At a certain temperature, 2.00 moles of phosphorus(V) chloride, PCl5, was placed in a 1.0 L vessel and permitted to react as shown:
PCl5 (g) <-> PCl3 (g) + Cl2(g)
At equilibrium, the container held 0.40 PCl5. What is the numerical value of Kc for the system as written?
A) 10
B) 6.4
C) 2.0
D) 1.2
To solve this problem, we need to use the equilibrium constant expression, Kc, which is calculated using the concentrations of the reactants and products at equilibrium.
The balanced equation for the reaction is:
PCl5 (g) <-> PCl3 (g) + Cl2(g)
The equilibrium constant expression for this reaction is:
Kc = [PCl3] * [Cl2] / [PCl5]
We are given that at equilibrium, the container held 0.40 moles of PCl5 in a 1.0 L vessel. Therefore, the concentration of PCl5 is:
[PCl5] = 0.40 moles / 1.0 L = 0.40 M
Since PCl3 and Cl2 are both products in the reaction, we need to determine their concentrations at equilibrium based on their stoichiometry. From the balanced equation, we can see that for every 1 mole of PCl5 that reacts, 1 mole of PCl3 and 1 mole of Cl2 are formed. Therefore, at equilibrium:
[PCl3] = [Cl2] = 0.40 M
Substituting these values into the equilibrium constant expression, we get:
Kc = (0.40 M) * (0.40 M) / (0.40 M) = 0.40
Therefore, the numerical value of Kc for the system as written is 0.40.
Answer: There is no option that matches the correct value for Kc, which is 0.40.
To determine the value of Kc for the system as written, we first need to understand how to calculate Kc.
Kc is the equilibrium constant expressed in terms of concentrations. It is defined as the ratio of the product concentrations to the reactant concentrations, each raised to the power of their respective stoichiometric coefficients.
In this case, the balanced equation is:
PCl5 (g) <-> PCl3 (g) + Cl2(g)
The stoichiometric coefficients are 1 for PCl5, 1 for PCl3, and 1 for Cl2.
Let's denote the initial concentration of PCl5 as [PCl5]₀ and the equilibrium concentration as [PCl5]eq.
According to the problem, at equilibrium, the container holds 0.40 moles of PCl5.
Therefore, [PCl5]₀ = 2.00 moles and [PCl5]eq = 0.40 moles.
Since the volume of the container is 1.0 L and the number of moles is directly proportional to concentration, we can conclude that the initial concentration [PCl5]₀ = 2.00 M and the equilibrium concentration [PCl5]eq = 0.40 M.
Now, we can calculate Kc using the equation:
Kc = ([PCl3]eq * [Cl2]eq) / [PCl5]eq
Given that there was no PCl3 or Cl2 initially in the container, we can assume that [PCl3]eq and [Cl2]eq are both zero.
Substituting the values into the equation, we have:
Kc = (0 * 0) / 0.40
Since any number divided by zero is undefined, the value of Kc for the system cannot be determined from the information given.
Therefore, the answer is not listed among the options provided (A, B, C, D).