Gavin Howe
Rate laws provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. They are determined experimentally and cannot be predicted by reaction stoichiometry. The rate law for a reaction between two substances is determined by measuring the rate of reaction at different initial concentrations of the two substances. The rate law can then be formulated using the reaction orders and the rate constant. The rate constant can be determined through various methods, such as changes in mass, NMR chemical shift, colour (UV absorption band), fluorescence emission, and circular dichroism signal.
| Characteristics | Values |
|---|---|
| Reaction rate | Depends on the concentration of reactants |
| Rate law | A mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction |
| Order of reaction | First order, second order, zero order, fractional order, or negative order |
| Rate constant | Determined experimentally by observing how the rate of reaction changes as the concentrations of reactants change |
| Units of rate constant | Determined by the required units for the rate of reaction |
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What You'll Learn
Reaction orders
The reaction order is the relationship between the concentrations of species and the rate of a reaction. The order of a rate law is the sum of the exponents of its concentration terms. Once the rate law of a reaction has been determined, the same law can be used to understand the composition of the reaction mixture.
The differential method, also known as the initial rates method, uses an experimental data table to determine the order of a reaction with respect to the reactants used. This method involves measuring reaction rates for multiple experimental trials carried out using different initial reactant concentrations. Comparing the measured rates for these trials allows for the determination of the reaction orders and, subsequently, the rate constant, which together are used to formulate a rate law.
The rate constant k is independent of the reactant concentrations, but it does vary with temperature. The reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations. For example, if a reaction is “first order in A,” doubling the concentration of A will double the reaction rate. If a reaction is “second order in B,” doubling the concentration of B will quadruple the reaction rate. Reactants with negative orders inversely impact the rate of reaction when their concentrations are increased, and those reactants that are zero-order have no effect on the reaction rate at all.
For a reaction that is zero order in A, a plot of the concentration of A ( [A]) versus time gives a straight line with a slope equal to the rate constant k. The units of the rate constant k are thus 1/s (“per second”). A reaction is second order overall when it is second order in one reagent, zero order in all others, or first order for two reagents (1 + 1 = 2). For example, the combination reaction A + B → C would be second-order overall if first-order in both A and B.
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Reaction rates
The rate law of a reaction provides a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. In other words, it describes the relationship between the rate of a chemical reaction and the concentration of its reactants.
Rate laws are determined experimentally and cannot be predicted by reaction stoichiometry. The rate of a reaction is affected by the concentrations of reactants. The order of reaction describes how much a change in the amount of each substance affects the overall rate. For example, if a reaction is "first order in A", doubling the concentration of A will double the reaction rate. If a reaction is ""second order in B", doubling the concentration of B will quadruple the reaction rate. The overall order of a reaction is the sum of the orders for each substance present in the reaction.
The rate constant of a reaction can be measured using any method that can distinguish between the reaction product and its starting reagent(s). Changes in mass, NMR chemical shift, colour (UV absorption band), fluorescence emission maximum or quantum yield, and circular dichroism signal are all commonly used markers to monitor the transformation of reactants to products.
Differential rate laws express the rate of a reaction in terms of the change in the concentration of reactants over a small interval of time. Differential rate equations can be used to calculate the instantaneous rate of a reaction. Integrated rate equations express the concentration of reactants as a function of time.
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Rate constants
The rate constant of a reaction is represented by the symbol 'k' and is a crucial component of the rate law, which mathematically describes the relationship between the rate of a chemical reaction and the concentrations of its reactants. The rate constant itself is independent of the concentration of the reactants but depends on factors such as temperature and surface area.
The rate constant can be determined through various experimental methods, including monitoring changes in mass, NMR chemical shift, colour (UV absorption band), fluorescence emission, and circular dichroism. One common experimental approach is the method of initial rates, where reaction rates are measured for multiple trials with different initial reactant concentrations. By comparing these measured rates, the reaction orders and the rate constant can be determined.
The rate constant can also be calculated for elementary reactions through molecular dynamics simulations. One approach is to calculate the mean residence time of the molecule in the reactant state, although this is more applicable to small systems with short residence times. Other methods such as Divided Saddle Theory, the Bennett Chandler procedure, and Milestoning have been developed to overcome this limitation.
In terms of its mathematical representation, the rate constant 'k' is used in the rate law expression to ensure that the equation produces the appropriate units for the rate. For example, if the concentration units are mol3/L3, the units for 'k' should be mol−2 L2/s so that the rate is in terms of mol/L/s.
