Question

Under typical conditions, the production of ammonia in the Haber process has a yield of about 28.5%. What mass of nitrogen would you need in order to produce 1000 kg of ammonia?

N2 + 3 H2 → 2 NH3

Answer 1

The reaction is

N₂ + 3H₂ → 2NH₃

The yield of 28.5% means that only 25.8% of the theoretical yield calculated mathematically will produce the actual yield. Therefore, theoretically, we must produce

$$m_\text{theor}=\frac{m_\text{actual}}{\eta}=\frac{1000}{0.285}=3508.8\text{ kg}.$$

Now calculate how many moles this is:

$$n_{\text{NH}_3}=\frac{m_\text{theor}}{\Mu_{\text{NH}_3}}=\frac{3508.8}{14+1\cdot3}=206.4\text{ mol}.$$

We see that one molecule of nitrogen N₂ is required to produce 2 molecules of NH₃. Therefore, we need two times less nitrogen:

$$n_{\text{N}_2}=\frac{n_{\text{NH}_3}}{2}=103.2\text{ mol},\\ \space\\ m_{\text{N}_2}=n_{\text{N}_2}\Mu_{\text{N}_2}=103.2\cdot28=2889.6\text{ kg}.$$