The pH of 1 L solution is 2. It is diluted with water till its becomes 4. How many litres of water are added?

Options

A. 99
B. 9
C. 999
D. 9.9

Answer

A

Explanation

`pH = 2 i.e., [H^(+)] = 10^(-2) i.e., N_(1) = 10^(-2)`
`V_(1) = 1 L`
`pH = 4 i.e., [H^(+)] = 10^(-4) i.e., N_(2) = 10^(-4)`
`V_(2) = (V_(1) + "added water") = (1 + x)`
`:. N_(1)V_(1) = N_(2)V_(2)`
`10^(-2) xx 1 = 10^(-4) xx (1+x)`
`implies 1+x = 10^(-2)/10^(-4)`
`x = 10^(2) - 1 = 99 L`