For a first-order reaction, the plot of [R] against time ( t in seconds) yields a straight line with a slope of -3.01 10⁻³ s ⁻¹ . The half-life of the reaction is:

Step-by-step solution

For a first-order reaction, the integrated rate equation is: k = 2.303 t [R]₀ [R] Rearranging this equation gives: [R] = - k 2.303 t + [R]₀ Comparing this with the equation of a straight line y = mx + c , the slope ( m ) of the plot of [R] versus t is - k 2.303 . Given slope = -3.01 10⁻³ s ⁻¹ - k 2.303 = -3.01 10⁻³ k = 2.303 3.01 10⁻³ = 6.93 10⁻³ s ⁻¹ The half-life ( t_ 1/2 ) for a first-order reaction is: t_ 1/2 = 0.693 k = 0.693 6.93 10⁻³ = 100 s Answer: 100 s