In gas-phase reactions, volume variations can occur as the reaction progresses. In this situation, we will use a simplified expression that gives the volume as a function of conversion: \(V = V_0(1 + \epsilon_Ax_A)\), where \(\epsilon_A\) is the relative volume change factor with the conversion of reactant A.
\(\epsilon_A = \frac{V(x_A=1) - V(x_A=0)}{V(x_A=0)}\)
Example of calculating \(\epsilon_A\): Consider the reaction \(A \rightarrow 4P\). Starting with 1 initial mole of A, when \(x_A=1\), we will have 4 moles of product. \(\epsilon_A = \frac{4-1}{1} = 3\).
\(\epsilon_A\) takes into account the presence of inerts. If we start with 1 initial mole of A and 1 mole of inerts, when \(x_A=0\), we have 2 moles, and when \(x_A=1\), we obtain 5 moles:
\(\epsilon_A = \frac{5-2}{2} = \frac{3}{2}\)