# How to calculate K_c? "N"_2(g) + "O"_2(g) rightleftharpoons 2"NO"(g)

## The equilibrium concentrations of the gases at 1500K are O2 = 1.7×10-3M; N2 = 6.4×10-3M; NO = 1.1 10-5M. Calculate the value of Kc at 1500K from these data.

Dec 5, 2017

${K}_{c} = 1.1 \cdot {10}^{- 5}$

#### Explanation:

The equilibrium constant is simply a measure of the position of the equilibrium in terms of the concentration of the products and of the reactants in a given equilibrium reaction.

In other words, the equilibrium constant tells you if you should expect the reaction to favor the products or the reactants at a given temperature.

This is done by comparing the equilibrium concentrations and the stoichiometric coefficients of the chemical species involved in the reaction.

${\text{N"_ (2(g)) + "O"_ (2(g)) rightleftharpoons color(red)(2)"NO}}_{\left(g\right)}$

the equilibrium constant takes the form

${K}_{c} = \left(\left[{\text{NO"]^color(red)(2))/(["N"_2] * ["O}}_{2}\right]\right)$

Now, you know that $\text{1500 K}$, the equilibrium concentrations of the three chemical species are equal to

• $\left[\text{NO}\right] = 1.1 \cdot {10}^{- 5}$ $\text{M}$
• $\left[{\text{N}}_{2}\right] = 6.4 \cdot {10}^{- 3}$ $\text{M}$
• $\left[{\text{O}}_{2}\right] = 1.7 \cdot {10}^{- 3}$ $\text{M}$

Right from the start, the fact that, at equilibrium, you have significantly less nitric oxide than nitrogen gas and oxygen gas tells you that at $\text{1500 K}$, the reverse reaction is favored.

This means that at this temperature, if you start with nitrogen gas and oxygen gas, only a very small fractions of the molecules will react to form nitric oxide.

Similarly, if you start with nitric oxide, a very large fraction of the molecules to react and form nitrogen gas and oxygen gas.

This means that you should expect to find

${K}_{c} < 1$

which would be consistent with the fact that the equilibrium lies to the left at this temperature.

${K}_{c} = {\left(1.1 \cdot {10}^{- 5}\right)}^{\textcolor{red}{2}} / \left(6.4 \cdot {10}^{- 3} \cdot 1.7 \cdot {10}^{- 3}\right)$
${K}_{c} = \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{1.1 \cdot {10}^{- 5}}}}$
${K}_{c} < 1$