Initially, we place 2 mol of A and 4 mol of B in a 0.5 L flask. At equilibrium, the flask contains 0.3 mol of C. Determine the value of K.
A(g) + B(g) <--> 3C(g) + 2D(g)
.........A + B ==> 3C + 2D
I........2...4.....0....0
C.......-x..-x...+3x...+2x
E.......2-x.4-x..0.3...+2x
Column 3C means x must be 0.3/3 = 0.1 (I didn't change C, it still is 0.3 since 0.1 x 3 = 0.3) That makes column D equilibrium = 0.1*2 = 0.2 mols
Column A = 2-0.1 and colum B = 4-0.1.
Convert mols A, B, C, and D at equilibrium to molarity (mols/L = M) and substitute into the K expression. Solve for K.
My chem teacher said that initial concentrations of A and B and the equilibrium concentration of C need to be doubled to put the experiment into a L from the 0.5L we started with in the question.
To determine the value of K, we need to write the equilibrium expression based on the given chemical equation:
K = [C]^3[D]^2 / [A][B]
Given that at equilibrium, the flask contains 0.3 mol of C, we can substitute the value into the equilibrium expression:
K = (0.3 mol)^3[D]^2 / [A][B]
However, we don't have information about the concentration of D, so we cannot determine the exact value of K without that information.
To determine the value of K, we need to first set up the balanced equilibrium equation and express the concentration of each component at equilibrium.
The balanced equilibrium equation is:
A(g) + B(g) ⇌ 3C(g) + 2D(g)
Let's define the following variables:
[A]eq - concentration of A at equilibrium
[B]eq - concentration of B at equilibrium
[C]eq - concentration of C at equilibrium
[D]eq - concentration of D at equilibrium
Given:
Initial moles of A = 2 mol
Initial moles of B = 4 mol
Total volume of the flask = 0.5 L
Since there is no information about moles of C or D initially, we assume they are zero.
Now, let's calculate the concentrations of A, B, C, and D at equilibrium:
[A]eq = (moles of A at equilibrium) / (volume of the flask)
= (2 - 1.5) mol / 0.5 L
= 0.5 mol/L
[B]eq = (moles of B at equilibrium) / (volume of the flask)
= (4 - 1.5) mol / 0.5 L
= 5 mol/L
[C]eq = (moles of C at equilibrium) / (volume of the flask)
= 0.3 mol / 0.5 L
= 0.6 mol/L
[D]eq = (moles of D at equilibrium) / (volume of the flask)
= (moles of C formed) / (volume of the flask)
= 0.3 mol / 0.5 L
= 0.6 mol/L
Now, let's calculate the value of K using the concentration values at equilibrium:
K = ([C]eq^3 * [D]eq^2) / ([A]eq * [B]eq)
= (0.6^3 * 0.6^2) / (0.5 * 5)
= 0.216 / 2.5
= 0.0864
Therefore, the value of K for the given chemical equilibrium is approximately 0.0864.