Introduction:
In this hypothetical equilibrium, we have the reaction 2B(g) ⇔ B2(g). The degree of association (α) refers to the extent to which the reactant B(g) molecules associate to form B2(g) molecules. It is a measure of the degree of dissociation or association of a substance in a gaseous state.

Explanation:
To determine the degree of association (α), we need to compare the observed vapor density (d) with the theoretical vapor density (D) of the gas.

Observed vapor density:
The observed vapor density (d) can be determined experimentally by comparing the mass of a given volume of the gas to the mass of the same volume of a known gas at the same temperature and pressure. It represents the actual mass of the gas per unit volume.

Theoretical vapor density:
The theoretical vapor density (D) is calculated based on the stoichiometry of the reaction. In this case, the stoichiometry tells us that 2 moles of B(g) react to form 1 mole of B2(g). Therefore, the theoretical vapor density can be calculated by dividing the molar mass of B2(g) by 2.

Calculating the degree of association:
The degree of association (α) can be determined by comparing the observed vapor density (d) with the theoretical vapor density (D). It is calculated using the formula:

α = (d / D) * 100

If the observed vapor density (d) is equal to the theoretical vapor density (D), then the degree of association will be 100%. This indicates that all the B(g) molecules have associated to form B2(g) molecules.

If the observed vapor density (d) is less than the theoretical vapor density (D), then the degree of association will be less than 100%. This indicates that only a fraction of the B(g) molecules have associated to form B2(g) molecules.

If the observed vapor density (d) is greater than the theoretical vapor density (D), then the degree of association will be greater than 100%. This indicates that more than one B(g) molecule has associated to form B2(g) molecules.

Conclusion:
The degree of association (α) is a measure of the extent to which the reactant B(g) molecules associate to form B2(g) molecules. It can be calculated by comparing the observed vapor density (d) with the theoretical vapor density (D). The degree of association provides valuable information about the behavior of the substance in the gaseous state and the equilibrium of the reaction.

D-d/d