How many moles of $H_2O_2$ are required for the decolorization of $1$ mole of $KMnO_4$?

Calculate the volume of $CO_2$ at $NTP$ that can be obtained by heating $200 \ g$ of $80 \%$ pure $CaCO_{3(s)}$.

At $298 \ K$,equal volumes of $SO_2, CH_4$ and $O_2$ are mixed in an empty container. The total pressure exerted is $2.1 \ atm$. The partial pressure of $CH_4$ in the mixture is $.......... \ atm$.

Calculate percentage atom economy when $46 \ g$ ethanol is obtained from $64.5 \ g$ chloroethane and $56 \ g$ $KOH_{(aq)}$. (in $\%$)

The reduction of boron trichloride $(BCl_3)$ by hydrogen yields elemental boron (atomic mass $10.8 \ g/mol$). If $21.6 \ g$ of boron is produced,what is the volume of hydrogen gas required at $273 \ K$ and $1 \ atm$ pressure (in $L$)?

The moles of methane required to produce $81 \ g$ of water after complete combustion is $.... \times 10^{-2} \ mol.$ [nearest integer]