The equilibrium pressure of a reaction can be calculated using the ideal gas law and the concept of partial pressure. In this case, we are given the vapor density of the reaction mixture at equilibrium, which can be used to determine the partial pressure of the components.

1. Vapor Density Calculation:
Vapor density is the ratio of the molar mass of a gas to the molar mass of hydrogen gas. In this case, the vapor density is given as 100, which means that the molar mass of the reaction mixture is 100 times greater than that of hydrogen gas.

2. Determining the Molar Mass of the Reaction Mixture:
The molar mass of hydrogen gas (H2) is 2 g/mol. Therefore, the molar mass of the reaction mixture can be calculated as follows:
Molar Mass of Reaction Mixture = 100 × Molar Mass of Hydrogen Gas
Molar Mass of Reaction Mixture = 100 × 2 g/mol
Molar Mass of Reaction Mixture = 200 g/mol

3. Calculating the Number of Moles:
We are given that 1 mole of PCl5 is taken in a 10 L flask. Since the reaction is at equilibrium, the number of moles of PCl5, PCl3, and Cl2 will be the same. Therefore, the number of moles of each component is 1 mole.

4. Determining the Partial Pressure:
The partial pressure of each component can be calculated using the ideal gas law equation:
PV = nRT

Since we know the volume (V), number of moles (n), and temperature (T), we can rearrange the equation to solve for pressure (P):
P = (nRT) / V

5. Calculating the Equilibrium Pressure:
Using the above equation, we can calculate the partial pressure of each component:
Partial Pressure of PCl5 = (1 mole × R × 300 K) / 10 L
Partial Pressure of PCl3 = (1 mole × R × 300 K) / 10 L
Partial Pressure of Cl2 = (1 mole × R × 300 K) / 10 L

The equilibrium pressure is the sum of the partial pressures:
Equilibrium Pressure = Partial Pressure of PCl5 + Partial Pressure of PCl3 + Partial Pressure of Cl2

This calculation will give us the equilibrium pressure of the reaction mixture.