The equilibrium constant, Kp, for the following reaction is 0.497 at 500 K:
PCl5(g) PCl3(g) + Cl2(g)
Calculate the equilibrium partial pressures of all species when PCl5(g) is introduced into an evacuated flask at a pressure of 1.46 atm at 500 K.
PPCl5 = atm
PPCl3 = atm
PCl2 = atm
......PCl5 ==> PCl3 + Cl2
I.....1.46......0......0
C.....-p........p......p
E.....1.46-p....p......p
Substitute into the Kp expression and solve for p, then evaluate 1.46-p.
To solve this problem, we need to use the equilibrium constant expression and the given information to set up a system of equations. We can then solve this system of equations to find the equilibrium partial pressures of all species.
First, let's set up the equilibrium constant expression for this reaction:
Kp = (PPCl3 * PCl2) / PPCl5
Given that Kp = 0.497, we can substitute this value into the equation:
0.497 = (PPCl3 * PCl2) / PPCl5
Next, let's assign variables to the unknown partial pressures:
Let x be the partial pressure of PCl3 (PPCl3).
Let y be the partial pressure of Cl2 (PCl2).
Since PPCl5 is initially introduced into the flask at a pressure of 1.46 atm, its partial pressure is simply 1.46 atm.
Now, we can express the equilibrium partial pressures of PCl3 and Cl2 in terms of x and y:
PPCl3 = x
PPCl2 = y
Substituting these values into the equilibrium constant expression, we have:
0.497 = (x * y) / 1.46
To solve for x and y, we can rearrange the equation and solve for y:
0.497 * 1.46 = x * y
0.72422 = xy
Now, we have two equations:
x * y = 0.72422
PPCl3 = x
PPCl2 = y
To find the values of x and y, we need to use an iterative method or a calculator that can solve equations numerically. However, since the values of x and y are not explicitly given, we cannot provide the specific values in this response.
You may use a scientific calculator or online tools to solve for the values of x and y.
To calculate the equilibrium partial pressures of all species, we need to use the stoichiometry and the given equilibrium constant (Kp) for the reaction.
Step 1: Write the balanced equation for the reaction:
PCl5(g) -> PCl3(g) + Cl2(g)
Step 2: Use the ideal gas law to relate pressure, volume, and number of moles:
PV = nRT
Step 3: Set up a table to keep track of the initial and equilibrium moles and pressures:
Species | Initial Moles | Change in Moles | Equilibrium Moles | Equilibrium Pressure
------------------------------------------------------------
PCl5 | ? | | | PPCl5
PCl3 | 0 | | | PPCl3
Cl2 | 0 | | | PCl2
Step 4: Determine the initial number of moles for PCl5(g):
Since the flask is initially evacuated, there are no moles of any species present. Therefore, the initial number of moles of PCl5(g) is 0.
Step 5: Calculate the change in moles using the stoichiometry of the balanced equation:
From the balanced equation, we can see that 1 mole of PCl5 produces 1 mole of PCl3 and 1 mole of Cl2. Therefore, the change in moles for both PCl3 and Cl2 is +1, and the change in moles for PCl5 is -1.
Step 6: Calculate the equilibrium moles:
The equilibrium moles for PCl5 will be the initial moles minus the change in moles. Since the initial moles of PCl5 are 0 and the change in moles is -1, we get 0 - 1 = -1.
The equilibrium moles for PCl3 and Cl2 will be the initial moles plus the change in moles. Since the initial moles of both PCl3 and Cl2 are 0, and the change in moles for each is +1, we get 0 + 1 = 1 for both species.
Step 7: Calculate the equilibrium pressures:
Since PCl5 is the only species with an initial pressure given (1.46 atm), we can directly substitute this value into the equilibrium pressure for PCl5 (PPCl5).
PPCl5 = 1.46 atm
For the other species, we need to use the ideal gas law to calculate their equilibrium pressures:
PPCl3 = (moles of PCl3 * R * T) / V
= (1 * 0.0821 L·atm/mol·K * 500 K) / V
PCl2 = (moles of Cl2 * R * T) / V
= (1 * 0.0821 L·atm/mol·K * 500 K) / V
Step 8: Convert the equilibrium pressures to atmospheres:
The equilibrium pressures are already in atmospheres, so no conversion is needed.
Now, we need the volume of the flask to calculate the equilibrium pressures.
Please provide the volume (V) of the flask in liters.