Keith Mack
The order of a rate law is the sum of the exponents of its concentration terms, and it describes how much a change in the amount of each substance affects the overall rate. The order of reaction can be determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. The order of a reaction can be first, second, or zero, but fractional and even negative orders are possible. A reaction that is first order in A will double in rate when the concentration of A is doubled. As the reaction progresses, the reaction can change from second order to first order as the reactant is consumed.
| Characteristics | Values |
|---|---|
| Reaction orders in the rate law | Same as the coefficients in the chemical equation for the reaction |
| Rate laws | May exhibit fractional orders for some reactants |
| Rate laws | May exhibit negative reaction orders when an increase in the concentration of one reactant causes a decrease in reaction rate |
| Reaction orders in a rate law | Describe the mathematical dependence of the rate on reactant concentrations |
| Reaction orders | Typically positive integers, though they can be fractions, negative, or zero |
| Reaction orders | Determined experimentally by observing how the rate of a reaction changes as the concentrations of the reactants are changed |
| First-order reaction | Depends on the concentration of only one reactant (a unimolecular reaction) |
| First-order reaction | The half-life is independent of concentration |
| Second-order reaction | First order for two reagents (1 + 1 = 2) |
| Zero-order reaction | The reaction rate is independent of any change in the concentration of any of the reactants |
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What You'll Learn
Reaction orders are determined experimentally
The order of a reaction is the relationship between the concentrations of species and the rate of a reaction. The reaction order is the exponent to which the concentration of a species is raised. This indicates the extent to which the concentration of a species affects the rate of a reaction, as well as which species has the greatest effect.
The order of a rate law is the sum of the exponents of its concentration terms. The rate law for a reaction that is second order in A, for instance, will be first order in A and first order in B. The overall reaction order is the sum of the orders for each reactant.
The differential rate law or the integrated rate law can be used to determine the reaction order from experimental data. The exponents in the rate law are often positive integers, such as 1 and 2, or even 0. Thus, reactions are categorized as zeroth, first, or second order in each reactant.
Other methods for determining reaction order include the integration method, the half-life method, and the isolation method.
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Reaction orders can be positive, negative, or zero
The order of a reaction is a number that quantifies the degree to which the rate of a chemical reaction depends on the concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. The overall reaction order is the sum of the orders for each reactant. For example, a reaction that is first order in A and second order in B would be described as a third-order reaction.
Reaction orders can be positive, negative, zero, or even fractional. A positive reaction order means that an increase in the concentration of a reactant will increase the rate of the reaction. For example, in a reaction that is second order in B, doubling the concentration of B will quadruple the reaction rate.
On the other hand, negative reaction orders are observed when an increase in the concentration of a reactant causes a decrease in the reaction rate. For example, the conversion of ozone (O3) to oxygen follows the rate equation v0=k[O3]2[O2]-1, which corresponds to second order in ozone and order (-1) with respect to oxygen.
Zero-order reactions are those in which the reaction rate is independent of any change in the concentration of the reactants. In other words, changing the concentration of the reactants has no effect on the rate of the reaction. For example, in the hydrolysis of sucrose, the water performing the hydrolysis is far in excess of the sucrose dissolved in the solution, making it a zero-order reaction. Many enzyme-catalyzed reactions are also zero order, as long as the reactant concentration is much greater than the enzyme concentration, which controls the rate.
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First-order reactions depend on one reactant
A first-order reaction is one in which the rate of reaction is proportional to the concentration of a single reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on changes in the concentration of only one of the reactants. For example, if a reaction is "first order in A", doubling the concentration of A will double the reaction rate.
The rate expression of the reaction is written as r = k [A]x [B]y, where 'r' refers to the rate of reaction, 'k' is the rate constant of reaction, and [A] and [B] are the concentrations of the reactants. The exponents of the reactant concentrations, x and y, are referred to as partial orders of the reaction. The sum of all the partial orders of the reaction yields the overall order of the reaction.
