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how much water should be added to 500.0ml of a solution of HCI with pH of 2.00 to bring the pH to 2.50?
The concentration of the HCl solution is (log)^-1(2) = 0.01M

You want to make it pH 2.5 which has a concentration of (log)^-1(2.5) = 0.00316M

concentration = no of moles*volume

c = n/v

you are going to add x Litres of water to a solution that contains 0.5*.01 = 0.005 moles of HCl

so 0.00316 = .005/(0.5 + x)

0.5 + x = 0.005/0.00316 = 1.582L

x = 1.582 - 0.5 = 1.082L