Consider the following reaction:
2NOCl(g) 2NO(g) + Cl2(g)
Initially pure NOCl(g) is placed in a vessel at 3.00 atm. At equilibrium, 0.416% of the NOCl has decomposed. Determine the
value for Kp.
To find the value for Kp, we can use the ideal gas law and the given information about the reaction.
Step 1: Write the balanced equation for the reaction:
2NOCl(g) -> 2NO(g) + Cl2(g)
Step 2: Assume the initial moles of NOCl to be 1.
This assumption will not affect the final value of Kp, as Kp is a ratio of partial pressure and is independent of the initial amount of reactants.
Step 3: At equilibrium, 0.416% of NOCl has decomposed.
This means that 0.00416 moles of NOCl has decomposed.
Step 4: Calculate the moles of NO and Cl2 produced at equilibrium.
Since the stoichiometric coefficient of NOCl and NO/Cl2 is 1:1, the moles of NO and Cl2 produced will be equal to the moles of NOCl decomposed:
moles of NO = moles of Cl2 = 0.00416
Step 5: Calculate the total moles of gas at equilibrium.
Initially, there was 1 mole of NOCl. After decomposition, there are 0.99584 moles of NOCl remaining. Since NO and Cl2 were produced in equal amounts, there are also 0.00416 moles of each. Therefore, the total moles of gas at equilibrium is:
1 + 0.00416 + 0.00416 = 1.00832 moles
Step 6: Calculate the partial pressures of each gas at equilibrium.
Since the total moles of gas at equilibrium is 1.00832, we can calculate the partial pressures using the ideal gas law:
P = (n/V) * R * T
Let's assume the temperature and volume are constant, so the equation simplifies to:
P = n * R * T
For NO:
P(NO) = (0.00416 moles / 1.00832 moles) * 3.00 atm
P(NO) = 0.00412 atm
For Cl2:
P(Cl2) = (0.00416 moles / 1.00832 moles) * 3.00 atm
P(Cl2) = 0.00412 atm
Step 7: Calculate the partial pressure of NOCl at equilibrium.
Since 0.416% of NOCl has decomposed, there are 0.99584 moles of NOCl remaining.
P(NOCl) = (0.99584 moles / 1.00832 moles) * 3.00 atm
P(NOCl) = 2.9479 atm
Step 8: Calculate the equilibrium constant Kp.
Kp is defined as the ratio of the product partial pressures to the reactant partial pressures, each raised to the power of their stoichiometric coefficients:
Kp = (P(NO) * P(Cl2)) / (P(NOCl))^2
Plugging in the values:
Kp = (0.00412 atm * 0.00412 atm) / (2.9479 atm)^2
Kp = 1.694 x 10^-6 (rounded to the nearest 3 significant figures)
Therefore, the value for Kp is 1.694 x 10^-6.
To determine the value for Kp, we need to find the equilibrium concentrations of the reactants and products.
Given:
Initial pressure of NOCl (P_initial) = 3.00 atm
Percent of NOCl decomposed = 0.416 %
Step 1: Calculate the equilibrium pressure of NOCl (P_eq).
Since 0.416% of NOCl decomposed, we can find the amount of NOCl remaining at equilibrium by subtracting the decomposed amount from the initial amount.
Remaining NOCl = (100% - 0.416%) * Initial NOCl
P_eq(NOCl) = Remaining NOCl / Initial volume of the container (Assuming volume remains constant)
Step 2: Calculate the equilibrium pressures of NO and Cl2.
From the balanced equation, we can see that the molar ratio between NOCl and NO is 2:2 and between NOCl and Cl2 is 1:1.
So the amount of NO and Cl2 produced will be the same as the amount of NOCl decomposed.
P_eq(NO) = P_eq(Cl2) = Decomposed NOCl / Initial volume of the container
Step 3: Calculate the equilibrium partial pressure of each species.
Since the molar ratio between NOCl and the other two species is 2:2:1, the equilibrium partial pressures are the same as the equilibrium pressures calculated in Step 2.
P_eq(NOCl) = P_eq(NO) = P_eq(Cl2)
Step 4: Calculate Kp.
Kp is the equilibrium constant defined as the ratio of the product partial pressures to the reactant partial pressures, each raised to the power of their respective stoichiometric coefficients.
Kp = (P_eq(NO))^2 * P_eq(Cl2) / (P_eq(NOCl))^2
Substitute the values calculated in Step 3 to get the value for Kp.
........2NOCl ==> 2NO + Cl2
I.......3..........0.....0
C....-0.00416*3.0.0125...1/2*0.0125
E. ..etc.