La réaction CH3 Br+HO^-=CH3 OH+Br^-a une loi de vitesse de la forme v =k c(CH3 Br) c(HO^-)et son

step 1 missile chloride and the hydroxide ion has a rate of reaction that is found to be linearly depen

La réaction CH3 Br+HO^-=CH3 OH+Br^-a une loi de vitesse de...

La réaction $\mathrm{CH}_3 \mathrm{Br}+\mathrm{HO}^{-}=\mathrm{CH}_3 \mathrm{OH}+\mathrm{Br}^{-}$a une loi de vitesse de la forme $v$ $=k \mathrm{c}\left(\mathrm{CH}_3 \mathrm{Br}\right) \mathrm{c}\left(\mathrm{HO}^{-}\right)$et son coefficient de vitesse, à $298 \mathrm{~K}$ vaut $2,8 \cdot 10^{-4} \mathrm{~L} \cdot \mathrm{mol}^{-1} \mathrm{~s}^{-1}$. Quelle est sa vitesse initiale et quelle proportion de $\mathrm{CH}_3 \mathrm{Br}$ a-t-elle été consommée après 1 heure de réaction, dans chacun des cas suivants : a) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=\mathrm{c}_0\left(\mathrm{HO}^{-}\right)=8.10^{-2} \mathrm{~mol}^{-\mathrm{L}^{-1}}$ b) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=\mathrm{c}_0\left(\mathrm{HO}^{-}\right)=2 \mathrm{~mol} \cdot \mathrm{L}^{-1}$ c) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=8.10^{-2} \mathrm{~mol} \cdot \mathrm{L}^{-1} ; \mathrm{c}_0\left(\mathrm{HO}^{-}\right)=2 \mathrm{~mol} \cdot \mathrm{L}^{-1}$

La réaction $\mathrm{CH}_3 \mathrm{Br}+\mathrm{HO}^{-}=\mathrm{CH}_3 \mathrm{OH}+\mathrm{Br}^{-}$a une loi de vitesse de la forme $v$ $=k \mathrm{c}\left(\mathrm{CH}_3 \mathrm{Br}\right) \mathrm{c}\left(\mathrm{HO}^{-}\right)$et son coefficient de vitesse, à $298 \mathrm{~K}$ vaut $2,8 \cdot 10^{-4} \mathrm{~L} \cdot \mathrm{mol}^{-1} \mathrm{~s}^{-1}$. Quelle est sa vitesse initiale et quelle proportion de $\mathrm{CH}_3 \mathrm{Br}$ a-t-elle été consommée après 1 heure de réaction, dans chacun des cas suivants :
a) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=\mathrm{c}_0\left(\mathrm{HO}^{-}\right)=8.10^{-2} \mathrm{~mol}^{-\mathrm{L}^{-1}}$
b) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=\mathrm{c}_0\left(\mathrm{HO}^{-}\right)=2 \mathrm{~mol} \cdot \mathrm{L}^{-1}$
c) $\mathrm{c}_0\left(\mathrm{CH}_3 \mathrm{Br}\right)=8.10^{-2} \mathrm{~mol} \cdot \mathrm{L}^{-1} ; \mathrm{c}_0\left(\mathrm{HO}^{-}\right)=2 \mathrm{~mol} \cdot \mathrm{L}^{-1}$

Key Concepts

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentrations of its reactants. It is a mathematical equation where the rate is proportional to the concentration(s) of the reactant(s) raised to a certain power. This power is known as the order of reaction with respect to each reactant. In a bimolecular reaction, the rate law typically involves the product of the concentrations of the two reactants.

Reaction Order

Reaction order indicates how the rate of reaction depends on the concentration of each reactant. For a rate law expressed as v = k[A][B], the reaction is first order in each reactant, giving an overall second-order reaction. This means that if the concentration of either reactant is doubled, while keeping the other constant, the rate of reaction will also double.

Rate Constant and Its Units

The rate constant (k) is a proportionality factor in the rate law whose value depends on the temperature and the nature of the reaction. Its units provide insights into the reaction order. For a second-order reaction (first order in each of two reactants), the units of k are typically L·mol?¹·s?¹. The numerical value of k also influences the speed of the reaction under given concentrations.

Initial Rate Calculation

The initial rate of a reaction is determined by applying the rate law at the very beginning of the reaction, using the initial concentrations of the reactants. This helps in understanding how fast a reaction proceeds at the start, which is important for comparing reaction speeds under different conditions or concentrations.

Integrated Rate Laws for Second-Order Reactions

While the rate law gives the instantaneous rate of reaction, integrated rate laws relate the concentrations of reactants with time. For a second-order reaction involving two reactants, the integration can be more complex especially if the initial concentrations are different. Special cases, such as when one reactant is in large excess, can often be simplified to a pseudo-first order process, thereby making the analysis of reaction progress over time more straightforward.

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