$$0.3 \mathrm{~g}$$ of ethane undergoes combustion at $$27^{\circ} \mathrm{C}$$ in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by $$0.5^{\circ} \mathrm{C}$$. The heat evolved during combustion of ethane at constant pressure is ____________ $$\mathrm{kJ} ~\mathrm{mol}{ }^{-1}$$. (Nearest integer)

[Given : The heat capacity of the calorimeter system is $$20 \mathrm{~kJ} \mathrm{~K}^{-1}, \mathrm{R}=8.3 ~\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$.

Assume ideal gas behaviour.

Atomic mass of $$\mathrm{C}$$ and $$\mathrm{H}$$ are 12 and $$1 \mathrm{~g} \mathrm{~mol}^{-1}$$ respectively]

A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of $$2.0$$ and $$2.5\,\mathop A\limits^o $$ respectively. The ratio of densities of lattices fcc to bcc for the metal M is ____________. (Nearest integer)

The molality of a $$10 \%(\mathrm{v} / \mathrm{v})$$ solution of di-bromine solution in $$\mathrm{CCl}_{4}$$ (carbon tetrachloride) is '$$x$$'. $$x=$$ ____________ $$\times 10^{-2} ~\mathrm{M}$$. (Nearest integer)

[Given : molar mass of $$\mathrm{Br}_{2}=160 \mathrm{~g} \mathrm{~mol}^{-1}$$

atomic mass of $$\mathrm{C}=12 \mathrm{~g} \mathrm{~mol}^{-1}$$

atomic mass of $$\mathrm{Cl}=35.5 \mathrm{~g} \mathrm{~mol}^{-1}$$

density of dibromine $$=3.2 \mathrm{~g} \mathrm{~cm}^{-3}$$

density of $$\mathrm{CCl}_{4}=1.6 \mathrm{~g} \mathrm{~cm}^{-3}$$]

The spin only magnetic moment of $$\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$$ complexes is _________ B.M. (Nearest integer)

(Given : Atomic no. of Mn is 25)