Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equation: ${\mathrm{X}}_2\left(\mathrm{g}\right)\stackrel{ }{\rightleftharpoons }2\mathrm{X}\left(\mathrm{g}\right)$.

The standard reaction Gibbs energy, ${\Delta }_r{G}^0$,of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of  X formed is given by b. Thus, ${\beta }_{equilibrium}$ is the number of moles of  X formed  at equilibrium . The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given : R=0.083 L bar $K^{-1}mo{l}^{-1}$)