A mixture containing the same number of moles of SO2 and O2 is placed in a 2L container at 900K. The initial pressure is 1.90Atm. A reaction occurs leading to the formation of SO3: 2SO3 + O2 <--> 2SO3 After equilibrium is established the TOTAL pressure drops to 1.60 Atm. What is the equilibrium constant, Kp, at 900K?
Equal moles means equal pressures; therefore, initial pressure SO2 = 0.95 atm and initial pressure O2 = 0.95 atm. (You can go through PV = nRT to confirm this if you wish.).
2SO2 + O2 ==> 2SO3
initial:
SO2 = 0.95
O2 = 0.95
SO3 = 0
change:
SO2 = -2x
O2 = -x
SO3 = +2x
equilibrium:
SO2 = 0.95-2x
O2 = 0.95-x
SO3 = 2x
total pressure = 1.6 = 0.95-2x+0.95-x+2x and solve for x. Substitute these into the above ICE chart to find individual concns, substitute into Ka expression and solve for Kp.
To find the equilibrium constant, Kp, at 900K, we can use the given information about the initial and final pressures.
In the balanced equation, 2SO2 + O2 ⇌ 2SO3, it is stated that the initial number of moles of SO2 and O2 are equal. Let's denote the number of moles of each as x.
Initially, each of the reactants has a pressure of 1.90 Atm. Since the total pressure is the sum of the partial pressures of the gases, we can write:
Total initial pressure = (Partial pressure of SO2) + (Partial pressure of O2) = 1.90 Atm
Since both SO2 and O2 have the same number of moles and contribute equally to the total pressure, the partial pressure of each is:
(Partial pressure of SO2) = (Partial pressure of O2) = (Total initial pressure) / 2 = 1.90 Atm / 2 = 0.95 Atm
Now, after equilibrium is established, the total pressure drops to 1.60 Atm. According to the ideal gas law, the total pressure is proportional to the number of moles of gas:
Total pressure = (Number of moles of SO2 + Number of moles of O2 + Number of moles of SO3) * (RT / V)
In this case, the volume (V) is given as 2 L, and the temperature (T) is given as 900K. We know that at equilibrium, the number of moles of SO2 and O2 is x, and the number of moles of SO3 is 2x.
Let's substitute the values into the equation:
1.60 Atm = (x + x + 2x) * (R * 900 / 2)
Simplifying, we get:
1.60 = 4x * (R * 900 / 2)
1.60 = 4x * (450R)
1.60 = 1800xR
Dividing both sides by R, we get:
1.60 / R = 1800x
Now, we need to find the equilibrium constant expression, Kp, which is given by:
Kp = (Partial pressure of SO3)^2 / (Partial pressure of SO2)^2 * (Partial pressure of O2)
Since the moles of SO2 and O2 are both x, and the moles of SO3 are 2x, we can substitute these values into the equation:
Kp = ((Partial pressure of SO3) * 2)^2 / (x)^2 * (x)
Kp = (2 * (1.60 - 0.95))^2 / (x)^2 * (x)
Kp = (2 * 0.65)^2 / x^2 * x
Kp = 2.60^2 / x^3
Now, we have the expression for Kp in terms of x. To find the equilibrium constant, we need the value of x, which can be calculated using the equation obtained earlier:
1.60 / R = 1800x
Solving for x, we get:
x = 1.60 / (1800R)
Substituting this value of x back into the Kp expression, we obtain the equilibrium constant:
Kp = (2.60^2) / (1.60 / (1800R))^3
Now, you can calculate Kp using the given temperature of 900K and the value of the ideal gas constant (R), which is 0.0821 L·atm/(mol·K).