$250 \ mL$ of $0.5 \ M \ NaOH$ was added to $500 \ mL$ of $1 \ M \ HCl$. The number of unreacted $HCl$ molecules in the solution after complete reaction is $...... \times 10^{21}$. (Nearest integer) $(N_{A} = 6.022 \times 10^{23})$

When $5 \ mol$ of reactant $A$ reacts with $8 \ mol$ of reactant $B$ in a closed rigid container according to the reaction:
$3A_{(g)} + 4B_{(g)} \to 2C_{(g)}$
$10^{2} \ kJ$ of heat was liberated. The $\Delta_rH$ of the given balanced reaction in $kJ/mol$ at $300 \ K$ is: $[R = 8 \ J/mol \cdot K]$

If the heat of combustion of methane is $-100 \ kJ/mol$,then calculate the heat evolved when $32 \ g$ of methane reacts with $32 \ g$ of oxygen. (in $kJ$)

Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation:
$N_{2(g)} + 3H_{2(g)} \rightarrow 2NH_{3(g)}$
$(i)$ Calculate the mass of ammonia produced if $2.00 \times 10^{3} \, g$ of dinitrogen reacts with $1.00 \times 10^{3} \, g$ of dihydrogen.
$(ii)$ Will any of the two reactants remain unreacted?
$(iii)$ If yes,which one and what would be its mass?

$50.0 \ kg$ of $N_{2(g)}$ and $10.0 \ kg$ of $H_{2(g)}$ are mixed to produce $NH_{3(g)}$. Calculate the amount of $NH_{3(g)}$ formed. Identify the limiting reagent in the production of $NH_{3(g)}$ in this situation.

$KMnO_4$ reacts with $KI$ in basic medium to form $I_2$ and $MnO_2$. When $250 \ mL$ of $0.1 \ M \ KI$ solution is mixed with $250 \ mL$ of $0.02 \ M \ KMnO_4$ in basic medium, what is the number of moles of $I_2$ formed?