Thermal decomposition of gaseous X 2 to gaseous X at 298 K takes place according to the…

Chemistry · JEE Advanced · NTA Exams — Equilibrium


Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equation : X2(g) \(\text { ⇌ }\) 2X(g)
The standard reaction Gibbs energy, ∆rG°, 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 β. Thus, βequilibrium 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)
 
The equilibrium constant Kp for this reaction at 298 K,
in terms of βequilibrium, is (2016)
  1. \(\frac{8 \beta_{\text {equilibrium }}^{2}}{2-\beta_{\text {equilibrium }}}\)
  2. \[\frac{8 \beta_{\text {equilibrium }}^{2}}{4-\beta_{\text {equilibrium }}^{2}}\]
  3. \[\frac{4 \beta_{\text {equilibrium }}^{2}}{2-\beta_{\text {equilibrium }}}\]
  4. \[\frac{4 \beta_{\text {equilibrium }}^{2}}{4-\beta_{\text {equilibrium }}^{2}}\]

Answer

(B) 8 _ equilibrium ^ 2 4- _ equilibrium ^ 2

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