In the electrolysis of water...?

In water, #(H_2O)#, oxygen has a negative oxidation state #(-2)# and hydrogen has positive oxidation state #(+1)# because oxygen is more electronegative than hydrogen.

The structure of water is given below

Electronegativity is the measure that how much an atom can attract the shared pair of electrons in a covalent bond.

Opposite charges attract each other while like charges repel each other.

As a result during electrolysis , the negative part that is oxygen is attracted towards the positive electrode, i.e. the anode, while the positive part, that is hydrogen, is attracted towards the negative electrode, i.e. the cathode.

B. At cathode the volume of the gas #("Hydrogen")# is double than the volume of gas #"(Oxygen)"# at the anode because in each molecule of water #(H_2O)# you can see that there are #2# atoms of hydrogen and #1# atom of oxygen. One mole of both elements that are hydrogen and oxygen have equal volume at standard temperature and pressure.

Thus, the volume of hydrogen that is collected at the cathode is double the volume of oxygen that is collected at anode.

You can see in the figure , the volume of hydrogen gas evolved at the cathode is double to the volume of oxygen gas evolved at the anode.

C. #H_2SO_4# is added so the water becomes good conductor of electricity. Distilled water, which is usually used for electrolysis is a bad conductor of electricity.

Thus, #H_2SO_4# is added to it during electrolysis, so that the ions can break free from the electrical energy, and therefore the products that are oxygen and hydrogen gas can be collected.