Question

Give the individual reaction orders for all substances and the overall reaction order from the following rate law: $$ \text { Rate }=k\left[\mathrm{BrO}_{3}^{-}\right]\left[\mathrm{Br}^{-}\right]\left[\mathrm{H}^{+}\right]^{2} $$

Short answer

The orders are: \[\text{BrO}_3^-: 1, \text{Br}^-: 1, \text{H}^+: 2\]. The overall order is 4.

Step-by-step solution

Identify the Rate Law

The rate law given is \[\text{Rate} = k[\text{BrO}_3^-][\text{Br}^-][\text{H}^+]^2\]

Determine the Order of Each Substance

Look at the exponents of each reactant in the rate law: \[\text{BrO}_3^-\text{: Order = 1}\] \[\text{Br}^-\text{: Order = 1}\] \[\text{H}^+\text{: Order = 2}\]

Calculate the Overall Reaction Order

Sum the orders of all reactants: \[1 + 1 + 2 = 4\] So, the overall reaction order is 4.

Key concepts

rate law

In chemistry, a rate law is a mathematical equation that describes how the concentration of reactants affects the rate of a chemical reaction. The general form of a rate law is: \(\text{Rate} = k[A]^m[B]^n...\) where: \(\text{Rate}\) is the reaction rate, \(k\) is the rate constant, \[A\] and \[B\] are the concentrations of reactants, \(m\) and \(n\) are the reaction orders with respect to each reactant. The rate constant \(k\) is a proportionality constant unique to a particular reaction at a given temperature. Its value changes with temperature but does not depend on the concentration of reactants. Reaction orders (\(m\) and \(n\)) indicate how the rate is affected by the concentration of each reactant. These orders are determined experimentally and do not necessarily correspond to the stoichiometric coefficients in the balanced chemical equation, though they often do. In the given rate law: \(\text{Rate} = k[\text{BrO}_3^-][\text{Br}^-][\text{H}^+]^2\), the exponents indicate the reaction order with respect to each reactant.

overall reaction order

The overall reaction order is the sum of the individual reaction orders of all reactants in the rate law. It gives a general idea of how the reaction rate will change if the concentrations of all reactants are varied simultaneously. To find the overall reaction order, you add up the exponents of all the reactants in the rate law. For example, in the given rate law: \[ \text{Rate} = k[\text{BrO}_3^-][\text{Br}^-][\text{H}^+]^2 \], the exponents are: 1 for \(\text{BrO}_3^-\text{ORDER}\), 1 for \(\text{Br}^-\text{ORDER}\), and 2 for \(\text{H}^+\text{ORDER}\). So, the overall reaction order is \[ 1 + 1 + 2 = 4 \]. This means the reaction is fourth-order overall, implying that the rate of reaction is very sensitive to changes in the concentration of reactants.

individual reaction orders

Individual reaction orders specify how the rate of reaction depends on the concentration of a single reactant. These orders are represented by the exponents in the rate law formula. They must be determined experimentally and are not necessarily related to the stoichiometry of the reaction. For each reactant in the given rate law: \[ \text{Rate} = k[\text{BrO}_3^-][\text{Br}^-][\text{H}^+]^2 \], we find the following individual reaction orders: \(\text{BrO}_3^-\text{: Order = 1}\) \(\text{Br}^-\text{: Order = 1}\) \(\text{H}^+\text{: Order = 2}\). This means: - The rate of the reaction increases linearly with the concentration of \[ \text{BrO}_3^- \]. - The rate of the reaction also increases linearly with the concentration of \[ \text{Br}^- \]. - The rate of the reaction increases quadratically with the concentration of \[ \text{H}^+ \]. Understanding these orders helps in predicting how changes in reactant concentrations will affect the reaction rate.