For a first-order gas-phase decomposition reaction, a graph is plotted for ₁₀(P) versus time t (in minutes), where P is the partial pressure of the reactant. The graph is a straight line with a slope of -3 10⁻³ min ⁻¹ . The time required for 75 % completion of the reaction is ________ minutes. (Given: ₁₀(2) = 0.3 )

Step-by-step solution

For a first order reaction, the integrated rate law is given by: k = 2.303 t ₁₀ ( P₀ P ) ₁₀(P) = ₁₀(P₀) - k 2.303 t Comparing this with the equation of a straight line y = mx + c , the slope is: Slope = - k 2.303 = -3 10⁻³ min ⁻¹ k = 3 10⁻³ 2.303 min ⁻¹ The half-life of the reaction is: t_ 1/2 = 0.693 k = 2.303 ₁₀(2) k t_ 1/2 = 2.303 0.3 3 10⁻³ 2.303 = 0.3 3 10⁻³ = 100 minutes. For a first order reaction, the time required for 75 % completion is exactly two half-lives: t_ 75 % = 2 t_ 1/2 = 2 100 = 200 minutes. Answ