The equilibrium constant is equal to 7.09 * 10⁻³ atm³.
The expression for the equilibrium constant (Kp) for this reaction will look like this:
Kp = (pNH₃)²pCO₂
pNH₃ - partial pressure of NH₃
pCO₂ - partial pressure of CO₂
Because ammonium carbamate is solid, its concentration and pressure cannot change (they are constant), so there is no need to include it in the expression. We know that all the gas present in the mixture is formed by the decomposition of ammonium carbamate. We also know that for every two moles of ammonia formed, 1 mole of carbon dioxide is also formed.
Because partial pressure is proportional to the molar ratio, we can establish that:
pNH₃ = 2 * pCO₂
pNH₃ + pCO₂ = 0.363 atm
2 * pCO₂ + pCO₂ = 0.363 atm
3 * pCO₂ = 0.363 atm
pCO₂ = 0.363 atm / 3
pCO₂ = 0.121 atm
pNH₃ = 2 * 0.121 atm
pNH₃ = 0.242 atm
We can now plug these values into the expression for the equilibrium constant:
Kp = (0.242 atm)² * 0.121 atm = 7.09 * 10⁻³ atm³
You can learn more about the equilibrium constant here:
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