$5$ The hetesogeneous gas$-$phase hydrogenation of acetylene to ethane at $1000K$

$C_2{H}_2+2H_2=C_2{H}_6$

has been found to proceed with a seaction rate that may be sepsesented by the sate equeation

$$

$-{}_{C_2{H}_2}=K[H_2{]}^2[C_2{H}_2]$

Laboratory expesiments at $1000K$ indicates that the reaction rate consfant $K=1{10}^5$gmo$\frac{l}{m}in.L.$ If a muxtuse of $75$ mole pescent $H_2$ and $25$ mole percent $C_2{H}_2$ is charged to a $1\mathrm{.}0$ litre batch reactor and o$.$ ool gmol acetylene is present initially in the reactor, Calculate the holding time necessary to acheive $90\%$ convess con of acetylene to ethaneThe reactor is to be opesated at constant temperature