I am given the following reaction:

2NH3(g) -------> N2(g) + 3H2(g)

My question is:
6.4 mols of ammonia gas has been put into a 1.7 L flask and has been permitted to reach equilibrium in accordance to the reaction listed above. If the equilibrium mixture has 4.2 mols of nitrogen, what is the value of the equilibrium constant supposed to be?

Thank you

To determine the value of the equilibrium constant (K) for the given reaction, we first need to understand the expression for K and how it relates to the reaction equation.

The equilibrium constant is defined as the ratio of the concentration (or partial pressure) of the products to the concentration (or partial pressure) of the reactants, with each concentration term raised to the power of its stoichiometric coefficient in the balanced chemical equation.

For the given reaction: 2NH3(g) → N2(g) + 3H2(g)

The equilibrium constant expression (K) would be:

K = ([N2]^1 * [H2]^3) / ([NH3]^2)

Where [N2], [H2], and [NH3] represent the concentrations of N2, H2, and NH3, respectively, at equilibrium.

Now, let's calculate the value of K using the given information.

Given:
Initial moles of NH3 = 6.4 mol
Final moles of N2 = 4.2 mol
Volume of the flask = 1.7 L

To calculate the concentrations at equilibrium, we need to convert the moles into concentrations by dividing the moles by the volume (in liters).

Initial concentration of NH3 = 6.4 mol / 1.7 L
Final concentration of N2 = 4.2 mol / 1.7 L

Substituting the values into the equilibrium constant expression:

K = ([4.2 / 1.7]^1 * [H2]^3) / ([6.4 / 1.7]^2)

Simplifying the expression:

K = ([2.47]^1 * [H2]^3) / ([3.76]^2)

Now, we do not have the partial pressure, so we cannot directly calculate the value of the equilibrium constant. However, we can determine the relationship between partial pressure and concentration using the ideal gas law.

The ideal gas law states:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Since the reaction takes place in a flask and the volume is constant, we can say that the pressure is directly proportional to the concentration of the gas.

Therefore, we can conclude that the equilibrium constant for this reaction is directly proportional to the ratio of the partial pressures of the products to the partial pressure of the reactants.

In summary, without information about the partial pressures, it is not possible to determine the precise value of the equilibrium constant (K) for the reaction 2NH3(g) → N2(g) + 3H2(g).