A gas phase reaction

$A2B$

takes place in two different BATCH isothermal reactors:

Isochoric $($constant volume$)$ BATCH

Isobaric $($constant pressure$)$ BATCH

The reaction is first order with respect to the concentration of compound A

$r_V=k{c}_A$

where $k$ is the rate constant equal to $1s^{-1}.$ The initial pressure in both reactors is $1$ bar and both contain compound A only.

Calculate the conversion of compound $A$ as function of time for both reactors $($analytical solution$).$

Calculate the concentration of compound $A$ as function of time for both reactors $($analytical solution$).$

Determine the volume and pressure at ${10}^{th}$ second after the reaction start for both reactors

Hint $1$: Perform $(1)$ the material balance of the system, $(2)$ material balance of the reactor, and $(3)$ integrate the resulting differential equation. Be aware that volume changes over time $($comersion$)$ in an isobaric BATCH!

Hint $2$: The concentration of $$ in the isochoric BATCH could be calculated as $c_A(t)=\frac{n_A(t)}{V_R(t)}$