Determine Kc for the following reaction:

1/2N2(g) + 1/2O2(g)+ 1/2Br(g) <-> NOBr(g)

from the following information (at 298K)

2No(g) <-> N2(g) + O2(g) Kc = 2.1x10^30

NO(g) + 1/2Br2(g) <-> NOBr(g) Kc = 1.4

Take equn 1, divide by 2, and reverse it. That makes Kc of 2.1E30 = k' [1/(sqrt 2.1E30)]. That is sqrt because you took 1/2 the equation and the reciprocal because you reversed it.

Then add eqn 2 and check to see that it is the equation you want. K for the final rxn is k'*k2 = 1.4/(sqrt 2.1E30) = ??

Thank you so much. I got 9.7 x 10^-16. The answer is correct. I was just confused because why did we only substitute the k values for 2 compounds in the equation rather then all 4?

To determine the equilibrium constant, Kc, for the reaction 1/2N2(g) + 1/2O2(g) + 1/2Br(g) <-> NOBr(g), we can use the given information and the concept of equilibrium constants.

The given information provides two equilibrium constants involving the substances that participate in the reaction we are interested in. We can use these equilibrium constants to derive the desired equilibrium constant.

First, let's examine the first equilibrium equation:
2NO(g) <-> N2(g) + O2(g) Kc = 2.1x10^30

Notice that the equation above can be multiplied by 1/2 to obtain the stoichiometry of the reaction we are looking for. By doing this, we obtain the following equation:
NO(g) + 1/2O2(g) <-> 1/2N2(g) + 1/2O2(g)

This equation is half of the desired reaction equation, and we can use it to derive the equilibrium constant for the half-reaction.

Next, let's examine the second equilibrium equation:
NO(g) + 1/2Br2(g) <-> NOBr(g) Kc = 1.4

Notice that this equation can be rearranged by multiplying it by 1/2 to obtain the stoichiometry of the desired reaction:
1/2NO(g) + 1/4Br2(g) <-> 1/2NOBr(g)

This equation is also half of the desired reaction equation, and we can use it to derive the equilibrium constant for the half-reaction.

Finally, let's combine the two half-reactions to obtain the desired reaction:
(1/2NO(g) + 1/4Br2(g)) + (NO(g) + 1/2O2(g)) <-> (1/2NOBr(g)) + (1/2N2(g) + 1/2O2(g))

Notice that the O2 terms in both sides of the equation cancel each other out. We can simplify the equation to:
1/2NO(g) + 1/4Br2(g) + NO(g) <-> 1/2NOBr(g) + 1/2N2(g)

Now, to calculate the equilibrium constant Kc for the desired reaction, we need to multiply the equilibrium constants for the two half-reactions:
Kc = (Kc1/2O2) * (Kc1/2Br2)
= (1.4) * (2.1x10^30)

To calculate Kc, multiply 1.4 by 2.1x10^30:

Kc ≈ 2.94 x 10^30

Therefore, the equilibrium constant, Kc, for the reaction 1/2N2(g) + 1/2O2(g) + 1/2Br(g) <-> NOBr(g), at 298K is approximately 2.94 x 10^30.

To determine Kc for the given reaction, we can use the concept of equilibrium constant expressions and the law of mass action. The equilibrium constant, Kc, expresses the ratio of the concentrations of products to reactants at equilibrium.

First, let's write the balanced chemical equation for the reaction:

1/2N2(g) + 1/2O2(g) + 1/2Br(g) ↔ NOBr(g)

Based on the given information, we can deduce that:

2NO(g) ↔ N2(g) + O2(g) : Kc = 2.1x10^30
NO(g) + 1/2Br2(g) ↔ NOBr(g) : Kc = 1.4

Now, we can use these equations to determine Kc for the given reaction.

To do this, we need to multiply the two equations by the appropriate factors to obtain the overall balanced equation. We can find these factors by examining the stoichiometric coefficients. Since the coefficient of NOBr in the second equation is 1, and there is no NOBr in the first equation, we don't need to multiply the first equation. However, since the coefficient of NO in the second equation is 1 and there are two NO molecules in the first equation, we need to double the second equation:

2(NO(g) + 1/2Br2(g) ↔ NOBr(g)) : Kc = (1.4)^2

Combining the equations, we get the overall balanced equation:

2NO(g) + 1/2Br2(g) + 1/2N2(g) + 1/2O2(g) ↔ 2NOBr(g)

From the overall equation, we can determine the value of Kc for the given reaction. Since Kc is a product/reactant ratio, we can multiply the individual Kc values:

Kc = (2.1x10^30) * (1.4)^2

Now, you can calculate Kc using the given values for Kc. Simply multiply 2.1x10^30 by (1.4)^2 to get the answer.