Equilibrium Constant and Kp

The equilibrium constant (Kc) is a numerical value that represents the ratio of the concentrations of products to reactants at equilibrium for a chemical reaction. It is determined at a specific temperature and does not depend on the initial concentrations of the reactants and products. Kc is calculated using the concentrations of the species in moles per liter (M).

On the other hand, Kp is the equilibrium constant expressed in terms of the partial pressures of the species involved in the reaction. It is determined at a specific temperature and does not depend on the initial pressures of the reactants and products. Kp is calculated using the partial pressures of the species in atmospheres (atm).

Converting Kc to Kp

To convert Kc to Kp, we need to use the ideal gas law, which states that the pressure of a gas is directly proportional to its concentration when the volume is constant. The equation for the ideal gas law is:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since the volume is constant, we can rearrange the equation to solve for concentration:

P = (n/V)RT

Using the Ideal Gas Law to Convert Kc to Kp

To convert Kc to Kp, we can use the equation:

Kp = Kc(RT)^(∆n)

Where:
Kp = equilibrium constant expressed in terms of partial pressures
Kc = equilibrium constant expressed in terms of concentrations
R = ideal gas constant
T = temperature
∆n = change in the number of moles of gas (moles of products - moles of reactants)

In the given reaction: 1/2 F2 (g) : F(g), there is a decrease in the number of moles of gas from the reactant side to the product side. This means that ∆n = moles of products - moles of reactants = 1 - (1/2) = 1/2.

Substituting the values into the equation, we have:

Kp = Kc(RT)^(∆n)
Kp = (7.90 × 10^–3)(R)(T)^(1/2)

Since the temperature is given as 842°C, we need to convert it to Kelvin by adding 273 to the Celsius temperature:

T(K) = 842 + 273 = 1115 K

Substituting the values into the equation, we have:

Kp = (7.90 × 10^–3)(R)(1115)^(1/2)

The value of R is 0.0821 L·atm/(mol·K), so we can substitute it into the equation:

Kp = (7.90 × 10^–3)(0.0821)(1115)^(1/2)

Calculating the value, we find:

Kp ≈ 0.088

Therefore, the equilibrium constant Kp for the reaction 1/2 F2 (g) : F(g) at 842°C is approximately 0.088.

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