A sample of gaseous PCl5 was introduced into an evacuated flask so that the pressure of pure PCl5 would be 0.54 atm at 425 K. However, PCl5 decomposes to gaseous PCl3 and Cl2, and the actual pressure in the flask was found to be 0.85 atm. Calculate Kp for the decomposition reaction below at 425 K. Also calculate K at this temperature.

Question

A sample of gaseous PCl5 was introduced into an evacuated flask so that the pressure of pure PCl5 would be 0.54 atm at 425 K. However, PCl5 decomposes to gaseous PCl3 and Cl2, and the actual pressure in the flask was found to be 0.85 atm. Calculate Kp for the decomposition reaction below at 425 K. Also calculate K at this temperature.

Answer 1

..........PCl5 ==> PCl3 + Cl2

I.........0.54......0......0
C..........-p.......p......p
E.......0.54-p

Ptotal = 0.85 = 0.54-p+p+p
p = 0.31 atm.
pPCl5 = 0.23
pPCl3 = 0.31
pCl2 = 0.31
Substitute these values into Kp expression and solve for Kp.
Kp = Kc*RT^deltan . Substitute Kp and solve for Kc.

Answer 2

Well, let's break down the decomposition reaction of PCl5. It forms PCl3 and Cl2.

Now, the partial pressure of PCl5 in the flask is 0.54 atm, but the actual pressure is 0.85 atm. So some of the PCl5 has decomposed and increased the pressure.

To determine the partial pressures of PCl3 and Cl2, we need to subtract the initial pressure of PCl5 (0.54 atm) from the total pressure (0.85 atm).

So, the partial pressure of PCl3 would be 0.85 atm - 0.54 atm = 0.31 atm.

Similarly, the partial pressure of Cl2 would also be 0.85 atm - 0.54 atm = 0.31 atm.

Now, to calculate Kp, which is the equilibrium constant in terms of partial pressures, we use the formula:

Kp = (PCl3 * PCl2) / PCl5

Substituting in the partial pressures we found, we get:

Kp = (0.31 atm * 0.31 atm) / 0.54 atm
≈ 0.178 atm

As for K, the equilibrium constant in terms of concentration, we need to convert the partial pressures to concentrations using the ideal gas law:

PV = nRT

First, let's find the number of moles of PCl5:

n = (PV) / RT
= (0.54 atm * V) / (0.0821 L atm/mol K * 425 K)

Now, since moles are conserved in the reaction, the moles of PCl3 and Cl2 formed would also be equal to n.

Now, we can write the expression for K:

K = [PCl3] * [Cl2] / [PCl5]
= (n/V) * (n/V) / (n/V)

Since n/V is just the concentration, we can simplify further:

K = [PCl3]^2 / [PCl5]
= (0.31 mol/L)^2 / (0.54 mol/L)
≈ 0.18

So, Kp for the decomposition reaction is approximately 0.178 atm, and K is approximately 0.18 at 425 K.

Answer 3

To calculate Kp for the decomposition reaction at 425 K, we need to use the expression:

Kp = (PCl3 * Cl2) / PCl5

where PCl3, Cl2, and PCl5 are the partial pressures of each gas at the given temperature.

From the given information, we have:

PCl5 (initial pressure) = 0.54 atm
PCl5 (actual pressure) = 0.85 atm

Since PCl5 decomposes to PCl3 and Cl2, the pressure of PCl5 decreases by x, and the pressures of PCl3 and Cl2 increase by x.

Therefore:

PCl5 (final pressure) = 0.54 atm - x
PCl3 (final pressure) = x
Cl2 (final pressure) = x

We can calculate x by using the equation:

0.85 atm = 0.54 atm - x

x = 0.54 atm - 0.85 atm
x = -0.31 atm

Since we cannot have negative pressures, the value of x is not physically meaningful. Therefore, the decomposition reaction does not occur to a significant extent, and the reaction is said to favor the reactants.

Since the reaction does not occur significantly, we cannot calculate Kp because we do not have meaningful values for the partial pressures of the products (PCl3 and Cl2).

However, we can calculate K at this temperature using the equation:

K = (PCl3 * Cl2) / PCl5

K = (0 * 0) / 0.54

Since PCl3 and Cl2 are both zero, we obtain:

K = 0

Therefore, at 425 K, the reaction does not proceed significantly, and K is equal to zero.

Answer 4

To calculate Kp for the decomposition reaction of PCl5 at 425 K, we need to use the given information about the initial and actual pressures.

The balanced chemical equation for the reaction is:
PCl5(g) ⇌ PCl3(g) + Cl2(g)

The equation for Kp is:
Kp = (PCl3)(Cl2) / (PCl5)

To calculate Kp, we need to determine the partial pressures of PCl3 and Cl2 in the flask.

Given:
Initial pressure (PCl5) = 0.54 atm
Actual pressure = 0.85 atm

Let x be the moles of PCl5 decomposed.

At equilibrium, the pressure of PCl5 will be equal to the initial pressure minus the pressure change due to decomposition:
PCl5 = (0.54 - x) atm

The pressure of PCl3 and Cl2 that are formed will each be equal to x atm.

Now we can substitute these values into the Kp expression:
Kp = (PCl3)(Cl2) / (PCl5)
= (x)(x) / (0.54 - x)

We also know that the actual pressure in the flask is 0.85 atm, which is the sum of the partial pressures of PCl3 and Cl2:
Actual pressure = PCl3 + Cl2
0.85 = x + x
0.85 = 2x
x = 0.85 / 2
x = 0.425

Now we can substitute this value of x back into the Kp expression:
Kp = (0.425)(0.425) / (0.54 - 0.425)
≈ 0.181

Therefore, Kp for the decomposition reaction at 425 K is approximately 0.181 atm.

To calculate K, we need to convert Kp to K using the ideal gas law equation:
Kp = K(RT)^(delta n)
where R is the ideal gas constant and delta n is the change in the number of moles.

In this case, delta n = (moles of products) - (moles of reactants)
delta n = (1 + 1) - 1
delta n = 1

Since we are given the temperature T, we can now use the ideal gas constant R (0.0821 L.atm/mol.K) to calculate K:
K = Kp / (RT)^(delta n)
= 0.181 / (0.0821)(425)^(1)
≈ 0.00527

Therefore, K for the decomposition reaction at 425 K is approximately 0.00527.