Recall that for a reaction **aA ****→**** bB**, the ** rate of a reaction** is given by:

$\overline{){\mathbf{Rate}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{a}}\frac{\mathbf{\Delta}\mathbf{\left[}\mathbf{A}\mathbf{\right]}}{\mathbf{\Delta t}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{b}}\frac{\mathbf{\Delta}\mathbf{\left[}\mathbf{B}\mathbf{\right]}}{\mathbf{\Delta t}}}$

We can simply do a ** rate-to-rate comparison** based on the stoichiometric coefficients.

Reaction: dinitrogen monoxide → nitrogen and oxygen

**Reaction: 2 N_{2}O(g) → 2 N_{2}(g) + O_{2}(g)**

Given:

$\mathbf{rate}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{}\raisebox{1ex}{$\mathbf{M}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{s}$}\right.$

Since N_{2}O is a reactant, the rate should be negative since reactants are used up/consumed.

Dinitrogen monoxide decomposes into nitrogen and oxygen when heated. The initial rate of the reaction is 2.4 × 10^{−2} M/s. What is the initial rate of change of the concentration of N_{2}O (that is, Δ[N_{2}O]/Δt)?

2 N_{2}O(g) → 2 N_{2}(g) + O_{2}(g)

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