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State (a) Le Chatelier's principle.(b) Dalton's law of partial pressures - Leaving Cert Chemistry - Question 9 - 2001
Question 9
State (a) Le Chatelier's principle.(b) Dalton's law of partial pressures. A mass of 16.68 g of phosphorus(V) chloride was heated in a scaled 5 dm³ vessel at 600 K. ... show full transcript
Worked Solution & Example Answer:State (a) Le Chatelier's principle.(b) Dalton's law of partial pressures - Leaving Cert Chemistry - Question 9 - 2001
Step 1
Write the equilibrium constant (Kc) expression for the reaction and calculate the value of Kc at 600 K.
Answer
The equilibrium constant expression for the reaction is given by:
From the information in the question, we find the moles of each substance at equilibrium:
- Moles of PCl₅ = ( \frac{16.68}{208.2} = 0.08 , \text{mol} )
- Moles of PCl₃ = ( \frac{8.25}{137.3} = 0.06 , \text{mol} )
- Moles of Cl₂ = 0.012 mol (calculated from the stoichiometry of the reaction)
Substituting these values into the Kc expression:
Step 2
Use the equation of state for an ideal gas to calculate the total pressure in the reaction vessel at equilibrium. Express the pressure in atmospheres.
Answer
Using the ideal gas equation, we have:
Where:
- P = pressure
- V = volume = 5 dm³ = 5 x 10⁻³ m³
- n = total moles of gas
- R = ideal gas constant = 8.314 J/(mol K)
- T = temperature = 600 K
Total moles (n) = 0.08 + 0.06 + 0.012 = 0.152 mol.
Substituting the values, we calculate:
P = ( \frac{nRT}{V} = \frac{0.152 \times 8.314 \times 600}{5 \times 10^{-3}} \approx 1.4 , \text{atm} )
Step 3
Write the equilibrium constant (Kp) expression for the reaction and calculate the value of Kp for the reaction in atmospheres at 600 K.
Answer
The equilibrium constant expression for Kp is given by:
Converting from Kc to Kp at 600 K: We can relate Kp and Kc as follows: Where \Delta n is the change in moles of gases (0.06 + 0.012 - 0.08 = 0.02).
Substituting the values, we find:
Step 4
Would the values of the equilibrium constants (Kc and Kp) have been greater, less or unchanged if the reactions were carried out at 700 K? Explain your answer.
Answer
As the reaction is endothermic (indicated by the positive ΔH), increasing the temperature would shift the equilibrium to the right to favor the formation of products, thus increasing the values of both Kc and Kp at higher temperatures. Therefore, at 700 K, Kc and Kp would be greater.