For the reaction: N2+3H2 <-----> 2NH3
1.000 mol N2 and 1.000 mol H2 are placed in a 1.000 L container and allowed to establish equilibrium. When equilibrium is established the [N2] =0.921M. Calculate the equilibrium concentrations of hydrogen and ammonia. Calculate K.
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To calculate the equilibrium concentrations of hydrogen (H2) and ammonia (NH3), we need to first determine the change in concentration of nitrogen (N2) and then use the stoichiometry of the balanced equation to calculate the changes in concentration for hydrogen and ammonia.
Given:
Initial [N2] = 1.000 M (1.000 mol in 1.000 L container)
[N2] at equilibrium = 0.921 M
Since we have the initial and equilibrium concentrations of N2, we can calculate the change in concentration:
Change in [N2] = Initial [N2] - [N2] at equilibrium
= 1.000 M - 0.921 M
= 0.079 M
According to the balanced equation, the stoichiometric ratio between N2 and H2 is 1:3, and the ratio between N2 and NH3 is 1:2. This means that the changes in concentration for H2 and NH3 will be related to the change in concentration of N2.
Change in [H2] = 3 * Change in [N2]
= 3 * 0.079 M
= 0.237 M
Change in [NH3] = 2 * Change in [N2]
= 2 * 0.079 M
= 0.158 M
To calculate the equilibrium concentrations:
[H2] at equilibrium = Initial [H2] + Change in [H2]
= 1.000 M + 0.237 M
= 1.237 M
[NH3] at equilibrium = Initial [NH3] + Change in [NH3]
= 0 M + 0.158 M
= 0.158 M
Finally, we can calculate the equilibrium constant (K) using the equilibrium concentrations:
K = ([NH3] at equilibrium)^2 / ([N2] at equilibrium * [H2] at equilibrium)
= (0.158 M)^2 / (0.921 M * 1.237 M)
= 0.019 M^2 / 1.139 M^2
≈ 0.0167
Therefore, the equilibrium concentrations of hydrogen and ammonia are approximately [H2] = 1.237 M and [NH3] = 0.158 M, respectively. And the equilibrium constant (K) for the reaction is approximately 0.0167.