Phosphorus pentachloride decomposes according to the chemical equation
PCl5(g) ⇌ PCl3(g) + Cl2(g)
A 0.304 mol sample of PCl5(g) is injected into an empty 4.75 L reaction vessel held at 250 °C. Calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium.
To find the concentrations of PCl5(g) and PCl3(g) at equilibrium, we need to calculate the equilibrium constant (K) for the given reaction. The equilibrium constant relates the concentrations of the reactants and products at equilibrium.
The equilibrium constant expression for the given reaction is:
K = ([PCl3] * [Cl2]) / [PCl5]
Given that the initial moles of PCl5 is 0.304 mol and the volume of the reaction vessel is 4.75 L, we can assume that the concentration of PCl5 is equal to its initial moles divided by the volume of the reaction vessel:
[PCl5] = 0.304 mol / 4.75 L
Since the reaction vessel is empty initially, the concentrations of PCl3 and Cl2 are both initially zero, so:
[PCl3] = [Cl2] = 0
Plugging these values into the equilibrium constant expression, we get:
K = (0 * 0) / (0.304 mol / 4.75 L)
Simplifying the expression, we find:
K = 0
Since the equilibrium constant (K) is zero, it indicates that the reaction proceeds in the backward direction (from right to left). Therefore, at equilibrium, the concentration of PCl5 will be 0, and the concentrations of PCl3 and Cl2 will also be 0.
To calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium, we need to use the concept of equilibrium constants and the given information. In this case, we're dealing with the equilibrium constant, Kc.
First, we need to write the balanced chemical equation:
PCl5(g) ⇌ PCl3(g) + Cl2(g)
The equilibrium constant expression for this reaction is given by:
Kc = [PCl3] * [Cl2] / [PCl5]
Now, let's convert the given information and set up an ICE table (Initial, Change, Equilibrium):
Given:
Initial moles of PCl5 = 0.304 mol
Volume of the reaction vessel = 4.75 L
Using the ideal gas law (PV = nRT), we can calculate the initial concentration of PCl5:
Initial concentration of PCl5 = moles / volume
Initial concentration of PCl5 = 0.304 mol / 4.75 L
Now, let's assume that the amount of PCl3 and Cl2 formed is "x" mol.
ICE table:
PCl5 ⇌ PCl3 + Cl2
Initial 0.304 0 0
Change -x +x +x
Equilibrium (0.304 - x) x x
Since we're given that the reaction vessel is empty initially, the initial concentration of PCl3 and Cl2 would be zero. So, we only need to consider the change and equilibrium concentrations for PCl5.
The equilibrium concentration of PCl5 can be expressed as (0.304 - x) / 4.75.
The equilibrium concentration of PCl3 can be expressed as x / 4.75.
Now, we need to use the value of Kc to determine the value of x. The equilibrium constant expression is given as:
Kc = [PCl3] * [Cl2] / [PCl5]
Substitute the equilibrium concentrations into the expression:
Kc = (x / 4.75) * (x / 4.75) / ((0.304 - x) / 4.75)
Simplify the expression:
Kc = x^2 / (0.304 - x)
Now, we have a quadratic equation in terms of x. We can rearrange it and solve for x using the quadratic equation formula.
Once we have the value of x, we can substitute it back into the equilibrium expressions for PCl5 and PCl3 to calculate their equilibrium concentrations.
Note: The value of Kc can be given in the question or you might need additional information to solve for Kc.