In the gaseous phase PCl5 dissociates according to the following equilibrium: PCl5⇌PCl3+Cl2 and Kc=0.8 at 613K .Determine the equilibrium composition when 0.12 moles/L of the three compounds are mixed at 613K.
First you must determine which way the reaction will shift to react equilibrium. That is done with Qc.
Qc = (PCl3)(Cl2)/(PCl5) = 0.12*0.12/0.12 = 0.12= Qc and Kc = 0.8 so Qc is too small which means products are too low and reactant is too high so shift must be from left to right.
......PCl5 ==> PCl3 + Cl2
I....0.12......0.12...0.12
C.....-x.........x......x
E..0.12-x....0.12+x...0.12+x
Substitute the E line into Kc expression and solve for x, then evaluate each component according to the E line. You will need to solve the quadratic; I get approx 0.07 M
Using your numbers, looks like Kc < Qc. Rx shifts from product side to reactant side. Shouldn't the PCl5 increase and PCl3 & Cl2 decrease?
No. Qc = 0.12; Kc = 0.8
Qc < Kc (or in your language Kc > Qc). Therefore, to make Qc = Kc requires products to increase and reactant to decrease. If you try shifting the reaction the other way you get a negative number for x and that can't be. Try working the problem and if x is 0.0732 then PCl5 = 0.12-0.0732 =0.0468. PCl3 = Cl2 = 0.12 + 0.0732 = 0.1932. Then (0.1932)^2/(0.0486) = 0.798 which rounds to 0.8. QED
To determine the equilibrium composition of the given equilibrium reaction, we need to use the concept of stoichiometry and the equilibrium constant expression.
Step 1: Write the balanced equation for the reaction:
PCl5 ⇌ PCl3 + Cl2
Step 2: Set up the equilibrium expression using the given equilibrium constant (Kc):
Kc = [PCl3] * [Cl2] / [PCl5]
Step 3: Define the initial and equilibrium concentrations:
Let x be the amount of PCl5 that dissociates.
Initial concentrations:
[PCl5]₀ = 0.12 moles/L
[PCl3]₀ = 0 moles/L (since none exists initially)
[Cl2]₀ = 0 moles/L (since none exists initially)
Equilibrium concentrations:
[PCl5] = 0.12 - x mole/L (moles of PCl5 remaining)
[PCl3] = x mole/L (moles of PCl3 formed)
[Cl2] = x mole/L (moles of Cl2 formed)
Step 4: Substitute the equilibrium concentrations into the equilibrium expression:
Kc = ([PCl3] * [Cl2]) / [PCl5]
Kc = (x * x) / (0.12 - x)
Step 5: Solve for x using the given equilibrium constant value (Kc = 0.8):
0.8 = (x * x) / (0.12 - x)
Step 6: Rearrange the equation and solve for x:
0.8 * (0.12 - x) = x^2
0.096 - 0.8x = x^2
x^2 + 0.8x - 0.096 = 0
This is a quadratic equation, which can be solved using various methods (factoring, completing the square, quadratic formula, etc.). After solving for x, substitute the obtained value of x back into the equilibrium concentration expressions to find the equilibrium composition.
Note: The equation provided in Step 6 will yield two values of x, but only the positive value should be considered, as negative concentrations are not physically meaningful.