `[H^(+)] = 10^(-8)` M
From `H_(2)O [H^(+)] = xM `
`[H^(+)] " or " [OH^(-)] != 10^(-7)` in presence of acid so , in the solution `[H^(+)] = 10^(-8) +xM `
`[OH^(-)] = xM `
` :. [H^(+)] [OH^(-)] = K_(w) = 10^(-14)`
` :. (10^(-8) +x) x = 10^(-14)`
or `10^(-8) x+ x^(2) - 10^(-1) = 0`
` :. x = (-10^(-8) pm sqrt(10^(-16)+4 xx 10^(-4)))/2 = 9.51 xx 10^(-8)`
` :. [OH^(-)] = 9.51 xx 10^(-8)`
` :. [H^(+)] = (10^(-14))/(9.51 xx 10^(-8)) = 1.0515 xx 10^(-7) M `
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