Natural gas is a mixture of methane and ethane. The heat produced by the complete combustion of $10 \, L$ of this mixture at $S.T.P.$ is $476.6 \, kJ$. Given $\Delta H_{comb} (CH_4) = -894 \, kJ \, mol^{-1}$ and $\Delta H_{comb} (C_2H_6) = -1500 \, kJ \, mol^{-1}$,calculate the percentage of methane and ethane in the mixture by volume.

Assume that a human body requires $2500 \, kcal$ of energy each day for metabolic activity and sucrose is the only source of energy,as per the equation $C_{12}H_{22}O_{11(s)} + 12 \, O_{2(g)} \longrightarrow 12 \, CO_{2(g)} + 11 \, H_2O_{(l)};$ $\Delta H = -5.6 \times 10^6 \, J$. (Fill in the blanks) $(a)$ The energy requirement of the human body per day is $.... \, kJ$. $(b)$ The mass of sucrose required to provide this energy is $........ \, g$ and the volume of $CO_2$ (at $STP$) produced is $......... \, litres.$

Match the following columns:

Column - $A$	Column - $B$
$(A)$ $88 \ g$ of $CO_2$	$(1)$ $0.2 \ mol$
$(B)$ $6.022 \times 10^{23}$ molecules of water	$(2)$ $2 \ mol$
$(C)$ $5.6 \ L$ of $O_2$ at $STP$	$(3)$ $1 \ mol$
$(D)$ $96 \ g$ of $O_2$	$(4)$ $6.022 \times 10^{23}$ molecules
$(E)$ One mole of any gas at $STP$	$(5)$ $3 \ mol$

Which of the following is the heaviest?

$25 \ mL$ of $0.1 \ N \ NaOH$ solution neutralises $12.5 \ mL$ of $HCl$ solution. The amount of water needed to convert $500 \ mL$ of such $HCl$ solution to $0.1 \ N$ is (in $mL$)

At $300 \ K$ temperature,$20 \ g \ H_2$,$220 \ g \ CO_2$,and $140 \ g \ N_2$ are filled in a vessel having volume $2 \ L$. Find the total pressure in $bar$ unit and which gas is removed from the vessel so that pressure can be reduced by $50 \%$. $(R = 8.34 \times 10^{-2} \ L \ bar \ K^{-1} \ mol^{-1})$