In the balanced equation of the following reaction,the ratio of $a / b$ is: $aCaCO_3 + bH_3PO_4 \rightarrow pCa_3(PO_4)_2 + qCO_2 + rH_2O$

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

$50.0 \, kg$ 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 $NH_3$ in this situation.

When $10 \ g$ of copper and $10 \ g$ of iodine are mixed,calculate the theoretical yield of $CuI$ according to the equation,$2Cu + I_2 \longrightarrow 2CuI$. (in $g$)

If $5$ moles of $BaCl_2$ is mixed with $2$ moles of $Na_3PO_4$,the maximum number of moles of $Ba_3(PO_4)_2$ formed is $..........$ (Nearest integer)

If $0.50 \ mol$ of $CaCl_2$ is mixed with $0.20 \ mol$ of $Na_3PO_4$,the maximum number of moles of $Ca_3(PO_4)_2$ which can be formed,is