The half-life of a first-order reaction is independent of the initial concentration of the reactant. This means that it takes the same amount of time for the concentration of a reactant to decrease from 1M to 0.5M as it does to decrease from 0.1M to 0.05M. The rate constant and the half-life of a first-order process are inversely related. The half-life of a first-order reaction is given by the equation: t1/2 = 0.693/k, where 'k' denotes the rate constant.
A first-order reaction can have one or two reactants, as in the case of a decomposition reaction. In a first-order reaction, the rate of reaction depends on the concentration of only one species. This may be the case in a unimolecular reaction (a reaction with only one reactant) or in a reaction with more than one reactant, in which all other reactants are zero order. A reaction may be dubbed pseudo-first order if all other reactants are present far in excess of one reactant, such that changing the concentration of these excess reactants has no effect on the reaction rate.
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Second-order reactions are possible but rare
To determine the order of a reaction, one can plot concentration vs. time (zeroth order), the natural log of concentration vs. time (first order), and one over concentration vs. time (second order). A second-order reaction will yield a straight line on the third graph. The slope of this line is the reaction constant, k.
The rate constant k and the reaction orders must be determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. The reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations. For example, a reaction that is first order in A and second order in B would be described by the rate law r = k[A]¹[B]².
While second-order reactions are rare, they do occur in important biological processes such as the formation of double-stranded DNA from two complementary strands. Additionally, some reactions, such as the hydrolysis of esters by dilute mineral acids, follow pseudo-second-order kinetics under certain conditions.
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Complex reactions may not follow stoichiometric coefficients
Complex reactions may not always follow stoichiometric coefficients. Stoichiometry is a critical concept in chemistry, used to understand and balance chemical reactions. It involves ensuring that a chemical equation has the same number of atoms on both sides and that the charges on both sides are equal. Stoichiometric coefficients, or the numbers placed in front of the chemical species in an equation, are essential for balancing these reactions.
However, the relationship between reactants and products in complex reactions can be more intricate than what stoichiometric coefficients alone can describe. This is because the rate of a chemical reaction depends on various factors, including the concentrations of reactants, temperature, and the reaction mechanism itself.
For instance, in some reactions, the rate may depend on the concentration of only one reactant, resulting in a first-order reaction. In such cases, doubling the concentration of that reactant will double the reaction rate. On the other hand, a reaction may be second-order in one reactant, meaning that doubling the concentration of that reactant will quadruple the reaction rate.
Furthermore, the overall reaction order, which is the sum of the orders for each reactant, can be influenced by the presence of reactants with fractional, negative, or zero reaction orders. Negative reaction orders occur when an increase in the concentration of one reactant causes a decrease in the reaction rate. Zero-order reactants, on the other hand, have no impact on the reaction rate, regardless of changes in their concentration. These variations in reaction orders can lead to complex reactions that do not follow simple stoichiometric coefficients.
Additionally, the concept of stoichiometric proportions comes into play when all reactants are in perfect balance, with no limiting reagent, which adds another layer of complexity. Considering these factors, it becomes evident that while stoichiometric coefficients provide a foundational understanding of chemical reactions, the dynamics of complex reactions may involve a more nuanced interplay of factors that influence reaction rates and overall reaction orders.
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Frequently asked questions
A rate law is a mathematical equation that describes the relationship between the rate of a chemical reaction and the concentrations of the reactants. The rate law is determined experimentally and cannot be predicted by reaction stoichiometry alone.
The order of a rate law is the sum of the exponents of its concentration terms. For example, if the rate law is given by the equation, Rate = k[A]^m[B]^n, then the order with respect to A is m, and the order with respect to B is n. The overall reaction order is the sum of the orders with respect to each reactant.
Yes, rate laws can exhibit different orders as the reaction progresses. This is known as a mixed-order rate law. For example, a reaction may exhibit second-order kinetics at high reactant concentrations but first-order kinetics at low reactant concentrations as the reactants are consumed. Additionally, some reactions may exhibit fractional or negative reaction orders, indicating a more complex relationship between reactant concentrations and reaction rates.
