To calculate the equilibrium constant (Kp) for this reaction, we need to use the partial pressures of the gases involved.
Given that the total pressure in the container is 421,959.129 Pa, we can assume that the partial pressure of each gas is equal to its mole fraction. Since the reaction produces 2 moles of nitrogen gas (N2) and 2 moles of hydrogen gas (H2) for every mole of ammonium azide (NH4N3), we can express the partial pressures as follows:
PN2 = 2x (where x is the mole fraction of NH4N3)
PH2 = 2x (where x is the mole fraction of NH4N3)
PNH4N3 = x (where x is the mole fraction of NH4N3)
At equilibrium, the total pressure can be written as the sum of the partial pressures:
421,959.129 Pa = PN2 + PH2 + PNH4N3
Since PN2 = 2x and PH2 = 2x, we can rewrite the equation as:
421,959.129 Pa = 2x + 2x + x
Combining like terms:
421,959.129 Pa = 5x
Solving for x:
x = 421,959.129 Pa / 5
x ≈ 84,391.826 Pa
Now that we have the mole fraction of NH4N3, we can substitute it back into the equations for PN2 and PH2 to find their partial pressures:
PN2 = 2x ≈ 2 * 84,391.826 Pa ≈ 168,783.652 Pa
PH2 = 2x ≈ 2 * 84,391.826 Pa ≈ 168,783.652 Pa
Finally, we can calculate Kp using the expression for Kp:
Kp = (PN2)^2 * (PH2)^2 / (PNH4N3)
Kp = (168,783.652 Pa)^2 * (168,783.652 Pa)^2 / (84,391.826 Pa)
Kp ≈ 173,436,898.036
Therefore, the equilibrium constant (Kp) for the given reaction is approximately 173,436,898.036.