A 0.750 M sample of phosphorus pentachloride decomposes to give phosphorus trichloride and chlorine gases.If the equilibrium concentration of PCl5 is 0.650M,what is the equilibrium constant for the reaction? PCl5(g) PCl3(g)+ Cl₂(g)

Question

A 0.750 M sample of phosphorus pentachloride decomposes to give phosphorus trichloride and chlorine gases.If the equilibrium concentration of PCl5 is 0.650M,what is the equilibrium constant for the reaction? PCl5(g)  PCl3(g)+ Cl₂(g)

Quizplus · Accepted Answer

The equilibrium constant expression for this reaction is:

Keq = [PCl3] * [Cl2] / [PCl5]

We are given that the equilibrium concentration of PCl5 is 0.650 M. Let's assume that at equilibrium, x moles of PCl5 has decomposed to form x moles each of PCl3 and Cl2. Therefore, the equilibrium concentrations of PCl3 and Cl2 will both be x M.

Using the given initial concentration of PCl5 (0.750 M), we can calculate the initial moles of PCl5:

n = C * V = (0.750 M) * (1.00 L) = 0.750 moles

At equilibrium, the amount of PCl5 remaining will be:

0.750 - x

The equilibrium concentrations of PCl3 and Cl2 will both be x M, so the total moles of both gases will be:

2x

Using the ideal gas law, we can relate the moles of gas to the partial pressure:

n = PV / RT

PV / RT = (2x) / V

P = (2xRT/V)

Substituting the equilibrium concentrations and partial pressures into the equilibrium constant expression, we get:

Keq = [PCl3] * [Cl2] / [PCl5]
Keq = (x) * (x) / (0.750 - x)
Keq = x^2 / (0.750 - x)

We are given that at equilibrium, the concentration of PCl5 is 0.650 M. Therefore, the amount of PCl5 that has decomposed is:

0.750 - 0.650 = 0.100 moles

Substituting this value into the equilibrium constant expression, we get:

Keq = x^2 / (0.750 - 0.100 - x)
Keq = x^2 / 0.650

We can solve for x by using the quadratic formula:

x = (-b +- sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 0, and c = -Keq * 0.650. Therefore:

x = (-0 +- sqrt(0 - 4(1)(-Keq*0.650))) / 2(1)
x = sqrt(Keq*0.650)

Squaring both sides:

x^2 = Keq * 0.650

Substituting into the equilibrium constant expression:

Keq = x^2 / (0.750 - 0.100 - x)
Keq = (Keq * 0.650) / (0.650)
Keq = 0.650

A 0750 M Sample of Phosphorus Pentachloride Decomposes to Give Phosphorus