QJEEAdv16Chd12f: JEE Advanced 2016 Chemistry - Class 11 JEEAdv16Chd12f Solution: Paragraph Thermal decomposition of gaseous X 2 to gaseous X at…

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Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equations:
X₂ (g) $\leftrightharpoons$ 2X (g)
The standard reaction Gibbs energy, $\Delta _rG^o$ , 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 $\beta$ . 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 mol^-1)
Question
The equilibrium constant K_p for this reaction at 298 K, in terms of $\beta _{equilibrium}$ , is