To determine how much energy is released or absorbed by the reaction when 21.7 grams of nitrogen is consumed, we need to carry out the following steps:
1. Determine the molar mass of nitrogen gas (N₂):
Nitrogen gas is diatomic, meaning each molecule is composed of two nitrogen atoms. Using the periodic table, we know that the atomic mass of a single nitrogen atom (N) is approximately [tex]\( 14.01 \)[/tex] g/mol.
Molar mass of [tex]\( N_2 \)[/tex]:
[tex]\[
\text{Molar mass of } N_2 = 2 \times 14.01 \, \text{g/mol} = 28.02 \, \text{g/mol}
\][/tex]
2. Calculate the number of moles of nitrogen gas ([tex]\( N_2 \)[/tex]) consumed:
Use the mass of nitrogen given (21.7 grams) and the molar mass of [tex]\( N_2 \)[/tex] calculated above to find the moles of [tex]\( N_2 \)[/tex]:
[tex]\[
\text{Moles of } N_2 = \frac{\text{Mass of } N_2}{\text{Molar mass of } N_2} = \frac{21.7 \, \text{g}}{28.02 \, \text{g/mol}} = 0.774 \, \text{mol}
\][/tex]
This result is accurate to three significant figures because the given mass of nitrogen (21.7 g) is provided to three significant figures.
3. Calculate the energy change ([tex]\( \Delta H \)[/tex]) for the reaction:
From the given information, the enthalpy change ([tex]\( \Delta H \)[/tex]) for the reaction shows that 1 mole of nitrogen releases [tex]\( -91.8 \)[/tex] kJ during the reaction.
Calculate the total energy change for [tex]\( 0.774 \)[/tex] moles of [tex]\( N_2 \)[/tex]:
[tex]\[
\text{Energy released} = \text{Moles of } N_2 \times \Delta H = 0.774 \, \text{mol} \times (-91.8 \, \text{kJ/mol}) = -71.1 \, \text{kJ}
\][/tex]
Here, we have rounded our final answer to three significant figures to match the precision of the given data.
Thus, the chemical reaction of 21.7 grams of nitrogen to produce ammonia releases approximately [tex]\(-71.1\)[/tex] kilojoules of energy.
