A sample of gaseous pcl5 was introduced into an evacuated flask so that the pressure of pure pcl5 would be 0.50 atm at 523 k. However, pcl5 decomposes to gaseous pcl3 and cl2, and the actual pressure in the flask was found to be 0.74 atm. Calculate kp for the decomposition reaction pcl5(g) pcl3(g) + cl2(g) at 523 k. Also, calculate k at this temperature.
Answers
The Kp = 0.2215 and Kc = 0.0052 respectively.
Explanation:
Step 1: The balanced equation
PCl5(g) → PCl3(g) + Cl2(g)
Step 2: given data
Initial pressure PCl5 = 0.50 atm
Temperature = 523 Kelvin
The actual pressure in the flask was found to be 0.74 atm.
Step 3: Calculate the pressure after the decomposition
Pressure of PCl5 after decomposition = 0.5 - X
Since the equation has a ratio 1:1 the pressure after the decomposition of PCl3 and Cl2 is X
Step 4: Calculate total pressure at equilibrium
0.74 atm = 0.5 atm - X + 2X
X = 0.74 - 0.5 = 0.24 atm
Step 5: Calculate Kp
Kp = P(PCl3) x P(Cl2) / P(PCl5)
Kp = 0.24² / 0.26 = 0.2215
Step 6: Calculate Kc
The ideal gas wet: P x V = nRT
with P= the pressure of the gas in atm
with V= the volume of the gas in L
with n = the number of moles
With R = the gas constant in L x atm/mol x K
T = the temperature in Kelvin
P = nRT/V
Kp = Kc x (RT)^Δn
Kc = Kp / (RT)^Δn
Kc= 0.2215 / (0.08206 x 523)^1
Kc= 0.0052