a chemist puts 6 moles of nitrogen gas and 7 moles hydrogen gas into an evacuated 1 liter container. The system reaches equilibrium at a certain temperature according to the process outlined above. when the system is at equilibrium the chemist determines the ammonia concentration is 4.0M. What is the equilibrium constant Kc for this process at this temperature?
To calculate the equilibrium constant, Kc, for the given process, we can use the balanced chemical equation for the formation of ammonia (NH3) from nitrogen gas (N2) and hydrogen gas (H2). The balanced equation is:
N2(g) + 3H2(g) ⇌ 2NH3(g)
The stoichiometric coefficients in the balanced equation show that 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas to produce 2 moles of ammonia gas.
Now, we can use the given information to determine the initial and equilibrium concentrations of the reactants and products.
The initial concentration of nitrogen gas (N2) is 6 moles in a 1-liter container, so its initial concentration is 6 M (moles per liter).
The initial concentration of hydrogen gas (H2) is 7 moles in a 1-liter container, so its initial concentration is 7 M.
The initial concentration of ammonia gas (NH3) is zero since none of it was initially present.
At equilibrium, the concentration of ammonia gas (NH3) is given as 4.0 M.
Now, we need to determine the concentrations of nitrogen gas (N2) and hydrogen gas (H2) at equilibrium.
Using the stoichiometry of the balanced equation, we know that for every 1 mole of nitrogen gas reacting, 2 moles of ammonia gas are produced. Therefore, the concentration of nitrogen gas at equilibrium would be 6 moles - (1 mole * 2) = 4 moles. Since the volume remains constant at 1 liter, the concentration of nitrogen gas is 4 M.
Similarly, for every 3 moles of hydrogen gas reacting, 2 moles of ammonia gas are produced. Therefore, the concentration of hydrogen gas at equilibrium would be 7 moles - (3 moles * 2) = 1 mole. Again, since the volume remains constant at 1 liter, the concentration of hydrogen gas is 1 M.
Now, we have all the necessary concentrations to calculate the equilibrium constant, Kc, which is defined as the ratio of the product concentrations to the reactant concentrations, with each concentration raised to the power of its stoichiometric coefficient.
Kc = [NH3]^2 / ([N2] * [H2]^3)
Plugging in the values we determined:
Kc = (4.0 M)^2 / (4.0 M * (1.0 M)^3)
Simplifying:
Kc = 16.0 M^2 / 4.0 M = 4.0 M
Therefore, the equilibrium constant (Kc) for this process at the given temperature is 4.0 M.