For a reaction X Y , the plot of reactant concentration [X] versus time is a straight line with a slope of -4 10⁻³ M s ⁻¹ . If the initial concentration of X is 0.24 M , what is the half-life of the reaction?

Step-by-step solution

The plot of reactant concentration [X] versus time is a straight line, which indicates that the reaction follows zero-order kinetics. For a zero-order reaction, the integrated rate equation is [X] = -kt + [X]₀ . Comparing this with the equation of a straight line y = mx + c , the slope m = -k . Given slope = -4 10⁻³ M s ⁻¹ , so the rate constant k = 4 10⁻³ M s ⁻¹ . The half-life for a zero-order reaction is given by t_ 1/2 = [X]₀ 2k . Substituting the given values: t_ 1/2 = 0.24 2 4 10⁻³ = 0.24 0.008 = 30 s . Answe