To find the number of liters of ammonia gas produced, we need to determine the balanced chemical equation for the reaction between nitrogen and hydrogen to form ammonia. The balanced equation is as follows:
N₂ + 3H₂ → 2NH₃
From the equation, we can see that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.
Next, we need to calculate the number of moles of nitrogen and hydrogen given the volume of gas provided. The molar volume of a gas at standard conditions (0°C and 1 atm) is 22.4 liters/mol. Therefore, the number of moles of nitrogen is:
moles of Nâ‚‚ = volume of Nâ‚‚ gas / molar volume = 6 liters / 22.4 liters/mol = 0.268 moles
Similarly, the number of moles of hydrogen is:
moles of Hâ‚‚ = volume of Hâ‚‚ gas / molar volume = 18 liters / 22.4 liters/mol = 0.804 moles
According to the stoichiometry of the balanced equation, the limiting reactant is the one with a lower number of moles. In this case, nitrogen is the limiting reactant since it has fewer moles compared to hydrogen. It means that nitrogen will be completely consumed in the reaction, and some excess hydrogen may be left.
Since 1 mole of nitrogen reacts with 2 moles of ammonia, we can determine the number of moles of ammonia produced using the stoichiometry:
moles of NH₃ = moles of N₂ × (2 moles of NH₃ / 1 mole of N₂) = 0.268 moles × (2/1) = 0.536 moles
Finally, to find the volume of ammonia gas produced, we can use the molar volume of the gas at standard conditions:
volume of NH₃ gas = moles of NH₃ × molar volume = 0.536 moles × 22.4 liters/mol = 12.0 liters
Therefore, when 6 L of nitrogen gas reacts with 18 L of hydrogen gas, 12 L of ammonia gas will be produced.