PCl5 dissociates according to the reaction: PCl5(g) ↔ PCl3(g) + Cl2(g). One mole of PCl5 was placed in one liter of solution. When equilibrium was established, 0.5 mole of PCl5 remained in the mixture. What is the equilibrium constant for this reaction?
............PCl5 ==> PCl3 + Cl2
initial......1.0M......0......0
change.......-x.......x.......x
equil.......1-x.......x.......x
The problem tells you that 1-x = 0.5; therefore, x = 1.0-0.5= 0.5M which means Pl3 = 0.5M and Cl2 = 0.50M
Then K = (PCl3)(Cl2)/(PCl5) \
Substitute and solve for K.
To find the equilibrium constant (Kc) for the reaction, we can use the concentrations of the products and reactants at equilibrium.
The balanced equation for the reaction is: PCl5(g) ↔ PCl3(g) + Cl2(g)
Given:
Initial concentration of PCl5 (C0) = 1 mole/L
Final concentration of PCl5 (C) = 0.5 mole/L
Since PCl3 and Cl2 are the products of the reaction, their concentrations can be calculated by subtracting the final concentration of PCl5 (C) from the initial concentration (C0):
PCl3 concentration at equilibrium (C) = 1 - 0.5 = 0.5 mole/L
Cl2 concentration at equilibrium (C) = 0.5 mole/L
Now, we can calculate the equilibrium constant (Kc) using the formula:
Kc = [PCl3] * [Cl2] / [PCl5]
Substituting the values into the formula, we get:
Kc = (0.5 * 0.5) / 0.5 = 0.25
Therefore, the equilibrium constant (Kc) for this reaction is 0.25.
To determine the equilibrium constant for the given reaction, we need to calculate the concentration of each species at equilibrium.
We are given that initially, one mole of PCl5 was placed in one liter of solution. Since the volume remains constant, the initial concentration of PCl5 is also one mole per liter.
At equilibrium, we are told that 0.5 mole of PCl5 remains in the mixture. So the concentration of PCl5 at equilibrium is 0.5 moles per liter.
The reaction equation tells us that for each mole of PCl5 that dissociates, one mole of PCl3 and one mole of Cl2 are formed. Therefore, the change in concentration for both PCl3 and Cl2 is also 0.5 moles per liter.
The equilibrium concentration of PCl3 and Cl2 can be calculated as follows:
PCl3: Initial concentration (0) + Change in concentration (0.5) = 0.5 moles per liter
Cl2: Initial concentration (0) + Change in concentration (0.5) = 0.5 moles per liter
Now, we can use the equilibrium concentrations to calculate the equilibrium constant (Kc) using the formula:
Kc = [PCl3][Cl2] / [PCl5]
Substituting the values we calculated:
Kc = (0.5)(0.5) / (0.5) = 0.25
Therefore, the equilibrium constant (Kc) for this reaction is 0.25.