At what temperature in Kelvin would ${\mathrm{N}}_2$ molecules have the same average speed as $\mathrm{He}$ atoms at $300 \mathrm{K}?$

Calculate the kinetic energy of Avogadro constant of gaseous molecules at $0°\mathrm{C}$.

[Report answer in multiple of ${10}^3 \mathrm{joule}$]

At $627°\mathrm{C}$ and $1 \mathrm{ATM}$, ${\mathrm{SO}}_3$ partially dissociates into ${\mathrm{SO}}_2$ and ${\mathrm{O}}_2$. $1 \mathrm{L}$ of the equilibrium mixture weighs $0.94 \mathrm{g}$ under the above conditions. Calculate the partial pressures of the constituent gases in the mixture.

The degree of dissociation of ${\mathrm{N}}_2{\mathrm{O}}_4$ according to the equation ${\mathrm{N}}_2{\mathrm{O}}_4\rightleftharpoons 2{\mathrm{NO}}_2$ at $70°\mathrm{C}$ and atmospheric pressure is $65.6\%.$ Calculate the apparent molecular weight of ${\mathrm{N}}_2{\mathrm{O}}_4$ under the above conditions.

$1$ mole of a gas is changed from its initial state $(15 \mathrm{L}; 2 \mathrm{atm})$ to final state $(4 \mathrm{L}; 10 \mathrm{atm})$ reversibly. If this change can be represented by a straight line in $p-V$ curve, calculate maximum temperature the gas attained.

Calculate the volume(in millilitres) occupied by $7 \mathrm{g}$ of ${\mathrm{N}}_2$ under a pressure of $100 \mathrm{atm}$ at $27°\mathrm{C}$.

$\left(\mathrm{a}=1.39 \mathrm{atm} {\mathrm{L}}^2 {\mathrm{mole}}^{-2}, \mathrm{b}=0.391 \mathrm{L} \mathrm{mole}{ }^{-1}\right)$

The van der Waals constant $\mathrm{b}$ for a gas is $4.2\times {10}^{-2} \mathrm{L} {\mathrm{mole}}^{-1}$. How close the nuclei of the two molecules come together?

[Report answer (in $\mathrm{cm}$) in multiple of ${10}^{-8}$ after rounding-off.]