Give reasons of the following:
Sodium carbonate is made by Solvay process but the same process is not extended to the manufacture of potassium carbonate.

The vapour pressure of pure benzene is 639.7 mm of mercury and the vapour of a solution of a solute in benzene at the same temperature is 631.9 mm of mercury. Calculate this molality of the solution.

Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C₀, C₁ ,....C_n are constants, and $${C_n} \ne 0$$ , then the value of n is _____.

The general solution of the trigonometric equation sin x+cos x=1 is given by: