The degree of dissociation of a compound is a measure of the extent to which it splits into its constituent ions in a chemical reaction. In this case, we are given that the degree of dissociation of PCl5 at a certain temperature and pressure is 0.4. We need to calculate the pressure at which the degree of dissociation will be 0.6 at the same temperature.

To solve this problem, we can use the concept of the equilibrium constant (Kp) and the relationship between pressure and the degree of dissociation.

The equilibrium constant (Kp) for the dissociation reaction of PCl5 is given by:

Kp = (PCl3)^2 / (PCl5)

Where (PCl3) represents the concentration of PCl3 and (PCl5) represents the concentration of PCl5. The degree of dissociation (α) can be defined as the ratio of the concentration of dissociated molecules to the initial concentration of the compound:

α = (PCl3) / (PCl5)

We are given that α = 0.4, so we can substitute this value into the equation and solve for Kp:

0.4 = (PCl3) / (PCl5)

Simplifying the equation, we have:

(PCl3) = 0.4 * (PCl5)

Now, we need to find the pressure at which the degree of dissociation will be 0.6. Let's assume the pressure at this point is P2. Using the equilibrium constant equation, we can write:

0.6 = (PCl3) / (PCl5)

Substituting the value of (PCl3) from the previous equation, we have:

0.6 = (0.4 * P2) / PCl5

Now, we can solve for PCl5:

PCl5 = (0.4 * P2) / 0.6

Simplifying the equation, we get:

PCl5 = 0.67 * P2

We know that the pressure at the initial degree of dissociation (0.4) is 2 atm. So, we can substitute this value into the equation and solve for P2:

2 = 0.67 * P2

P2 = 2 / 0.67

P2 ≈ 2.985

Therefore, the pressure at which the degree of dissociation of PCl5 will be 0.6 at the same temperature is approximately 2.985 atm. Rounding this value to two decimal places, we get the correct answer as between 0.63 and 0.71 atm.