Use the following information to answer numerical$-$response question $4$ and questions $6$ and $7.$

Hydrogen cyanide gas, $HCN(g),$ is used in the production of many plastics. This gas can be prepared by the reaction of methane, $C{H}_4(g),$ and ammonia, $N{H}_3(g),$ in the presence of a catalyst, as represented by the following equation.

$C{H}_4(g)+N{H}_3(g)$catalystHCN$(g)+3H_2(g),H=$

Relevant Equations

Equation I $,N_2(g)+3H_2(g)2N{H}_3(g)$

$H=-91\mathrm{.}8kJ$

$H=-74\mathrm{.}6kJ$

$H=+270\mathrm{.}3kJ$

Equation $IIC(s)+2H_2(g)C{H}_4(g)$

Equation III $,H_2(g)+2C(s)+N_2(g)2HCN(g),H=+270\mathrm{.}3kJ$

In Equation I, the molar enthalpy of reaction for $H_2(g)$ is $\frac{+}{-}$

$k\frac{J}{m}ol.$

$($Record your three$-$digit answer in the numerical$-$response section on the answer sheet.$)$