Express the rate of reaction in terms of the rate of change...

Express the rate of reaction in terms of the rate of change of each reactant and each product in the following equations. (a) $3 \mathrm{ClO}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ClO}_{3}^{-}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$ (b) $2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})$ (c) $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Br}_{2}(\mathrm{~g})$ (d) $\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}+\mathrm{I}_{2} \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}+2 \mathrm{HI}$ (liquid phase)

Express the rate of reaction in terms of the rate of change of each reactant and each product in the following equations.
(a) $3 \mathrm{ClO}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ClO}_{3}^{-}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$
(b) $2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})$
(c) $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Br}_{2}(\mathrm{~g})$
(d) $\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}+\mathrm{I}_{2} \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}+2 \mathrm{HI}$
(liquid phase)

Key Concepts

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products, typically expressed as the change in concentration per unit time. It provides a common framework for comparing the speeds of different reactions and is defined consistently for all species involved in a balanced chemical equation when adjusted for their stoichiometric coefficients.

Stoichiometric Coefficients

Stoichiometric coefficients, which appear as the numbers before reactants and products in a balanced chemical equation, indicate the relative amounts in which substances react and are produced. They are essential in rate expressions because they scale the rates of change in concentration to match the overall progress of the reaction, ensuring that differences in the amounts consumed or produced are accurately represented.

Differential Rate Expressions

Differential rate expressions involve representing the rate of reaction in terms of the time derivatives of the concentrations of reactants and products. For a reactant, the rate is given by a negative derivative divided by its stoichiometric coefficient to reflect its consumption, while for a product, it is given by a positive derivative divided by its stoichiometric coefficient to reflect its formation. This method allows for the consistent comparison of how the concentrations of various species change over time during a reaction.

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