2 moles of an ideal gas are expanded isothermally and reversibly from 20 L to 40 L at 300 K . Calculate work done. ( $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$).

Identify the product P of following reaction.

$$\mathrm{CH}_3 \mathrm{OH}+\mathrm{CH}_3 \mathrm{MgX} \longrightarrow \mathrm{P}+\mathrm{MgX}\left(\mathrm{OCH}_3\right)$$

Calculate number of atoms per unit cell of an element having molar mass $92.0 \mathrm{~g} \mathrm{~mol}^{-1}$ and density $8.6 \mathrm{~g} \mathrm{~cm}^{-3}$ forming cubic unit cell structure. $\left[\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}=21.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$

What is the product obtained when phenylethene is treated with $\mathrm{KMnO}_4$ in dilute $\mathrm{H}_2 \mathrm{SO}_4$ ?