Calculate the concentration equilibrium constant for the decomposition of ammonia at the final temperature of the mixture. Round your answer to 2 significant digits.

Steps to Solve

1. Identify the reaction and stoichiometry

The decomposition of ammonia can be represented by the following balanced chemical equation:

$$ 2 \text{NH}_3 (g) \rightleftharpoons \text{N}_2 (g) + 3 \text{H}_2 (g) $$

From the stoichiometry of the reaction, for every 2 moles of ammonia, 3 moles of hydrogen are produced, and 1 mole of nitrogen is produced.

2. Calculate the initial and change in moles

Initial amount of ammonia = 6.4 mol.

Amount of hydrogen at equilibrium = 7.7 mol.

From the balanced equation:

Let ( x ) be the change in moles of NH(_3). The relationship is:

• 2 moles of NH(_3) decomposes to produce 3 moles of H(_2).

Using this stoichiometry:

$$ \frac{3}{2} \text{ of } x = 7.7 $$

This helps us find ( x ).

3. Calculate ( x )

To find ( x ):

$$ x = \frac{2}{3} \times 7.7 $$

Calculate ( x ).

4. Determine equilibrium moles of ammonia

Now calculate the moles of NH(_3) at equilibrium:

$$ \text{Equilibrium moles of NH}_3 = \text{Initial NH}_3 - x $$

5. Calculate concentrations

The volume of the tank is 100 L.

The concentrations at equilibrium are:

• For NH(_3):

$$ [\text{NH}_3] = \frac{\text{Equilibrium moles of NH}_3}{100} $$

• For H(_2):

$$ [\text{H}_2] = \frac{7.7}{100} $$

6. Calculate the equilibrium constant ( K_c )

The equilibrium constant ( K_c ) is given by:

$$ K_c = \frac{[\text{N}_2][\text{H}_2]^3}{[\text{NH}_3]^2} $$

Since the number of moles of nitrogen produced is half of ( x ), find ( [\text{N}_2] ) and substitute all concentrations into this equation.

7. Final Calculation

Substitute the values into ( K_c ) and calculate. Round the final answer to 2 significant digits.