Question

In electrolysis of water, why is the volume of gas collected over one electrode double the volume of gas collected over the other electrode?

Answer 1

balance reaction for electrolysis of water is:

H2O  ------------------------------>  H2  +  1/2O2
the electrolysis of one mole water produce one mole of H2 and half mole O2. at the same condition (temperature, pressure) from ideal gas equation
PV = nRT                        where R is gas constant
apply for Hydrogen:
   PV1 = RT        ----------------------(1)
apply for Oxygen:
PV2 = RT/2      --------------------------(2)
(1)÷(2)
V1/V2 = 2
hence in the electrolysis of water volume of gas over one electrode is double the volume of gas collected over other electrode.

Answer 2

due to the decomposition reeaction H2O gets converted in to H2 & O2.
since water contains 2 atoms of hydrogen & one atom of oxygen. so hydrogens volume is =2(volume of oxygen produced)