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.

1 Answer
Dec 5, 2017

#K_c = 1.1 * 10^(-5)#


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.

For your equilibrium reaction

#"N"_ (2(g)) + "O"_ (2(g)) rightleftharpoons color(red)(2)"NO"_ ((g))#

the equilibrium constant takes the form

#K_c = (["NO"]^color(red)(2))/(["N"_2] * ["O"_2])#

Now, you know that #"1500 K"#, the equilibrium concentrations of the three chemical species are equal to

  • #["NO"] = 1.1 * 10^(-5)# #"M"#
  • #["N"_2] = 6.4 * 10^(-3)# #"M"#
  • #["O"_2] = 1.7 * 10^(-3)# #"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 #"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.

So, plug in your values to find--I'll skip the added units

#K_c = (1.1 * 10^(-5))^color(red)(2)/(6.4 * 10^(-3) * 1.7 * 10^(-3))#

#K_c = color(darkgreen)(ul(color(black)(1.1 * 10^(-5))))#

As predicted, you have

#K_c < 1#

which confirms why you have higher concentrations of nitrogen gas and oxygen gas than nitric oxide at equilibrium.