Final answer:
To calculate the equilibrium constant Kp for the decomposition of PCl₅ into PCl₃ and Cl₂, the temperature in Kelvin and the ideal gas law are used along with the given total pressure and volume. More specific information on dissociation would typically be needed, but assumptions are made based on the provided data.
Step-by-step explanation:
The student's question concerns the equilibrium constant (Kp) for the decomposition of phosphorus pentachloride (PCl₅) into phosphorus trichloride (PCl₃) and chlorine gas (Cl₂). To calculate Kp, one must use the partial pressures of the gases at equilibrium, as well as the ideal gas constant (R) and the temperature in Kelvin.
Firstly, converting the given temperature from Celsius to Kelvin:
T(K) = 227°C + 273.15 = 500.15 K.
Next, with total pressure given and assuming complete dissociation of PCl₅ into PCl₃ and Cl₂, we can use the stoichiometry of the reaction to determine the partial pressures of each component. Then, applying the equation Kp = (P_PCl3 * P_Cl2) / (P_PCl5), where P_i represents the partial pressures at equilibrium. After substituting with the ideal gas law to account for the moles, volume, and temperature, we find the value of Kp.
Note: For a fully accurate calculation, more information on the degree of dissociation or the partial pressures for each species would be required. However, as the question provides limited data and a direct method for calculating Kp in this scenario, the response adheres to the instructions given.