use the equation below to answer the following question. how many grams of hydrogen are necessary to react…

Explanation:

Step1: Calculate moles of nitrogen

The molar mass of $N_2$ is $M_{N_2}=2\times14.01\ g/mol = 28.02\ g/mol$. The number of moles of $N_2$, $n_{N_2}=\frac{m_{N_2}}{M_{N_2}}$, where $m_{N_2} = 50.0\ g$. So $n_{N_2}=\frac{50.0\ g}{28.02\ g/mol}\approx1.785\ mol$.

Step2: Determine moles of hydrogen

From the balanced chemical equation $N_2 + 3H_2\rightarrow2NH_3$, the mole - ratio of $N_2$ to $H_2$ is $1:3$. So the number of moles of $H_2$, $n_{H_2}=3\times n_{N_2}$. Substituting $n_{N_2}=1.785\ mol$, we get $n_{H_2}=3\times1.785\ mol = 5.355\ mol$.

Step3: Calculate mass of hydrogen

The molar mass of $H_2$ is $M_{H_2}=2\times1.01\ g/mol=2.02\ g/mol$. The mass of $H_2$, $m_{H_2}=n_{H_2}\times M_{H_2}$. Substituting $n_{H_2}=5.355\ mol$ and $M_{H_2}=2.02\ g/mol$, we get $m_{H_2}=5.355\ mol\times2.02\ g/mol\approx10.8\ g$.

Answer:

$10.8\ g\ H_2$