The standard reduction potential for the half-cell
$$NO_3^-$$ + 2H⁺ (aq) + e $$\to$$ NO₂ (g) + H₂O is 0.78 V
(i) Calculate the reduction potential in 8 M H⁺
(ii) What will be the reduction potential of the half-cell in a neutral solution? Assume all the other species to be at unit concentration.

Chromium metal can be plated out from an acidic solution containing CrO₃ according to the following equation
CrO₃ (aq) + 6H⁺ (aq) + 6e^- $$\to$$ Cr(s) + 3H₂O
Calculate (i) how many grams of chromium will be plated out by 24,000 coulombs and (ii) how long will it take to plate out 1.5 g of chromium by using 12.5 amp current.

A first order reaction A $$\to$$ B, requires activation energy of 70 kJ mol^-1. When 20% solution of A was kept at 25^oC for 20 minutes, 25% decomposition tooks place. What will be the percentage decomposition in the same time in a 30% solution maintained at 40^oC? Assume that activation energy remains constant in this range of temperature.

If $$K = \sin \left( {\pi /18} \right)\sin \left( {5\pi /18} \right)\sin \left( {7\pi /18} \right),$$ then the numerical value of K is ______.