Decomposition of A is a first order reaction at T ( K ) and is given by A ( g ) B ( g )+ C ( g ) . In a closed 1 L vessel, 1 bar A ( g ) is allowed to decompose at T ( K ) . After 100 minutes, the total pressure was 1.5 bar. What is the rate constant ( in min ⁻¹ ) of the reaction ? ( 2=0.3)

Step-by-step solution

For the reaction A(g) B(g) + C(g) , initially pressure of A is 1 bar. Initially: total pressure = 1 bar. After 100 min: total pressure = 1.5 bar. Using initial and final pressures, if x bar of A decomposes, then A becomes (1-x), B = x, C = x. Total pressure = 1-x+x+x = 1+x = 1.5, so x = 0.5 bar. For a first-order reaction: k = 2.303 t [A]₀ [A] . Using pressures instead: k = 2.303 100 1 0.5 = 2.303 100 2 = 2.303 0.3 100 = 0.691 100 = 6.91 10⁻³ min ⁻¹ ≈ 6.9 10⁻³ min ⁻¹