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.

Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n}}} \right) = \log 6$$

For a biased die the probabilities for the different faces to turn up are given below :

This die tossed and you are told that either face $$1$$ or face $$2$$ has turned up. Then the probability that it is face $$1$$ is ...............