MHT CET202526 Apr 2025Evening ShiftChemistryChemical KineticsActual
The slope of a graph [A]_t versus ' t ' for first order reaction is -2.5 10⁻³ ~s ⁻¹ . Find rate constant of the reaction?
Options
- A1.263 10⁻³ ~s ⁻¹
- B3.471 10⁻³ ~s ⁻¹
- C5.757 10⁻³ ~s ⁻¹
- D8.125 10⁻³ ~s ⁻¹
Correct answer
C. 5.757 10⁻³ ~s ⁻¹
Step-by-step solution
The integrated rate law for a first-order reaction is expressed as [A]_t = -kt + [A]₀ . Converting to base-10 logarithms using the identity x = 2.303 x yields: [A]_t = - k 2.303 t + [A]₀ This represents a linear relationship where the slope is - k 2.303 . Given the measured slope of the plot of [A]_t versus time is -2.5 10⁻³ , s ⁻¹ , we equate: - k 2.303 = -2.5 10⁻³ , s ⁻¹ Solving for the rate constant k : k = 2.303 2.5 10⁻³ , s ⁻¹ = 5.7575 10⁻³ , s ⁻¹ Rounded to three significant figures, k 5.76 10⁻³ , s ⁻¹ , conf