Calculation of moles of Cl2 produced at equilibrium

Equation:
PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)

Given:
Initial moles of PCl5 = 1 mole
Volume of vessel = 10 dm3
Kc = 0.041

Step 1: Write the equilibrium expression
Kc = [PCl3][Cl2]/[PCl5]

Step 2: Define the change in moles
Let x be the number of moles of PCl5 that reacts to form PCl3 and Cl2.
Therefore, the moles of PCl3 and Cl2 formed will also be x.

Step 3: Write the equilibrium concentrations
[PCl5] = (1-x)/10
[PCl3] = x/10
[Cl2] = x/10

Step 4: Substitute the equilibrium concentrations and Kc into the equilibrium expression
0.041 = (x/10)*(x/10)/((1-x)/10)

Step 5: Simplify and solve for x
0.041(1-x) = x^2
0.041 - 0.041x = x^2
x^2 + 0.041x - 0.041 = 0
Using the quadratic formula:
x = 0.198 moles

Therefore, at equilibrium, 0.198 moles of Cl2 will be produced.

Explanation:
The given equation is in the form A ⇌ B + C. This means that one mole of A can react to form one mole of B and one mole of C. At equilibrium, the rate of the forward reaction is equal to the rate of the backward reaction. The equilibrium constant Kc is the ratio of the concentration of the products to the concentration of the reactants at equilibrium. In this case, Kc = [PCl3][Cl2]/[PCl5].

To solve for the moles of Cl2 produced at equilibrium, we need to set up an equation that represents the concentrations of PCl5, PCl3, and Cl2 at equilibrium. We can use the change in moles (x) to represent the amount of PCl5 that reacts to form PCl3 and Cl2. Using this information, we can write the equilibrium concentrations of each species in terms of x.

Substituting these equilibrium concentrations and Kc into the equilibrium expression gives us an equation that we can solve for x. Once we know x, we can calculate the moles of Cl2 produced at equilibrium.

Overall, this problem demonstrates how to use the equilibrium constant and the law of mass action to calculate the concentrations of species at equilibrium. It also shows how to use the concept of stoichiometry to relate the concentrations of different species in a chemical reaction.