Find the void volume of fcc unit cell in $\mathrm{cm}^3$ if the volume of fcc unit cell $1.25 \times 10^{-22} \mathrm{~cm}^3$.

Find work done on 2 mole of an ideal gas at $27^{\circ} \mathrm{C}$ if it is compressed reversibly and isothermally from $5.05 \times 10^6 \mathrm{Nm}^{-2}$ to $1.01 \times 10^5 \mathrm{Nm}^{-2}$ pressure.

Rate of reaction, $\mathrm{A}+\mathrm{B} \rightarrow$ product, is $7.2 \times 10^{-2} \mathrm{moldm}^{-3} \mathrm{~s}^{-1}$ at $[\mathrm{A}]=0.4 \mathrm{~mol} \mathrm{dm}^{-3}$ and $[B]=0.1 \mathrm{~mol} \mathrm{dm}^{-3}$. The reaction is first order in A and second order in B. Calculate rate constant.

Identify the product obtained when alkenes react with cold and dilute alkaline potassium permanganate.