A 0.229 mol sample of PCL5 is injected into an empty 3.20 L reaction vessel held at 250 degrees celsius. Calculate the concentration of PCl5 and PCl3 at equilibrium.
Kc=1.80 M
PCl5 -------> PCl3 + Cl2
(PCl5) = 0.229/3.20 = approx 0.072 but you should start over and calculate more accurately.
......PCl5 -------> PCl3 + Cl2
I.....0.072..........0......0
C.......-x...........x......x
E....0.072-x.........x......x
Substitute the E line into Kc expression and solve for x = (PCl3) = (Cl2) and 0.072-x = (PCl5)
To calculate the concentration of PCl5 and PCl3 at equilibrium, we need to use the given equilibrium constant (Kc) and the initial moles of PCl5.
1. First, calculate the initial concentration of PCl5:
Concentration (initial) = Moles / Volume in liters
Initial concentration of PCl5 = (0.229 mol) / (3.20 L)
2. Since we are dealing with a reaction in which one component dissociates into two components, we need to express the equilibrium concentrations of PCl5, PCl3, and Cl2 in terms of 'x' (change in concentration) in the reaction.
3. The reaction is:
PCl5 ------> PCl3 + Cl2
At equilibrium, the concentration of PCl5 will be (0.229 - x) M,
the concentration of PCl3 will be x M, and
the concentration of Cl2 will also be x M.
4. Use the information above to set up the equilibrium expression:
Kc = [PCl3] * [Cl2] / [PCl5]
Kc = (x * x) / (0.229 - x)
5. Substitute the given value of Kc (1.80) and solve for 'x':
1.80 = (x * x) / (0.229 - x)
Rearrange the equation and set it equal to zero:
(x^2) - (1.80 * 0.229) + (1.80 * x) = 0
6. Solve the quadratic equation using the quadratic formula. The quadratic equation (ax^2 + bx + c = 0) can be solved using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = (-1.80 * 0.229), and c = (1.80 * 0.229).
Substitute these values into the quadratic formula to solve for 'x'.
7. Once you find the value of 'x', substitute it back into the expressions for the equilibrium concentrations:
[PCl5] (at equilibrium) = 0.229 - x
[PCl3] (at equilibrium) = x
[Cl2] (at equilibrium) = x
These concentrations will give you the equilibrium concentrations of PCl5 and PCl3 in the reaction vessel.