pure phosphene gas 3x10^-2 mol was placed in a 1.5L container. it was heated to 800K. at equilibrium the pressure of CO was found to be 0.497atm. calculate the Kp for the reaction:
CO + Cl2 <---> COCl2
To calculate the equilibrium constant, Kp, for the reaction, we need to determine the partial pressures of CO and Cl2 in the equilibrium state.
Given:
- Amount of pure phosphene gas (COCl2) = 3x10^-2 mol
- Volume of the container = 1.5L
- Temperature = 800K
- Pressure of CO at equilibrium = 0.497 atm
First, we need to convert the amount of COCl2 from moles to pressure using the ideal gas law:
PV = nRT
Since we have the volume (V), temperature (T), and number of moles (n), we can rearrange the equation to solve for pressure (P):
P = (nRT) / V
P = (3x10^-2 mol * 0.0821 L·atm/(mol·K) * 800K) / 1.5L
P = 0.131 atm
Now we can set up an ICE table for the reaction equation:
CO + Cl2 <---> COCl2
Initial (at equilibrium):
CO: 0 | x | x
Cl2: 0 | x | x
COCl2: 0.131 | 0.131-x | 0.131-x
Since we're given the equilibrium pressure of CO as 0.497 atm, we can substitute this value (0.497) for (0.131-x) in the ICE table. We can now solve for x, which will give us the partial pressure of Cl2:
0.497 = 0.131 - x
x = 0.131 - 0.497
x = -0.366
Since we cannot have a negative concentration or pressure, we discard the negative value for x. Therefore, it means that the equilibrium concentration of Cl2 is zero (0). Using this information, we can calculate the equilibrium partial pressures:
P(CO) = 0.131 atm
P(Cl2) = 0 atm
P(COCl2) = 0.131 atm
Finally, we can calculate the equilibrium constant, Kp:
Kp = (P(COCl2)) / (P(CO) * P(Cl2))
Kp = (0.131 atm) / (0.131 atm * 0 atm)
Kp = 1
Therefore, the equilibrium constant, Kp, for the given reaction is 1.