# Homework Help: Doubt in chemical equilibrium question.

1. Sep 24, 2009

### pc2-brazil

1. The problem statement, all variables and given/known data

For the chemical equilibrium $$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$$ , the following values were found for the constant Kc (chemical equilibrium constant), at the indicated temperatures:
(The table is attached as an image)
Code (Text):

Table in text format:
Temperature (K)    Kc (10^-4)
I   1800               1.21
II  2000               4.08
III 2100               6.86
IV  2200               11.0
V   2300               16.9
There is higher molar concentration of NO(g) in:
a) I
b) II
c) III
d) IV
e) V

2. Relevant equations

General form of the formula for finding the chemical equilibrium constant with respect to the molar concentrations of the reagents and products at the state of equilibrium:
$$K_c = \frac{[P]^p}{[R]^r}$$
Where P are the products of the chemical reaction, R are the reagents, [] denotes molar concentration (mol/L) and p and r are the coefficients of each product and reagent in the chemical equation.

3. The attempt at a solution

The expression for the equilibrium constant of the given reaction is:
$$K_c = \frac{[NO]^2}{[N_2][O_2]}$$
Where [X] denotes molar concentration of X.
As the concentration of NO, [NO], gets bigger, the fraction with [NO]2 as numerator also gets bigger; so, Kc gets bigger.
Then, the situation where Kc is the biggest should be the one with the highest concentration of NO. In this case, the answer would be letter E) V, since, in V, Kc equals 16.9.
So, the correct answer should be E (the highest Kc).
But the book says the correct answer is A (the smallest Kc), not E.
What is wrong with this reasoning?

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Last edited: Sep 25, 2009
2. Sep 25, 2009

### Staff: Mentor

Have you shown all information? Are you perhaps told something about volume of the reaction vessel? Is it the same mixture each time? Was it started with known amount of substances?

And why do you think "a" is a correct answer?

--
methods

3. Sep 25, 2009

### pc2-brazil

Yes, that is all the information of the problem.
We weren't clear at the end: we think the correct answer is E (for the reasons explained in the message, that is, from the equilibrium constant expression, higher Kc means higher [NO]), but the book says it is A.
NOTE: Although the problem didn't tell anything, it is probably the same mixture each time, and temperature is the factor which is changing Kc and shifting the equilibrium of the reaction. We also assume that the volume remains the same.

Last edited: Sep 25, 2009
4. Sep 25, 2009

### pc2-brazil

We have just confirmed that the answer given in the book is wrong... It is actually E, just as we thought.