Consider the following equation:

$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \Delta H=-190 \mathrm{~kJ}$

The number of factors which will increase the yield of $\mathrm{SO}_{3}$ at equilibrium from the following is _______.

A. Increasing temperature

B. Increasing pressure

C. Adding more $\mathrm{SO}_{2}$

D. Adding more $\mathrm{O}_{2}$

E. Addition of catalyst

Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Nearest integer).

Given $\mathrm{K}_{f}=1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If density of the $\mathrm{FeO}$ in the crystal is $4.0 \mathrm{~g} \mathrm{~cm}^{-3}$, then the number of $\mathrm{FeO}$ units present per unit cell is __________. (Nearest integer)

Given: Molar mass of $\mathrm{Fe}$ and $\mathrm{O}$ is 56 and $16 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively. $\mathrm{N}_{\mathrm{A}}=6.0 \times 10^{23} \mathrm{~mol}^{-1}$

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\circ}$, to the $y$-axis at 45 and to the $z$-axis at an acute angle. If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then :