Final answer:
To find the degree of dissociation of PCl₅ in a mixture, divide the measured vapor density by the theoretical vapor density and multiply by 100%. The degree of dissociation is approximately 88.9%.
Step-by-step explanation:
To find the degree of dissociation of PCl₅, we need to understand the concept of vapor density and how it relates to the composition of a mixture. Vapor density is defined as the ratio of the molar mass of a gas to the molar mass of hydrogen gas. In this case, we have a mixture of PCl₅, PCl₃, and Cl₂, and the vapor density is given as 92. To calculate the degree of dissociation, we need to compare the vapor density of the mixture to the theoretical vapor density based on the complete dissociation of PCl₅.
The theoretical vapor density of PCl₅ can be calculated using the molar masses of the elements involved. The molar mass of PCl₅ is 207 g/mol, and the molar mass of hydrogen gas is 2 g/mol. Therefore, the theoretical vapor density of PCl₅ is 207/2 = 103.5.
To find the degree of dissociation, we divide the measured vapor density (92) by the theoretical vapor density (103.5) and multiply by 100%:
degree of dissociation = (measured vapor density / theoretical vapor density) * 100%
degree of dissociation = (92 / 103.5) * 100% ≈ 88.9%