at an equilibrium mixture of PCl5, PCl3, and Cl2 has partial pressures of 217.0 Torr, 13.2 Torr and 13.2 Torr respectively. a quantity of Cl2 is injected into the mixture, and the total pressure jumps to 263.0 Torr (at the moment of mixing). the system then re-equilibrates. calculate the new partial pressures after equilibrium is reestablished.
To calculate the new partial pressures after the system re-equilibrates, we need to determine the changes in the amounts of each substance involved. This can be done using the principles of Le Chatelier's principle.
1. Start by calculating the initial total pressure (before the injection):
P_total_initial = P_PCl5_initial + P_PCl3_initial + P_Cl2_initial
P_total_initial = 217.0 Torr + 13.2 Torr + 13.2 Torr
P_total_initial = 243.4 Torr
2. Calculate the initial moles of each substance using the ideal gas law:
PV = nRT
For PCl5:
n_PCl5_initial = (P_PCl5_initial * V) / (R * T)
(Assuming constant volume, temperature, and using the ideal gas constant, R)
For PCl3:
n_PCl3_initial = (P_PCl3_initial * V) / (R * T)
For Cl2:
n_Cl2_initial = (P_Cl2_initial * V) / (R * T)
Note: As the volume and temperature are constant, we can ignore them for comparison purposes.
3. Calculate the initial moles of each substance:
n_total_initial = n_PCl5_initial + n_PCl3_initial + n_Cl2_initial
4. Determine the changes in moles based on the changes in the total pressure:
Δn_Cl2 = n_Cl2_initial * (P_total_final - P_total_initial) / P_total_initial
5. Calculate the new moles of each substance after equilibrium re-establishes:
n_PCl5_new = n_PCl5_initial + Δn_Cl2
n_PCl3_new = n_PCl3_initial + Δn_Cl2
n_Cl2_new = n_Cl2_initial - Δn_Cl2
6. Calculate the new partial pressures using the ideal gas law:
For PCl5:
P_PCl5_new = n_PCl5_new * (R * T) / V
For PCl3:
P_PCl3_new = n_PCl3_new * (R * T) / V
For Cl2:
P_Cl2_new = n_Cl2_new * (R * T) / V
7. Calculate the new total pressure:
P_total_new = P_PCl5_new + P_PCl3_new + P_Cl2_new
Now we have calculated the new partial pressures after equilibrium is re-established.
To calculate the new partial pressures after the equilibrium is reestablished, we need to consider the effect of adding Cl2 to the mixture.
1. Calculate the initial moles of each component in the equilibrium mixture:
Since we are given the partial pressure of each component, we can use the ideal gas law to calculate the moles of each substance. The ideal gas law is given by: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Rearranging the formula to solve for n, we get: n = PV / RT.
For PCl5:
n1 = (217.0 Torr) / (R * T) - Equation (1)
For PCl3 and Cl2:
n2 = n3 = (13.2 Torr) / (R * T) - Equation (2)
2. Calculate the total initial moles of PCl5, PCl3, and Cl2:
n_total = n1 + n2 + n3
3. Calculate the mole fraction of PCl5, PCl3, and Cl2 in the initial mixture:
X1 = n1 / n_total
X2 = n2 / n_total
X3 = n3 / n_total
4. Calculate the total moles of the mixture after Cl2 is injected:
Since the total pressure jumps to 263.0 Torr, we can use the ideal gas law to calculate the total moles:
n_total_new = (263.0 Torr) / (R * T) - Equation (3)
5. Calculate the new moles of Cl2:
Since Cl2 was injected, the moles of Cl2 will increase. Let the additional moles of Cl2 injected be n_injected.
n3_new = n3 + n_injected
6. Calculate the new total moles of the mixture after re-equilibration:
n_total_new = n1 + n2 + n3_new
7. Calculate the new mole fractions of PCl5, PCl3, and Cl2:
X1_new = n1 / n_total_new
X2_new = n2 / n_total_new
X3_new = n3_new / n_total_new
8. Calculate the new partial pressures after equilibrium is reestablished:
The new partial pressure of each component can be calculated using the mole fractions and the total pressure of the mixture after re-equilibration.
P1_new = X1_new * P_total_new
P2_new = X2_new * P_total_new
P3_new = X3_new * P_total_new
By following these steps, you should be able to calculate the new partial pressures of PCl5, PCl3, and Cl2 after equilibrium is reestablished.
..........PCl5 --> PCl3 + Cl2
E.........217.......13.2 13.2
Kp = pPCl3*pCl2/pPCl5.
Substitute the E line into Kp expression and solve for Kp.
Cl2 added.
Total P = 217 + 13.2 + 13.2 = 243.4
New total P = 263
Cl2 added = 263-243.4= 19.6 torr
New Cl2 = 19.6 + 13.2 = 32.8 torr
...........PCl5 ==> PCl3 + Cl2
I..........217......13.2...32.8
C...........x.......-x......-x
E.........217+x....13.2-x..32.8-x
Substitute the E line into Kp expression and evaluate x and the others.
Post your work if you get stuck.