Equilibrium constant (Kp) for homogeneous systems

• The equilibrium constant ($K_p$) enables us to calculate how an equilibrium yield will be influenced by the partial pressures of reactants and products.
• The equilibrium constant ($K_p$) is deduced from the equation for a reversible reaction occurring in the gas phase.
• $K_p$is the equilibrium constant calculated from partial pressures for a system at constant temperature.
• The mole fraction of a component, A, is an gaseous mixture is denoted $X_A$and is calculated by dividing the amount, in moles, of A by the total amount of moles of gas in the mixture.
• What is the equation to calculate the mole fraction?

  For $A(g)+$$B(g)\leftrightarrow C(g)$

  $X_A=$$\frac{n_a}{n_A+n_B+n_C}$

  Where $n_A$, $n_B$ and $n_C$​ are the amount, in moles, of A, B and C present in the mixture.
• What should the sum of mole fractions add up to?

  Mole fractions can only have values in the range 0 to 1. The sum of the mole fractions of all the components in a mixture will be equal to 1.
• What is partial pressure?

  The partial pressure of a component, A, in a mixture of gases is the contribution which that gas makes to the total pressure of the gas mixture. It can be calculated by multiplying the total pressure of the mixture by the mole fraction of that component.
• What is the equation for partial pressure?

  $P_A=$$X_A\times P$

  $P_A$ is partial pressure, $X_A$ is the mole fraction of that component and $P$ is the total pressure.
• What is an expression for Kp for a homogeneous system in equilibrium?

  $K_p=$$\frac{p\left(C\right)^cp\left(D\right)^d}{p\left(A\right)^ap\left(B\right)^b}$

  • Where $p\left(A\right)^a$ is the partial pressure of A raised to the power of a.
  • Where $p\left(B\right)^b$ is the partial pressure of B raised to the power of b.
  • Where $p\left(C\right)^c$​ is the partial pressure of C raised to the power of c.
  • Where $p\left(D\right)^d$ is the partial pressure of D raised to the power of d.
• What equation do you use when trying to find the number of moles at equilibrium when calculating Kp?

  Partial pressure = Mole fraction x Total pressure
• What equation do you use when trying to find the number of moles at equilibrium when calculating Kp?

  $p\left(A\right)=$$X_A\times P$
• Particle pressures in Pa:

  Units of $K_p=$$\frac{\left(Pa\right)^2}{\left(Pa\right)\left(Pa\right)^3}=$$\frac{\left(Pa\right)^2}{\left(Pa\right)^4}=$$\frac{1}{\left(Pa\right)^2}=$$Pa^{-2}$
• Kp is constant at a particular temperature.
• Kp is affected by changes in temperature, but is not affected by changes in pressure, the presence of a catalyst or changes in concentration or amount of substance present in the mixture.
• Predict the qualitative effects of changes in temperature on the position of equilibrium.

  Increasing the temperature will favour the reverse reaction and the position of the equilibrium will move to the left. This will decrease the partial pressure of the product and the value of Kp will decrease.
• Predict the qualitative effects of changes in pressure on the position of equilibrium.

  Increasing the pressure will favour the forward reaction and the position of equilibrium will move to the right. This will have no effect on the value of Kp as long as the temperature remains constant.
• Predict the qualitative effects of changes in concentration or amount of substance present in the mixture on the position of equilibrium.

  Increasing the amount of substance will increase the partial pressure of that component and will move the position of equilibrium to the right. This will have no effect on the value of Kp as long as the temperature remains constant.
• What effect does a catalyst have on the value of Kp?

  Whilst a catalyst can affect the rate of attainment of an equilibrium, it does not affect the value of the equilibrium constant (Kp).