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: $[R = 8 \ J/mol \cdot K]$

How many moles of $P_4$ can be produced by reaction of $0.10 \ mol$ $Ca_5(PO_4)_3F$,$0.36 \ mol$ $SiO_2$,and $0.90 \ mol$ $C$ according to the following reaction?
$4Ca_5(PO_4)_3F + 18SiO_2 + 30C \to 3P_4 + 2CaF_2 + 18CaSiO_3 + 30CO$

$2 \ L$ 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).

Phosphoric acid is prepared commercially from phosphate ore as follows:
$Ca_3(PO_4)_2 + 3SiO_2 + 5C + 5O_2 + 3H_2O \to 3CaSiO_3 + 5CO_2 + 2H_3PO_4$
If $1.0 \ kg$ each of calcium phosphate and silica are used with an excess of $C$,$O_2$,and $H_2O$,what is the maximum quantity of phosphoric acid that can be produced (in $kg$)? (Atomic masses: $Ca = 40, P = 31, Si = 28, O = 16, H = 1$)

Calculate the mass of $AgCl$ precipitated when $25 \ mL$ of $35 \%$ solution of $AgNO_3$ and $25 \ mL$ of $11.6 \%$ solution of $NaCl$ are mixed. (in $g$)

One mole of $P_4$ reacts with $8$ moles of $SOCl_2$ to give $4$ moles of $A$,$x$ moles of $SO_2$ and $2$ moles of $B$. $A$,$B$ and $x$ respectively are