A solution contains 0.01M ethyl acetate, 0.10M acetic acid and 0.10M ethanol. For the same equilibriujm constant of 2.00, calculate the equilibrium concentrations of ethyl acetate, ethanol, and acetic acid in the solution.
To calculate the equilibrium concentrations of ethyl acetate, ethanol, and acetic acid in the solution, we need to use the equilibrium constant expression and set up an ICE (Initial, Change, Equilibrium) table.
The equilibrium constant expression for the reaction is given as:
Kc = [ethanol] * [acetic acid] / [ethyl acetate]
Where [ethanol], [acetic acid], and [ethyl acetate] represent the equilibrium concentrations of each respective species.
Let's denote the change in concentration of each species as x. Since we have the initial concentrations of each species, we can set up the ICE table as follows:
Species Initial Concentration (M) Change (M) Equilibrium Concentration (M)
Ethyl acetate 0.01 -x 0.01 - x
Acetic acid 0.10 -x 0.10 - x
Ethanol 0.10 +x 0.10 + x
Now, we need to use the equilibrium constant expression to relate the changes in concentrations:
Kc = [ethanol] * [acetic acid] / [ethyl acetate]
Substituting the equilibrium concentrations from the ICE table into the expression:
2.00 = (0.10 + x) * (0.10 - x) / (0.01 - x)
Simplifying the equation:
2.00 = (0.01 - x)(0.10 + x) / (0.01 - x)
Multiplying both sides of the equation by (0.01 - x) to eliminate the denominator:
2.00 * (0.01 - x) = (0.01 - x)(0.10 + x)
Expanding and rearranging:
0.0200 - 0.02x = 0.001 - 0.09x^2
0.09x^2 - 0.02x + 0.019 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
By substituting a = 0.09, b = -0.02, and c = 0.019 into the quadratic formula:
x = (-(-0.02) ± √((-0.02)^2 - 4 * 0.09 * 0.019)) / (2 * 0.09)
Simplifying the equation:
x = (0.02 ± √(0.0004 - 0.00684)) / 0.18
x = (0.02 ± √(-0.00644)) / 0.18
Since the discriminant is negative, the equation does not yield real solutions. It suggests that the reaction may not proceed to form a significant amount of either ethyl acetate or acetic acid. Thus, under these conditions, the equilibrium concentrations of ethyl acetate, acetic acid, and ethanol are essentially equal to their initial concentrations of 0.01 M, 0.10 M, and 0.10 M, respectively.