At a certain temperature, this reaction establishes an equilibrium with the given equilibrium constant, kc. if, at this temperature, 2.20 mol of a and 3.70 mol of b are placed in a 1.00-l container, what are the concentrations of a, b, and c at equilibrium?

Explanation:

Hello,

In this case, probably, the undergoing chemical reaction is:

Nonetheless, the equilibrium constant is not given, but could be assumed, therefore, let me assume it is 1.13x10¹⁹ (very close to a constant I found for a similar exercise on the Ethernet), thus, the initial concentrations of A and B are computed below based on the given moles and the container volume:

In such a way, by applying the law of mass action in addition to the ICE table, the equilibrium statement turn out into:

Now, by inserting the initial concentrations of both A and B and the reaction change, , one obtains:

Such equation is a highly non-lineal one, that is why we must apply a method such as Newton-Raphson to compute the roots which define the value of the change , thus, after applying it, the roots are:

The valid root is as the other one produces a negative concentration of A at equilibrium, therefore, the requested concentration turn out into:

However, you can just modify Kc if is different to the one I assumed and perform the Newton-Raphson method to compute the adequate root.

Best regards.