Solve Equilibrium for Chemical Reaction: 2A <-> B + C

[Hollysmoke]

Homework Statement

The following reaction initially contains [A]o = 0.2150 M and o = [C]o = 0.4150 M. If the equilibrium constant for the reaction is Keq = 2.03, what are the concentrations of reactants and products when the reaction has achieved equilibrium? What is the value of deltaG for the reaction at 25oC?

2 A <-> B + C

Homework Equations

I am stuck as on how to proceed with the math. I'm not sure if I am doing it correctly or not. Could someone please take a look?

The Attempt at a Solution

Initial: 2A B C
0.2150M 0.4150M 0.4150M

Change: +x -x -x
Since Q>Kc, as Qc = [C]/[A]^2

Equil. 0.2150+x 0.4150-x 0.4150-x

I'm stuck on the whole rearranging and solving for x bit. I know I'm supposed to use quadratic formula.

 

[chemisttree]

Substitute the values you know for the equilibrium concentration of A, B and C (A=0.2150+x, B=0.4150-x, C=0.4150-x) into the expression for equilibrium and solve it.

Keq=2.03=[(0.4150-x)^2/(0.2150+x)^2] and expand it out, multiply both sides by (A+x)^2, do the algebra until the expression for Keq is in the form:

0 = ax^2 + bx + c (note that here the terms a, b and c are not the same as A, B and C given in the problem)

Hint: The first step should look like this:

2.03*(0.2150+x)^2 = (0.4150-x)^2, after multiplying both sides by (0.2150+x)^2

 

[Blueshift5]

To solve for equilibrium concentrations, you need to set up an equilibrium expression using the equilibrium constant, Keq. In this case, the equilibrium expression would be Keq = ([C])/([A]^2). Then, you can substitute the given values for initial concentrations and Keq to solve for the unknown concentration (x).

Using the quadratic formula, you can solve for x by setting the expression equal to zero and solving for x. Once you have the value of x, you can plug it back into the equilibrium concentrations equation to find the equilibrium concentrations of reactants and products.

To find the value of deltaG for the reaction at 25oC, you can use the equation deltaG = -RTln(Keq), where R is the gas constant (8.314 J/mol*K) and T is the temperature in Kelvin (25oC + 273.15 = 298.15 K). By plugging in the given value for Keq, you can solve for deltaG. Keep in mind that deltaG is a measure of the spontaneity of a reaction, with negative values indicating a spontaneous reaction and positive values indicating a non-spontaneous reaction.