(a) One litre of a sample of hard water contains 1 mg of CaCl₂ and 1 mg of MgCl₂. Find the total hardness in terms of parts of CaCO₃ per 10⁶ parts of water by weight.

(b) A sample of hard water contains 20 mg of Ca⁺⁺ ions per litre. How many milli-equivalent of Na₂CO₃ would be required to soften 1 litre of the sample?

(c) 1 gm of Mg is burnt in a closed vessel which contains 0.5gm of O₂.
      (i) Which reactant is left in excess?
      (ii) Find the weight of the excess reactants.
      (iii) How many milliliters of 0.5N H₂SO₄ will dissolve the residue in the vessel?

4.215 g of a metallic carbonate was heated in a hard glass tube and the CO₂ evolved was found to measure 1336 ml at 27^oC and 700 mm pressure. What is the equivalent weight of metal?

(a). 5.5 g of a mixture FeSO₄.7H₂O and Fe₂(SO₄)₃.9H₂O requires 5.4 ml of 0.1 N KMnO₄ solution for complete oxidation. Calculate the number of gram mole of hydrated ferric sulphate in the mixture.

(b). The vapour density (hydrogen = 1) of a mixture consisting of NO₂ and N₂O₄ is 38.3 at 26.7^oC. Calculate the number of moles of NO₂ in 100 g of the mixure.

5 ml of a gas containing only carbon and hydrogen were mixed with an excess of oxygen (30 ml) and the mixture exploded by means of an electric spark. After the explosion, the volume of the mixed gases remaining was 25 ml. On adding a concentrated solution of potassium hydroxide, the volume further diminished to 15 ml of the residual gas being pure oxygen. All volumes have been reduced to N.T.P. Calculate the molecular formula of the hydrocarbon gas.