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:

$A$ closed $10 \, L$ vessel contains $1 \, L$ water gas $(1:1 \, CO : H_2)$ and $9 \, L$ air ($20 \% \, O_2$ by volume) at $STP$. The contents of the vessel are ignited. The number of moles of $CO_2$ in the vessel is closest to $.... \, mol$.

$A + 2B + 3C \rightleftharpoons AB_2C_3$. Reaction of $6.0 \ g$ of $A$,$6.0 \times 10^{23}$ atoms of $B$,and $0.036 \ mol$ of $C$ yields $4.8 \ g$ of compound $AB_2C_3$. If the atomic mass of $A$ and $C$ are $60$ and $80 \ amu$,respectively,the atomic mass of $B$ is .............. $amu$ (Avogadro no. $= 6 \times 10^{23}$)

For the given reaction:
$CaCO_{3} + 2HCl \to CaCl_{2} + H_{2}O + CO_{2}$
If $90 \ g$ of $CaCO_{3}$ is added to $300 \ mL$ of $HCl$ solution which contains $38.55\%$ $HCl$ by mass and has a density of $1.13 \ g \ mL^{-1}$, then which of the following options is correct?
[Given molar masses of $H$, $Cl$, $Ca$, and $O$ are $1$, $35.5$, $40$, and $16 \ g \ mol^{-1}$ respectively]

What is the number of moles of water molecules required to prepare $n$ moles of methane from $n$ moles of methyl magnesium iodide?

$8 \ L$ of $H_2$ and $6 \ L$ of $Cl_2$ react to the maximum extent. Find the final volume of the reaction mixture in $L$. Assume $P$ and $T$ remain constant throughout the process.