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JEE MainChemistryChemical Kinetics

A first-order gas-phase reaction A ( g ) 2 B ( g ) + C ( g ) takes place in a constant volume vessel. Initially, the vessel contains a mixture of reactant gas A and an unreactive (inert) gas. The initial total pressure of the mixture at t=0 is 200 mm Hg . The total pressure after 20 minutes is 280 mm Hg , and the total pressure after a very long time ( t ) is 500 mm Hg . The partial pressure of gas A after 20 minutes

Options

  1. A160 mm Hg
  2. B40 mm Hg
  3. C110 mm Hg
  4. D220 mm Hg

Correct answer

C. 110 mm Hg

Step-by-step solution

Let P₀ be the initial partial pressure of gas A and P_I be the partial pressure of the inert gas. At t = 0 , the total pressure is the sum of the partial pressures: P₀ + P_I = 200 mm Hg --- (Equation 1) At t , all of gas A has decomposed. Since 1 mole of A yields 3 moles of gaseous products ( 2 B + C ), the final partial pressure of the products will be 3P₀ . The inert gas pressure remains unchanged. Total pressure at t is: 3P₀ + P_I = 500 mm Hg --- (Equation 2) Subtracting Equation 1 from Equation 2: (3P₀ + P_I) -

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