If 0.35 moles of SO3 is placed in a 1 dm3 flask and allowed to come to equilibrium at a high temperature, 0.207 mole of S03 remains. Calculate Kc For the reaction
2SO3 Double arrow 2SO2 +02
Solution
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To calculate Kc for the given reaction, we need to use the equilibrium concentrations of the reactants and products.
Given:
Initial moles of SO3 = 0.35 moles
Final moles of SO3 = 0.207 moles
Since the stoichiometry of the reaction is 2:2:1, we can say that:
Initial moles of SO2 = 0 moles
Initial moles of O2 = 0 moles
Final moles of SO2 = 0.35 - 0.207 = 0.143 moles
Final moles of O2 = 0.207/2 = 0.1035 moles
Now, we can calculate the equilibrium concentrations (in moles per dm3) by dividing the moles by the volume (1 dm3):
[SO3] = 0.207/1 = 0.207 mol/dm3
[SO2] = 0.143/1 = 0.143 mol/dm3
[O2] = 0.1035/1 = 0.1035 mol/dm3
Finally, we can calculate Kc using the formula:
Kc = ([SO2]^2 * [O2])/[SO3]^2
Substituting the values we found:
Kc = (0.143^2 * 0.1035)/(0.207^2)
Now, we can solve this equation to find Kc.
To calculate the equilibrium constant, Kc, for the given reaction, we need to use the equilibrium concentrations of the reactants and products.
First, we need to calculate the initial concentration (C initial) of SO3:
C initial (SO3) = (0.35 moles) / (1 dm³) = 0.35 M
Then, we need to calculate the equilibrium concentration (C equilibrium) of SO3:
C equilibrium (SO3) = (0.207 moles) / (1 dm³) = 0.207 M
Now, let's consider the stoichiometry of the reaction. It shows that for every 2 moles of SO3, we get 2 moles of SO2 and 1 mole of O2.
Since we know that the volume remains constant at 1 dm³, the equilibrium concentration of SO2 (C equilibrium (SO2)) and O2 (C equilibrium (O2)) will be the same.
Let's assume x moles of SO2 and O2 are formed.
Thus, for the reaction: 2SO3 ⇌ 2SO2 + O2
At equilibrium:
C equilibrium (SO3) = C initial (SO3) - x (0.207 M = 0.35 M - x)
C equilibrium (SO2) = x
C equilibrium (O2) = x
To obtain the value of x, we can solve the equation:
0.207 M = 0.35 M - x
Rearranging the equation:
x = 0.35 M - 0.207 M
x = 0.143 M
Now that we know the equilibrium concentrations of all the species, we can calculate Kc using the formula for this reaction:
Kc = (C equilibrium (SO2))² * C equilibrium (O2) / (C equilibrium (SO3))²
Kc = (0.143 M)² * 0.143 M / (0.207 M)²
Kc = 0.02051
So, the equilibrium constant, Kc, for the reaction 2SO3 ⇌ 2SO2 + O2 is approximately 0.02051.