The rate constant is also essential in determining the order of a reaction. For instance, if doubling the concentration of a reactant 'A' results in a doubling of the reaction rate, the reaction is considered first order in 'A'. If doubling the concentration of 'A' results in a quadrupling of the reaction rate, the reaction is second order in 'A'. The overall order of the reaction is the sum of the orders of each individual reactant.
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Differential rate laws
The rate law, or rate equation, for a chemical reaction is a mathematical equation that expresses the relationship between the rate of the reaction and the concentrations of the reactants involved. It is expressed as:
Rate = k[A]^x[B]^y
Where k is the rate constant, and x and y are the reaction orders for reactants A and B, respectively. The overall order of the reaction is the sum of the reaction orders for each reactant.
For example, consider a reaction between formic acid (HCOOH) and bromine in aqueous solution:
HCOOH (aq) + Br2 (aq) → 2 H+ (aq) + 2 Br- (aq) + CO2 (aq)
In this reaction, the concentration of formic acid is much higher than that of bromine. Therefore, the change in the rate of reaction can be attributed to changes in the concentration of bromine. Using the isolation method, we can determine the order of the reaction with respect to bromine.
There are three commonly encountered differential rate laws:
- Zero-order reaction: The rate of reaction is constant and independent of the concentration of reactants. The differential rate law is expressed as r = k, where k is the rate constant with units of mole L-1 sec-1.
- First-order reaction: The rate of reaction is directly proportional to the concentration of one of the reactants. The differential rate law is given by r = k [A], where k has units of sec-1.
- Second-order reaction: The rate of reaction is directly proportional to the square of the concentration of one of the reactants. The differential rate law is r = k [A]^2, with k having units of L mole-1 sec-1.
By measuring the reaction rates for multiple experimental trials with different initial reactant concentrations, the reaction orders, and subsequently the rate constant, can be determined to formulate the differential rate law for a reaction.
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Reaction mechanisms
The rate law of a reaction is a mathematical expression that describes how the rate of a chemical reaction depends on the concentrations of the reactants. It is determined experimentally and provides information about the reaction mechanism, which is the step-by-step process by which the reaction occurs at the molecular level. Now, let's delve into the concept of reaction mechanisms and how they relate to rate laws.
A reaction mechanism describes the sequence of elementary reactions or steps that occur during a chemical reaction. These elementary reactions are often referred to as elementary steps because they are the simplest reactions that cannot be broken down into smaller, faster reactions. The overall reaction is the sum of these elementary reactions. It's important to note that the balanced chemical equation for an overall reaction does not reveal the individual elementary reactions or their rate laws.
To understand reaction mechanisms, let's consider the reaction between carbon monoxide (CO) and nitrogen dioxide (NO2) to form nitric oxide (NO) and carbon dioxide (CO2):
\NO2(g) + CO(g) → NO(g) + CO2(g)
Based on this balanced equation, one might assume that the reaction occurs through a simple collision between one molecule of NO2 and one molecule of CO. However, the experimentally determined rate law for this reaction is second order in [NO2] and independent of [CO]. This indicates that the reaction mechanism is more complex than a simple collision model.
The reaction likely proceeds through a two-step mechanism, where the first step is the rate-determining step, and the second step is much faster. In this case, the first step involves the formation of NO3, which occurs slowly, and the second step involves the rapid reaction of NO3 with CO to produce the final products. This two-step mechanism is consistent with the experimentally determined rate law.
Determining Rate Laws:
The rate law for a reaction can be determined experimentally by varying the initial concentrations of the reactants and measuring the reaction rates. For example, in the reaction between methanol (CH3OH) and ethyl acetate (CH3CH2OCOCH3), the rate law was determined to be first order in CH3OH and zero order in CH3CH2OCOCH3. This information helps us understand the reaction mechanism and the role of each reactant in the overall process.
In summary, reaction mechanisms provide a detailed understanding of how a chemical reaction proceeds at the molecular level, and the rate law is a crucial tool for quantifying the relationship between reactant concentrations and reaction rates. Together, they offer valuable insights into the kinetics and mechanisms of chemical reactions.
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Frequently asked questions
Rate laws provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction.
Rate laws are determined experimentally and cannot be predicted by reaction stoichiometry. The rate constant of a reaction can be measured using any method that can distinguish between the reaction product and its starting reagent(s).
The rate law equation, or differential rate law, takes the form: rate = k[A]^m[B]^n[C]^p, where [A], [B], and [C] represent the molar concentrations of reactants, and k is the rate constant.
The rate constant, k, is specific for a particular reaction at a particular temperature. The units of k depend on the units of the rate of the reaction.
