A catalytic chemical reaction can be represented by the following stoichiometric equation:

AharrB$+C$

The rate of disappearance of species $"A"$ is given by:

$(-r_A)=k[p_A-\frac{p_B{p}_C}{K_p}]$

Where:

$p_A$: Species $"A"$ partial pressure $($atm$).$

$p_B$: Species $"B"$ partial pressure $($atm$).$

$p_C$ : Species $"C"$ partial pressure $($atm$).$

$k$ : Riaction rate constant $($mole$/kg$ catalyst $$ atm $s)$

$K_p$ : Equilibrium constant $($atm$).$

The feed used in a variable volume batch reactor composes of $5\mathrm{.}0$ moles of species $"A"$ and $2$ moles of species $"F".$ Express the above rate equation in terms of conversion. State any assumption you may need to apply.