Question

when the current is passed through acidified water, the amount of gases generated at anode and at cathode is different. why ?

Answer 1

This is electrolysis reaction in water. This is one experimental method of showing water is a compound composed of the elements hydrogen and oxygen atoms i.e. by splitting liquid water into two gaseous element molecules of hydrogen (H2) and oxygen (O2).
Water only ionises to a tiny extent giving minute concentrations of hydrogen ions and hydroxide ions, so the presence of high concentrations of hydrogen ions (H+ or H3O+) andsulfate ions (SO42–) from the acid, makes water a much better electrical conductor (a much better electrolyte solution). These small extra ion concentrations of hydrogen ions (H+) and hydroxide ions (OH–) are from the self-ionisation of water itself

Answer 2

Because in water hydrogen is present in double amount than oxygen so at anode oxygen is present in single amout while hydrogen is present in double amount at cathode