The major product of the following reaction is P.

$$\mathrm{CH}_3 \mathrm{C}\equiv\mathrm{C}-\mathrm{CH}_3$$ $$\xrightarrow[\substack{\text { (ii) dil. } \mathrm{KMnO}_4 \\ 273 \mathrm{~K}}]{\text { (i) } \mathrm{Na} \text { /liq. } \mathrm{NH}_3}$$ 'P'

Number of oxygen atoms present in product '$$\mathrm{P}$$' is _______. (nearest integer)

Time required for $$99.9 \%$$ completion of a first order reaction is _________ times the time required for completion of $$90 \%$$ reaction.(nearest integer)

Consider the dissociation of the weak acid HX as given below

$$\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}), \mathrm{Ka}=1.2 \times 10^{-5}$$

[$$\mathrm{K}_{\mathrm{a}}$$ : dissociation constant]

The osmotic pressure of $$0.03 \mathrm{M}$$ aqueous solution of $$\mathrm{HX}$$ at $$300 \mathrm{~K}$$ is _________ $$\times 10^{-2}$$ bar (nearest integer).

[Given : $$\mathrm{R}=0.083 \mathrm{~L} \mathrm{~bar} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$]

An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $$298 \mathrm{~K}$$ and $$5 \mathrm{~atm}$$, respectively then the final temperature is _________ $$\mathrm{K}$$ (nearest integer).

[$$\overline{\mathrm{c}}_{\mathrm{v}}$$ is the molar heat capacity at constant volume]