For the reaction $\begin{array}{r}{\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)\\ m_{0}1400\mathrm{g}250\mathrm{g}\end{array}$

which of the following statement is not correct?

$\begin{array}{l}{n}_0\left({\mathrm{N}}_2\right)=\frac{m_0\left({\mathrm{N}}_2\right)}{M\left({\mathrm{N}}_2\right)}=\frac{1400\mathrm{g}}{28\mathrm{g}{\mathrm{mol}}^{-1}}=50.0\mathrm{mol}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{n}_0\left({\mathrm{H}}_2\right)=\frac{m_0\left({\mathrm{H}}_2\right)}{M\left({\mathrm{H}}_2\right)}=\frac{250\mathrm{g}}{2\mathrm{g}{\mathrm{mol}}^{-1}}=125.0\mathrm{mol}\\ {\xi }_{max}\left({\mathrm{N}}_2\right)=\frac{n_0\left({\mathrm{N}}_2\right)}{v\left({\mathrm{N}}_2\right)}=\frac{50.0\mathrm{mol}}{1}=50.0\mathrm{mol}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\xi }_{max}\left({\mathrm{H}}_2\right)=\frac{n_0\left({\mathrm{H}}_2\right)}{v\left({\mathrm{H}}_2\right)}=\frac{125.0\mathrm{mol}}{3}=41.67\mathrm{mol}\end{array}$since ${\xi }_{max}\left({\mathrm{H}}_2\right)<{\xi }_{max}\left({\mathrm{N}}_2\right),{\mathrm{H}}_2$ acts as a limiting, agent

The extent of reaction when the reaction is over will be ${\xi }_{max}\left({\mathrm{H}}_2\right)\text{, i.e. }41.67\mathrm{mol}$

$\begin{array}{r}\mathrm{\Delta }{n}_{{\mathrm{NH}}_3}=v_{{\mathrm{NH}}_3}{\xi }_{max}=2\times 41.67\mathrm{mol}=83.34\mathrm{mol}\\ m_{{\mathrm{NH}}_3}=\left(\mathrm{\Delta }{n}_{{\mathrm{NH}}_3}\right)\left(M_{{\mathrm{NH}}_3}\right)=\left(83.34\mathrm{mol}\right)\left(17\mathrm{g}{\mathrm{mol}}^{-1}\right)=1416.78\mathrm{g}\end{array}$