A 2.30 mole quantity of NOCl was initially in a 1.50 L reaction chamber at 400°C. After equilibrium was established, it was found that 20.0 percent of the NOCl had dissociated:
2NOCl(g) 2NO(g) + Cl2(g)
Calculate the equilibrium constant Kc for the reaction.
To calculate the equilibrium constant Kc for the given reaction, we need to use the information provided.
First, let's determine the moles of NOCl that dissociated.
Given:
Initial moles of NOCl = 2.30 moles
Percentage dissociation = 20%
The percentage dissociation represents the fraction of NOCl that dissociated. Therefore, we can calculate the moles of NOCl dissociated as follows:
Moles of NOCl dissociated = Initial moles of NOCl × percentage dissociation / 100
Moles of NOCl dissociated = 2.30 moles × 20 / 100
Moles of NOCl dissociated = 0.46 moles
Now, let's calculate the moles of NO and Cl2 formed. Since the reaction stoichiometry indicates that 2 moles of NOCl dissociate to form 2 moles of NO and 1 mole of Cl2, we have:
Moles of NO formed = Moles of NOCl dissociated × 2
Moles of NO formed = 0.46 moles × 2
Moles of NO formed = 0.92 moles
Moles of Cl2 formed = Moles of NOCl dissociated × 1
Moles of Cl2 formed = 0.46 moles × 1
Moles of Cl2 formed = 0.46 moles
Now, we need to calculate the final moles of NOCl present in the reaction chamber after dissociation:
Final moles of NOCl = Initial moles of NOCl - Moles of NOCl dissociated
Final moles of NOCl = 2.30 moles - 0.46 moles
Final moles of NOCl = 1.84 moles
Now that we have the mole quantities of each component at equilibrium, we can calculate the equilibrium constant Kc.
Kc is defined as the ratio of the product of the molar concentrations of the products raised to their stoichiometric coefficients, divided by the product of the molar concentrations of the reactants raised to their stoichiometric coefficients.
Kc = ([NO]^2 × [Cl2]) / [NOCl]^2
Here, [NO], [Cl2], and [NOCl] represent the molar concentrations of NO, Cl2, and NOCl, respectively.
Converting the moles to molar concentrations:
[NO] = Moles of NO / Volume of the reaction chamber
[NO] = 0.92 moles / 1.50 L
[NO] = 0.61 M
[Cl2] = Moles of Cl2 / Volume of the reaction chamber
[Cl2] = 0.46 moles / 1.50 L
[Cl2] = 0.31 M
[NOCl] = Moles of NOCl / Volume of the reaction chamber
[NOCl] = 1.84 moles / 1.50 L
[NOCl] = 1.23 M
Now substitute these values into the expression for Kc:
Kc = (0.61^2 × 0.31) / (1.23^2)
Kc = 0.449
Therefore, the equilibrium constant Kc for the reaction is approximately 0.449.