Using this data,

2 NO(g) + Cl2(g) == 2 NOCl(g) Kc = 3.20 X 10-3

NO2(g) == NO(g) + ½ O2(g) Kc = 3.93

calculate a value for Kc for the reaction,

NOCl (g) + ½ O2 (g) == NO2 (g) + ½ Cl2 (g)

So I understand that
2NO + Cl2 + 1/2O2 = NO2 + 1/2 Cl2 but I do not understand how you use the Kc values that are given since this equation is slightly different. 2NO + Cl2 is in the first equation but then the 1/2O2 is in the second equation and they both have different Kc values.

To calculate the value of Kc for the given reaction, we can use a concept called the equilibrium constant (Kc). The equilibrium constant is a mathematical representation of the ratio of product concentrations to reactant concentrations at equilibrium.

First, we need to write the balanced equation for the given reaction:

NOCl (g) + ½ O2 (g) → NO2 (g) + ½ Cl2 (g)

To calculate the value of Kc, we use the Kc values from the given equations through a process called equilibrium constant manipulation. Here's how to do it step by step:

1. Write the balanced equations and their corresponding Kc values:

a) 2NO (g) + Cl2 (g) → 2NOCl (g) Kc = 3.20 x 10^-3

b) NO2 (g) → NO (g) + ½ O2 (g) Kc = 3.93

2. Identify the common compounds and their stoichiometric coefficients between the given equation and the equation(s) with known Kc values.

In this case, we can see that NO is a common compound, but the stoichiometric coefficients are different. Let's multiply equation b) by 2 to match the stoichiometric coefficient of NO:

2NO2 (g) → 2NO (g) + O2 (g)

3. Combine the equations by adding them together, canceling out any spectator species (species that appear on both sides of the equation):

2NO (g) + Cl2 (g) + ½ O2 (g) → 2NOCl (g) + ½ O2 (g) + O2 (g)

4. Simplify the equation with the canceled species:

2NO (g) + Cl2 (g) → 2NOCl (g) + 1½ O2 (g)

5. Rewrite the equation by adjusting the stoichiometric coefficients:

2NO (g) + Cl2 (g) → 2NOCl (g) + ¾ O2 (g)

6. Write the corresponding Kc expression using the law of mass action. The exponents are determined by the stoichiometric coefficients:

Kc = [(NOCl)² * (O₂)^(¾)] / (NO)² * (Cl₂)

Since the stoichiometric coefficient of Cl₂ is 1, we can simplify further:

Kc = [(NOCl)² * (O₂)^(¾)] / (NO)²

7. Substitute the given Kc values from equations a) and b) into the Kc expression:

Kc = [(3.20 x 10^-3)² * (3.93)^(¾)] / (3.93)²

Calculate the value using this expression.

This step-by-step process allows us to manipulate the provided Kc values to calculate the Kc value for the given reaction.