The reaction of ${\mathrm{WCl}}_6$ with $\mathrm{Al}$ at about $400°\mathrm{C}$ gives black crystals of a compound that contains only tungsten and chlorine. A sample of this compound, when reduced with hydrogen gives $0.2232 \mathrm{g}$ of tungsten metal and hydrogen chloride, which is absorbed in water. Titration of the hydrochloric acid thus produced required $46.2 \mathrm{mL}$ of $0.1051 \mathrm{M} \mathrm{NaOH}$ to reach the endpoint. What is the empirical formula of the black tungsten chloride?

When an electron in an excited molybdenum atom falls from $\mathrm{L} \mathrm{to} \mathrm{K}$ shell, an X -ray is emitted. These X-rays are diffracted at an angle of $7.75°$ by planes with a separation of $2.64 \stackrel{\mathrm{o}}{\mathrm{A}}$. What is the difference in energy in joules between the $\mathrm{K}$ shell and the $\mathrm{L}$ shell in $\mathrm{Mo}$ assuming a first-order diffraction?

If the answer is of type $\mathrm{y}\times {10}^{-15} \mathrm{J}$, report the value of $\mathrm{y}$ correct up to two places of decimals.

A bottle of milk stored at $300 \mathrm{K}$ sours in $36 \mathrm{hours}$. When stored in a refrigerator at $275 \mathrm{K}$ it sours in $360 \mathrm{hours}.$ Calculate the energy of activation $\left(\text{in} \mathrm{kJ}/\mathrm{mole}\right)$ of the reaction involved in the sourcing process. $\left(\mathrm{R}=8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$.

Answer correct up to two places of decimals without rounding-off.

The rate constant for the first-order decomposition at $45 °\mathrm{C}$ of ${\mathrm{N}}_2{\mathrm{O}}_5$, dissolved in chloroform, is $6.2\times {10}^{-4} {\min }^{-1}. 2{\mathrm{N}}_2{\mathrm{O}}_5\to 4{\mathrm{NO}}_2+{\mathrm{O}}_2$.

(a) What is the rate of decomposition when $\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]=0.40 \mathrm{M}?$

(b) What are the rates of formation of ${\mathrm{NO}}_2$ and of ${\mathrm{O}}_2$ when $\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]=0.40 \mathrm{M}?$

A balloon weighing $50 \mathrm{kg}$ has a radius of $10 \mathrm{m}$. What will be its payload if it is filled with $\mathrm{He}$ at $1 \mathrm{atm}$and $25°\mathrm{C}$. Density of air$=1.22 \mathrm{kg} {\mathrm{m}}^{-3}$. Also calculate its payload if ${\mathrm{H}}_2$ is filled in place of $\mathrm{He}$.

Show that the excluded volume is four times the actual volume of a molecule.

A gas dimerizes to a small extent as $2\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{A}}_2\left(\mathrm{g}\right)$.

Show that to a first approximation

$\frac{\mathrm{pV}}{\mathrm{RT}}=1-\frac{{\mathrm{K}}_{\mathrm{c}}}{\mathrm{V}}$.

A vessel contains three gases $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ in the equilibrium $\mathrm{A}\rightleftharpoons 2\mathrm{B}+\mathrm{C}$

At equilibrium, the concentration of $\mathrm{A}$ was $3 \mathrm{M}$ and that of $\mathrm{B}$ was $4 \mathrm{M}$. On doubling the volume of the vessel, the new equilibrium concentration of $\mathrm{B}$ was $3 \mathrm{M}$ Calculate ${\mathrm{K}}_{\mathrm{c}}$ and the initial equilibrium concentration of $\mathrm{C}$.