Balance the following chemical equation by choosing the correct option for the coefficients $x, y, p, q, r,$ and $s$.
$x KNO_3 + y C_{12}H_{22}O_{11} \longrightarrow p N_2 + q CO_2 + r H_2O + s K_2CO_3$

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?

If $0.5 \ mol$ of $CaBr_2$ is mixed with $0.2 \ mol$ of $K_3PO_4$,then the maximum number of moles of $Ca_3(PO_4)_2$ obtained will be:

In the reaction $4NH_{3(g)} + 5O_{2(g)} \rightarrow 4NO_{(g)} + 6H_2O_{(g)}$,when $1 \ mol$ of ammonia and $1 \ mol$ of $O_2$ react to completion:

For a given unbalanced reaction,$MnO_2 + HCl \rightarrow MnCl_2 + H_2O + Cl_2$,which is the limiting reagent if the initial amount for each reactant is $100 \ g$? [Molar masses: $MnO_2 = 86.9 \ g/mol$; $HCl = 36.5 \ g/mol$]

$2 \ L$ of $0.2 \ M \ H_2SO_4$ is reacted with $2 \ L$ of $0.1 \ M \ NaOH$ solution. The molarity of the resulting product $Na_2SO_4$ in the solution is $X \ mM$. Find the value of $X$. (Nearest integer).