Question

example 3-3 the haber reaction for the formation of ammonia releases energy:
n₂ + 3 h₂ → 2 nh₃ δu = -40.9 kj
how much energy is released in the production of 1.00 kg of ammonia? (mw of nh₃ = 17.03 g/mol)
① (\frac{1,\text{kg} \text{nh}_3}{}) (\frac{1000,\text{g}}{{1,\text{kg}}}) (\frac{1,\text{mol}}{{17.03,\text{g} \text{nh}_3}})
② (delta u_{\text{molar}} = -\frac{40.9,\text{kj}}{2}) (per 1 mol of nh₃)

Explanation:

Step1: Calculate moles of \( NH_3 \)

First, convert the mass of \( NH_3 \) from kilograms to grams: \( 1.00 \, \text{kg} = 1000 \, \text{g} \).
Then, use the molar mass (\( 17.03 \, \text{g/mol} \)) to find moles:
\( \text{Moles of } NH_3 = \frac{1000 \, \text{g}}{17.03 \, \text{g/mol}} \approx 58.72 \, \text{mol} \)

Step2: Determine energy per mole of \( NH_3 \)

From the reaction \( N_2 + 3H_2
ightarrow 2NH_3 \) with \( \Delta U = -40.9 \, \text{kJ} \), the energy released per 2 moles of \( NH_3 \) is \( 40.9 \, \text{kJ} \).
So, energy per mole of \( NH_3 \) is \( \frac{40.9 \, \text{kJ}}{2 \, \text{mol}} = 20.45 \, \text{kJ/mol} \)

Step3: Calculate total energy released

Multiply moles of \( NH_3 \) by energy per mole:
\( \text{Total energy} = 58.72 \, \text{mol} \times 20.45 \, \text{kJ/mol} \approx 1199 \, \text{kJ} \) (or \( 1.20 \times 10^3 \, \text{kJ} \))

Answer:

Approximately \( \boldsymbol{1.20 \times 10^3 \, \text{kJ}} \) (or \( 1199 \, \text{kJ} \)) of energy is released.