The catalytic gas phase reaction $A \rightarrow$ products is carried out in an isothermal batch reactor of $10 \: \mathrm{L}$ volume using $0.1 \: \mathrm{kg}$ of a solid catalyst. The reaction is first-order with
$$\left(-r_{A}\right)=k^{\prime} a(t) C_{A}$$
where
$$k^{\prime}=1 \frac{\mathrm{~L}}{(\mathrm{~kg} \text { catalyst })(\mathrm{h})}$$
and $C_{A}$ is the concentration of $A$ in $\mathrm{mol} / \mathrm{L}$.
The catalyst activity $a(t)$ undergoes first-order decay with rate constant $k_{d}=0.01$ per hour and $a(0)=1$.
The reactant conversion after $1$ day of operation is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places).
