### Related Formula textRate = k cdot [textReactants]^textorder$\text{Rate} = k \cdot [\text{Reactants}]^{\text{order}}$ ### Core Logic The slowest elementary step controls the net kinetic pathway rate law : textRate = k_2[mathrmA][mathrmB2] quad dots textEquation (1)$\text{Rate} = k_2[\mathrm{A}][\mathrm{B}2] \quad \dots \text{Equation (1)}$ Since [mathrmA]$[\mathrm{A}]$ behaves as a transient intermediate species, replace it using the prior fast equilibrium step : frack_1k-1 = frac[mathrmA]^2[mathrmA2] implies [mathrmA]^2 = left(frack_1k-1 ight) [mathrmA2]$\frac{k_1}{k{-1}} = \frac{[\mathrm{A}]^2}{[\mathrm{A}2]} \implies [\mathrm{A}]^2 = \left(\frac{k_1}{k{-1}} ight) [\mathrm{A}2]$ [mathrmA] = sqrtfrack_1k-1 cdot [mathrmA2]^1/2$[\mathrm{A}] = \sqrt{\frac{k_1}{k{-1}}} \cdot [\mathrm{A}2]^{1/2}$ Substitute [mathrmA]$[\mathrm{A}]$ back into Equation (1) : textRate = k_2 sqrtfrack_1k-1 cdot [mathrmA2]^1/2[mathrmB2]$\text{Rate} = k_2 \sqrt{\frac{k_1}{k{-1}}} \cdot [\mathrm{A}2]^{1/2}[\mathrm{B}2]$ Sum of powers determining overall order: textOrder = frac12 + 1 = 1.5$\text{Order} = \frac{1}{2} + 1 = 1.5$ Hence, Option (1) is correct. ### Pattern Recognition Whenever a fast initial step dissociates a molecule into matching independent halves, it always injects a fractional order component of 0.5$0.5$ relative to that parent species. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Chemical Kinetics