Copper sulphate solution (250 mL) was electrolysed using platinum anode and a copper cathode. A constant current of 2mA was passed for 16 minutes. It was found that after electrolysis the absorbance of the solution was reduced to 50% of its original value. Calculate the concentration of copper sulphate in the solution to begin with.

The following electrochemical cell has been set up.
Pt(1) | Fe³⁺, Fe²⁺ (a = 1) | Ce⁴⁺, Ce³⁺ (a=1) | Pt(2)
E^o (Fe³⁺, Fe²⁺) = 0.77 V; E^o (Ce⁴⁺, Ce³⁺) = 1.61 V
If an ammeter is connected between the two platinum electrodes, predict the direction of flow of current. Will the current increase or decrease with time?

A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by 20 kJ mol^-1.

In any triangle $$ABC,$$ prove that $$$\cot {A \over 2} + \cot {B \over 2} + \cot {C \over 2} = \cot {A \over 2}\cot {B \over 2}\cot {C \over 2}.$$$