The equilibrium constant Kc for the reaction

C <--> D + E

is 7.90 * 10^-5. The initial composition of the reaction mixture is [C]=[D]=[E]=1.10*10^-3. What is the equilibrium concentrations of C, D, and E?

C=?
D=?
E=?
chemistry - DrBob222, Monday, November 5, 2012 at 12:21am
K = 7.9E-5 = (D)(E)/(C)
Qc = (0.0011)(0.0011)/(0.0011) = 0.0011
Qc > Kc; therefore, products are too large and reactants too small. The reaction most go to the left to reach equilibrium.

..........C ==> D ...+... E
I......0.0011..0.0011..0.0011
C.........x.....-x.......-x
E...0.0011+x..0.0011-x.0.0011-x

Substitute the equilibrium line from the ICE chart into Kc expression and solve for x, then 0.0011+x and 0.0011-x.

I got this when I used the quadratic formula(the answer to the quad form was 1.54*10^-3):
D: 0.0011- 1.5*10^-3= -0.00044
E: 0.0011- 1.5*10^-3= -0.00044
C: 0.0011 + 1.54*10^-3 = 0.00264

I got the wrong answers. It is saying I solved the equation correctly, but I need to use the other root of the equation in the ICE chart. What do they mean by that?

That's exactly right. Before I posted the answer for you last night I worked the problem out completely. You KNOW 1.5E-3 can't be right. Why? Because 1.5E-3 is more than you started with (1.10E-3) so you use the other root of the quadratic equation. (So I used the other root and it worked ok--I obtained a reasonable answer). (You know when you solve the quadratic of

[-b +/- sqrt(b^2-4ac)/2a].
So use the other root of the quadratic and things will work out ok. I think the other root gives x = about 0.00072 (I don't have notes--that's the number I remember so confirm that).

Oh! I see what you're saying! See, that's what I thought it meant, but I just wanted to make sure. I have a tendancy to second guess myself when it comes to chemistry.

Don't we all.

In this problem, the equilibrium constant (Kc) is given as 7.90 * 10^-5. The initial concentrations of C, D, and E are all 1.10 * 10^-3. We need to find the equilibrium concentrations of C, D, and E.

To solve this problem, we need to use the concept of the equilibrium constant expression and the ICE (Initial-Change-Equilibrium) chart.

The equilibrium constant expression for the given reaction is:

Kc = [D] * [E] / [C]

We can plug in the given values for Kc and the initial concentrations ([C], [D], and [E]) into this expression. However, before we do that, let's determine the reaction quotient (Qc) using the initial concentrations:

Qc = [D] * [E] / [C]
= (1.10 * 10^-3) * (1.10 * 10^-3) / (1.10 * 10^-3)
= 1.10 * 10^-3

Comparing Qc to Kc, we see that Qc is greater than Kc. This means that the reaction has not yet reached equilibrium and that the products are too large and the reactants are too small. Consequently, the reaction will proceed to the left to reach equilibrium.

To represent the changes that occur during the reaction, we introduce the variable "x" as the change in concentration for C, D, and E.

The ICE chart for this reaction would look like this:

C ==> D + E
Initial [0.0011] |__[0.0011]_|
Change [-x] |__[-x]____|___[+x]___|
Equilibrium [0.0011 - x] |__[0.0011 - x]_+_[+x]____|

Based on the ICE chart, the concentrations at equilibrium for C, D, and E are given as:

C: 0.0011 - x
D: 0.0011 - x
E: 0.0011 - x

We need to substitute these equilibrium concentrations into the equilibrium constant expression (Kc) and solve for x.

Kc = [D] * [E] / [C]
= (0.0011 - x) * (0.0011 - x) / (0.0011 - x)

Since the quadratic equation arises after substituting these values, you correctly used the quadratic formula, and one of the roots you found is 1.54 * 10^-3. However, it is important to note that in this case, the other root (-x) is the valid solution for x because the equilibrium concentrations cannot be negative.

Therefore, the correct equilibrium concentrations are:

C: 0.0011 + 1.54 * 10^-3 = 0.00264
D: 0.0011 - 1.54 * 10^-3 = -0.00044 (rounding to 4 decimal places)
E: 0.0011 - 1.54 * 10^-3 = -0.00044 (rounding to 4 decimal places)

It is important to note that the negative values for D and E are not physically meaningful since concentrations cannot be negative. In such cases, we generally treat them as zero in our calculations. Therefore, the correct equilibrium concentrations are:

C: 0.00264
D: 0 (treat as 0 since it is negative)
E: 0 (treat as 0 since it is negative)