Final answer:
The balanced chemical equation for the formation of 1 mol of PCl5 from its elements is: PCl3(g) + Cl2(g) -> PCl5(g). The change in entropy (ΔS) for this formation can be calculated using the given values of ΔS for each substance.
Step-by-step explanation:
The balanced chemical equation for the formation of 1 mol of PCl5 from its elements is:
PCl3(g) + Cl2(g) ➡️ PCl5(g)
According to the law of conservation of mass, the number of atoms of each element must be the same on both sides of the equation. Therefore, to balance the equation, we need to multiply PCl3 by 2:
2PCl3(g) + Cl2(g) ➡️ 2PCl5(g)
This balanced equation represents the formation of 2 moles of PCl5. To find the change in entropy (ΔS) for the formation of 1 mol of PCl5, we need to divide the change in entropy by 2:
ΔS/2 = ΔS for 2PCl5 - ΔS for 2PCl3 - ΔS for Cl2
Since ΔS is an extensive property, we can use the given values of ΔS for each substance:
ΔS/2 = (0.8934 - 2 * 0.0563) - (2 * 0) - (2 * 0.0784)
ΔS/2 = 0.7808 J/(mol·K)