The "REVERSIBLE" chemical reaction-
A + B <--> C + D
Kc = CD / AB =4.4
Concentration at the start and after equilibrium-
A = 1.00 M --> (1.00 - X) M
B = 2.00 M --> (2.00 - X) M
C = 0.00 M --> X M
D = 0.00 M --> X M
4.4 = X^2 / (1.00-X)(2.00 - X)
I'm not sure what to do next, Can someone please help me out?
You solve for x. I think you use the FOIL method
The chemistry is right. It's an algebra problem now. Solve for X. Chopsticks is right. Expand the denominator by using FOIL, gather terms and solve the quadratic equation.
To solve this equilibrium problem, you need to use the given equilibrium constant expression and the initial concentrations to determine the value of X, which represents the change in concentration.
Let's start with the given equation:
Kc = [C][D] / [A][B] = 4.4
To solve for X, you can rearrange the equation as follows:
4.4 = X^2 / [(1.00-X)(2.00 - X)]
Now, cross-multiply to get rid of the fraction:
4.4 * [(1.00-X)(2.00 - X)] = X^2
Expand the right side and simplify the left side:
4.4 * (1.00 - X)(2.00 - X) = X^2
8.8 - 10.4X + 3.2X^2 = X^2
Combine like terms:
3.2X^2 - X^2 - 10.4X + 8.8 = 0
2.2X^2 - 10.4X + 8.8 = 0
Now, you have a quadratic equation. You can solve it using the quadratic formula:
X = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2.2, b = -10.4, and c = 8.8.
X = (-(-10.4) ± √((-10.4)^2 - 4(2.2)(8.8))) / (2(2.2))
Simplify the equation:
X = (10.4 ± √(108.16 - 77.44)) / 4.4
X = (10.4 ± √30.72) / 4.4
Now, you can solve for X by calculating both the positive and negative roots:
X1 = (10.4 + √30.72) / 4.4
X2 = (10.4 - √30.72) / 4.4
Evaluate X1 and X2 to find the values of X. Keep in mind that X represents the change in concentration, so you need to subtract the values from the initial concentrations to obtain the concentrations at equilibrium.