Calculate the equilibrium concentrations of N2, H2, and NH3 present when a mixture that was initially 0.10M N2, 0.10M H2, and 0.10M NH3 comes to equilibrium at 500 degrees C.

N2(g) + 3H2(g) equilibrium arrows 2NH3(g)
Kc = 0.040 (at 500 degrees C)

To calculate the equilibrium concentrations of N2, H2, and NH3, we need to use the equilibrium constant expression and the given initial concentrations.

The equilibrium constant expression for the given reaction is:
Kc = [NH3]^2 / ([N2] * [H2]^3)

Given information:
Initial concentration of N2 ([N2]initial) = 0.10 M
Initial concentration of H2 ([H2]initial) = 0.10 M
Initial concentration of NH3 ([NH3]initial) = 0.10 M
Equilibrium constant (Kc) = 0.040

To solve for the equilibrium concentrations, we'll use an ICE table (Initial, Change, Equilibrium):

Step 1: Write the balanced chemical equation:
N2(g) + 3H2(g) ⇌ 2NH3(g)

Step 2: Set up the ICE table:

N2(g) + 3H2(g) ⇌ 2NH3(g)
Initial 0.10 M 0.10 M 0.10 M
Change -x -3x +2x
Equilibrium 0.10 - x 0.10 - 3x 0.10 + 2x

In the table, 'x' represents the change in concentration at equilibrium.

Step 3: Write the expression for Kc using the equilibrium concentrations:
Kc = [NH3]^2 / ([N2] * [H2]^3)

Plugging in the equilibrium concentrations from the ICE table, we get:
0.040 = (0.10 + 2x)^2 / ((0.10 - x) * (0.10 - 3x)^3)

Step 4: Solve the equation for x using the quadratic formula or other appropriate methods.

After solving the equation, you can substitute the value of x back into the expressions for the equilibrium concentrations to find their values.