What is the difference between the "degree of conversion" and the "relative degree of conversion" for a chemical reaction \(2 \mathrm{~A} \rightarrow \mathrm{B}\) ? What changes when the degree of conversion is expressed on a molar basis?

Degree of conversion (X) is a measure of the progress of a reaction. It is defined as the fraction of limiting reactant that has reacted. Mathematically, it is represented as: \[X = \frac{\text{moles of reactant used}}{\text{initial moles of reactant}}\] In the given reaction, \(2 \mathrm{~A} \rightarrow \mathrm{B}\), the degree of conversion can be calculated by substituting the moles of reactant A that have reacted and the initial moles of A.

Relative degree of conversion (Y) is the ratio of the rate of change of the concentration of product B to the initial rate of change of concentration of reactant A, considering the stoichiometric coefficients. It can be mathematically represented as: \[Y = \frac{\text{Rate of change of concentration of B}}{2 \times \text{Initial rate of change of concentration of A}}\] In the given reaction, the initial rate of change of concentration will be different for reactant A and product B, due to the stoichiometric coefficients. Thus, the relative degree of conversion helps the progress of the reaction in terms of the formation of B.

When the degree of conversion is expressed on a molar basis, instead of using concentrations, we use the number of moles. This changes the formulas for both degree of conversion and relative degree of conversion. For Degree of Conversion (X): \[X_\text{molar} = \frac{\text{moles of reactant A used}}{\text{initial moles of reactant A}}\] For Relative Degree of Conversion (Y): \[Y_\text{molar} = \frac{\text{moles of product B formed}}{2 \times \text{initial moles of reactant A}}\] In both cases, the calculation would now be based on moles without considering the volume of the reaction mixture. Therefore, molar based calculations are more suitable when dealing with a heterogeneous system or a reaction affected by the change in volume.