Calculate the value of the equilibrium constant (Kp) for the reaction shown, if F(g) was found to be 96.80 % decomposed at 1000 K when its initial pressure was 4.638 atm. The initial pressure of the reaction products is 0 atm.

2F(g) = F2(g)

To calculate the value of the equilibrium constant (Kp) for the given reaction, we need to use the concept of the equilibrium constant expression and the initial and final pressures of the reactant and product gases.

The equilibrium constant expression for a reaction in terms of partial pressures (Kp) is given by:

Kp = (P(products)^m) / (P(reactants)^n)

Where P(products) and P(reactants) are the partial pressures of the products and reactants at equilibrium, and m and n are the stoichiometric coefficients of the products and reactants in the balanced equation.

In this case, the balanced equation for the reaction is:

2F(g) = F2(g)

The stoichiometric coefficient of F2(g) is 1, and the stoichiometric coefficient of F(g) is 2.

Given that F(g) was found to be 96.80% decomposed at 1000 K when its initial pressure was 4.638 atm, we can calculate the partial pressure of F(g) at equilibrium.

Partial pressure of F(g) at equilibrium = Initial pressure of F(g) - Decomposition pressure

Decomposition pressure = Initial pressure of F(g) * (1 - Percentage decomposition in decimal form)

Decomposition pressure = 4.638 atm * (1 - 96.80% / 100) = 4.638 atm * (1 - 0.968) = 4.638 atm * 0.032 = 0.1485 atm

Partial pressure of F(g) at equilibrium = 4.638 atm - 0.1485 atm = 4.4895 atm

Since the initial pressure of the reaction products is given as 0 atm, the partial pressure of F2(g) at equilibrium is also 0 atm.

Now we can calculate the value of Kp using the equilibrium constant expression:

Kp = (P(F2(g))^1) / (P(F(g))^2) = (0 atm^1) / (4.4895 atm^2)

Kp = 0 / 20.166 atm^2

Therefore, the value of the equilibrium constant (Kp) for the given reaction is 0.