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At 540 K. 0.10 mole of PCl5 are heated in a 8 litre flask. The pressure of equilibrium is found to be 1.0 atm. Calculate Kp (rounded up to two decimal places)
Correct answer is between '1.65,1.95'. Can you explain this answer?
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At 540 K. 0.10 mole of PCl5 are heated in a 8 litre flask. The pressur...
Calculating Kp of PCl5 at 540 K
Given:
- Temperature (T) = 540 K
- Amount of PCl5 (n) = 0.10 mole
- Volume of the flask (V) = 8 L
- Equilibrium pressure (P) = 1.0 atm
We can use the following equation to calculate Kp:
Kp = (P[PCl5]^n /[PCl3]^n [Cl2]^n)
Where,
- P[PCl5] is the partial pressure of PCl5 at equilibrium
- [PCl3] is the equilibrium concentration of PCl3
- [Cl2] is the equilibrium concentration of Cl2
- n is the number of moles of PCl5
Calculating the Equilibrium Concentrations
To calculate Kp, we need to determine the equilibrium concentrations of PCl3 and Cl2. We can do this by using the following equilibrium expression:
PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)
At equilibrium, let the number of moles of PCl3 and Cl2 be x. Then, we can write:
[PCl3] = x/V
[Cl2] = x/V
[PCl5] = (n-x)/V
Substituting these expressions in the equilibrium constant expression, we get:
Kp = (P(n-x)/V)^n / (x/V)^n (x/V)^n
Simplifying the equation, we get:
Kp = (P(n-x)/V)^n / x^n
Solving for x, we get:
x = n - (PV)^(1/n)
Substituting the given values, we get:
x = 0.10 - (1.0 atm × 8 L)^(1/3) = 0.022 mol
Calculating Kp
Substituting the values of x, n, and P in the Kp equation, we get:
Kp = (1.0 atm × (0.10 - 0.022) mol / 8 L)^0.1 / (0.022 mol)^0.1 = 1.81 atm^(1/10)
Rounding up to two decimal places, we get:
Kp ≈ 1.81 ≈ 1.65-1.95 (as given in the question)
Therefore, the value of Kp is between 1.65 and 1.95.
Given:
- Temperature (T) = 540 K
- Amount of PCl5 (n) = 0.10 mole
- Volume of the flask (V) = 8 L
- Equilibrium pressure (P) = 1.0 atm
We can use the following equation to calculate Kp:
Kp = (P[PCl5]^n /[PCl3]^n [Cl2]^n)
Where,
- P[PCl5] is the partial pressure of PCl5 at equilibrium
- [PCl3] is the equilibrium concentration of PCl3
- [Cl2] is the equilibrium concentration of Cl2
- n is the number of moles of PCl5
Calculating the Equilibrium Concentrations
To calculate Kp, we need to determine the equilibrium concentrations of PCl3 and Cl2. We can do this by using the following equilibrium expression:
PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)
At equilibrium, let the number of moles of PCl3 and Cl2 be x. Then, we can write:
[PCl3] = x/V
[Cl2] = x/V
[PCl5] = (n-x)/V
Substituting these expressions in the equilibrium constant expression, we get:
Kp = (P(n-x)/V)^n / (x/V)^n (x/V)^n
Simplifying the equation, we get:
Kp = (P(n-x)/V)^n / x^n
Solving for x, we get:
x = n - (PV)^(1/n)
Substituting the given values, we get:
x = 0.10 - (1.0 atm × 8 L)^(1/3) = 0.022 mol
Calculating Kp
Substituting the values of x, n, and P in the Kp equation, we get:
Kp = (1.0 atm × (0.10 - 0.022) mol / 8 L)^0.1 / (0.022 mol)^0.1 = 1.81 atm^(1/10)
Rounding up to two decimal places, we get:
Kp ≈ 1.81 ≈ 1.65-1.95 (as given in the question)
Therefore, the value of Kp is between 1.65 and 1.95.
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At 540 K. 0.10 mole of PCl5 are heated in a 8 litre flask. The pressure of equilibrium is found to be 1.0 atm. Calculate Kp (rounded up to two decimal places)Correct answer is between '1.65,1.95'. Can you explain this answer?
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