When $500 \ mL$ of a gaseous hydrocarbon is burned in excess of $O_2$,it produces $2.5 \ L$ of $CO_2$ and $3.0 \ L$ of water vapor. What is the molecular formula of the hydrocarbon?

$15 \ mL$ of $0.2 \ N$ alkali is required to complete neutralization of $30 \ mL$ acid solution. The concentration of the acid solution is ..... $N$.

The density of $2 \ M$ aqueous solution of $NaOH$ is $1.28 \ g \ cm^{-3}.$ The molality of the solution is $... \ m$ [Given that molecular mass of $NaOH = 40 \ g \ mol^{-1}$]

$A$ gaseous mixture contains $CH_4$ and $C_2H_6$ in equimolecular proportion. The weight of $2.24 \ L$ of this mixture at $NTP$ is .............. $g$.

In a metal deficient oxide sample,$M_X Y_2 O_4$ ($M$ and $Y$ are metals),$M$ is present in both $+2$ and $+3$ oxidation states and $Y$ is in $+3$ oxidation state. If the fraction of $M^{2+}$ ions present in $M$ is $\frac{1}{3}$,the value of $X$ is. . . . . . .

In a chemical reaction,the sum of the formula weight of all reactants is $274 \ u$ and the atom economy is $50 \%$. Calculate the formula weight of the desired product. (in $u$)