What is the pH of 1 M solution of acetic acid ? To what volume one litre of this solution be diluted so that pH of the resulting solution will be twice of the original value ? `(K_(a)=1.8xx10^(-5))`

Explanation

`overset(1)(CH_(3)COOH) Leftrightarrow CH_(3)COO^(-)+H^+`
`" 1-x x x"`
`K_a=(x^2)/(1-x) approx x^2=1.8 xx 10^(-5) , x=4.2 xx 10^(-3) =[H^+]`
`pH =-log [H^+] =-log (4.2 xx 10^(-3)) =2.37`
Now, let 1 litre of 1M `CH_3COOH` be diluted to V litres so that that pH of the solution doubles. Let the concentration of the diluted solution be c moles/litre. Thus,
`overset(CH_(3)COOH) Leftrightarrow CH_(3)COO^(-)+H^+`
`"(c-x.) x. x."`
`K_(a)=(x..x.)/((c-x.))=1.8 xx 10^(-5)........(1)`
Further pH =-log x. `=2 xx 2.37 =4.74` (pH doubles on dilution)
or `log x.=-4.74 =bar5.26`
`x.=1.8 xx 10^(-5)`
Substituing x. in (1) we get, `c=3.6 xx 10^(-5)M`
As the number of moles of `CH_(3)COOH` before and after dilution will be the same
moles of `CH_(3)COOH="molarity "xx " volume in litres"`.
`3.6 xx 10^(-5) xx V= 1 xx 1 ({:(,"Initial molarity =1"),(,"Initial volume "=1):})`
`V=2.78 xx 10^(4)"litres"`