What concentration of acetic acid is needed to give a hudrogen ion concentration of `3.5xx10^(-4) M`?
`(K_(a)=1.8xx10^(-5))`?

Options

A. `3.5xx10^(-4) M`
B. `6.80xx10^(-3) M`
C. `4.2xx10^(-4) M`
D. `7.2xx10^(-4) M`

Answer

B

Explanation

`underset(C-Calpha)(CH_(3)COOH)hArrunderset(Calpha)(CH_(3)COO^(-))+underset(Calpha)(H^(+))`
Let the concentration of acetic acid be `'C'`.
`K=1.8xx10^(-5)=(Calpha.Calpha)/(C(1-alpha))=Calpha^(2)`
Now `alpha^(2)=(K_(a))/(C )` or `alpha=sqrt((K_(a))/(C ))` or `Calpha =sqrt(K_(a).C)`
`Calpha=[H^(+)]=3.5xx10^(-4)M`
`:. 3.5xx10^(-4)=sqrt(1.8xx10^(-5)C)`
or `sqrtC=(3.5xx10^(-4))/(1.8xx10^(-5))`
`=C=((3.5xx10^(-4))^(2))/(1.8xx10^(-5))`
`=(12.25xx10^(-8))/(1.8xx10^(-5))=6.80xx10^(-3)M`