Cecily Zamora
Rate laws, also known as rate equations, are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. The rate of a chemical reaction is determined and altered by factors such as the nature of the reactants, surface area, temperature, and catalysts. While rate laws can be written as equations to show how reactant concentrations affect the rate of the reaction, they cannot be deduced from the written reaction and must be determined experimentally. The rate law expression is used to gain insight into potential mechanisms and connect the macroscopic rate observed in the lab with microscopic or molecular ideas.
| Characteristics | Values |
|---|---|
| Definition | A rate law is a means by which we can relate the rate of a chemical reaction to the concentrations of the reactants |
| Formula | Rate = k[A]x[B]y; overall order of the reaction (n) = x+y |
| Rate Constant | K |
| Reaction Order | The relationship between the concentrations of species and the rate of a reaction |
| Rate Law Expression | Can only be determined experimentally |
| Determining Factors | Nature of reactants, surface area, temperature, concentration, catalysts |
| Units | The units for the rate of a reaction are mol/L/s |
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What You'll Learn
Rate laws and rate equations
Rate laws, also known as differential rate laws, are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. The rate of a reaction is often affected by the concentrations of reactants.
The rate law is experimentally determined and can be used to predict the relationship between the rate of a reaction and the concentrations of reactants. The rate law expression is given by Rate = k [A]x [B]y, where 'k' is the rate constant, and 'x' and 'y' are the reaction orders with respect to reactants 'A' and 'B', respectively. The overall order of the reaction is the sum of the exponents of the reactants in the rate equation. For example, if the rate law is given by Rate = k [A]^2 [B]^3, the overall order of the reaction is 2 + 3 = 5. The units of the rate constant 'k' depend on the overall order of the reaction. For instance, the units for a second-order reaction are mol-2 L2/s, while for a third-order reaction, they are mol-2 L3/s.
The reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations. For instance, if the rate law is Rate = k [A]^1 [B]^2, the reaction is first order with respect to 'A' and second order with respect to 'B'. The exponents in the rate law, such as 'x' and 'y' in the previous example, are typically positive integers but can also be fractions, negative, or zero.
The rate constant 'k' and the reaction orders are determined experimentally by observing how the rate of a reaction changes as the concentrations of the reactants are varied. A common experimental approach to determining rate laws is the method of initial rates, which involves measuring reaction rates for multiple trials with different initial reactant concentrations. By comparing the measured rates, the reaction orders and the rate constant can be determined, which are then used to formulate the rate law.
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Factors affecting reaction rate
The rate of a chemical reaction is affected by several factors. The rate of a reaction is a measure of how fast the reaction is proceeding. It is a measure of the change in concentration of the chemical species as a function of time.
One of the main factors is the concentration of the reactants. The rate of reaction depends on the activation energy, and a higher activation energy means that fewer molecules will have sufficient energy to undergo an effective collision. Increasing the concentration of one or more reactants will increase the rate of reaction as this leads to more collisions in a specific time period.
The physical state of the reactants is another factor. The reaction occurs at the surface, so a larger surface area will lead to a faster rate. For example, powders react faster than blocks as they have a greater surface area. If one of the reactants is a solid, the surface area of the solid will affect the rate.
The presence of a catalyst is another factor. Catalysts are substances that accelerate a reaction by participating in it without being consumed. They provide an alternate reaction pathway to obtain products and lower the activation energy required for the reaction to take place.
Finally, the temperature is a factor. The higher the temperature, the more molecules with sufficient energy, and therefore the faster the rate of reaction.
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Reaction orders
The order of a reaction refers to the relationship between the rate of a chemical reaction and the concentration of the species taking part in it. In other words, it describes the mathematical dependence of the rate on reactant concentrations. The reaction order is the exponent to which the concentration of a species is raised, and it indicates to what extent the concentration of a species affects the rate of a reaction, as well as which species has the greatest effect.
The order of a reaction can be defined as the power dependence of the rate on the concentration of all reactants. For example, the rate of a first-order reaction depends solely on the concentration of one species in the reaction. The rate of a second-order reaction is proportional to the square of the concentration of a single reactant or the product of the concentration of two reactants. A zero-order reaction proceeds at a constant rate, independent of the concentration of the reactants.
The overall reaction order is simply the sum of the orders for each reactant. For instance, a reaction that is first order in hydrogen peroxide and first order overall can be described as a second-order reaction. The reaction is second order in NO2 and zero order in CO.
There are several methods to determine the reaction order, such as the differential method, the graphical method, the mathematical method, and the method of flooding. 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. The graphical method involves plotting concentration versus time data and is most useful when one reactant is isolated by having the others in large excess. The mathematical method is useful when the means to graph are not available and involves determining the slope of the plot that linearizes the data. The method of flooding involves measuring the concentration of a single reactant when all the other reactants are present in huge excess.
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Determining rate laws from tables
Rate laws, or rate equations, are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. The rate of a reaction is often affected by the concentrations of reactants. The rate constant, k, and the reaction orders, m and n, must be determined experimentally by observing how the rate of a reaction changes as the concentrations of the reactants are changed.
To determine a rate law, we need to find the values of the exponents n, m, and p, and the value of the rate constant, k. For example, if we are told that a reaction is second order in A, we can deduce that n is equal to 2 in the rate law.
A common experimental approach to determining rate laws is the method of initial rates. This involves performing a series of experiments with various starting concentrations of reactants and measuring the initial rate law for each reaction. The initial concentration of each reactant must be changed while the other is held constant to compare the rates of reaction and determine the order with respect to each reactant.
Once the rate law for a reaction is determined, the specific rate constant can be found by substituting the data from any of the experiments into the rate law and solving for k. The units for the rate of a reaction are mol/L/s, and the units for k are whatever is needed so that substituting into the rate law expression gives the appropriate units for the rate.
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Rate laws with intermediates
Rate laws, or rate equations, are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. The rate of a chemical reaction at a constant temperature depends only on the concentration of the substances influencing it. These substances are usually the reactants, but they can also be the products or catalysts.
When writing a rate law based on order, intermediates are only included if the rate law is being written for a specific reaction step. Intermediates are molecules or elements found in the product of one step and the reactant of another. They are produced and then used up by the reaction. For example, in the reaction:
> A + B → C
> C → D
> Overall: A + B → D
Here, C is the intermediate, but it is not included in the rate law, which is instead expressed as k[A][B].
However, when there are no equilibrium arrows, the rate law includes only the reactants in the slow step. For instance, in the reaction:
> H2 + Br2 → 2HBr
Br and H are the intermediates and are cancelled out, so they don't appear in the overall reaction.
The rate law expression can be used to determine the rate constant k, which has units that ensure that the rate is in terms of mol/L/s.
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Frequently asked questions
A rate law, or rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of its reactants.
A rate law is determined experimentally by observing how the rate of a reaction changes as the concentrations of the reactants are changed.
The rate of a chemical reaction is influenced by the nature of the reactants, surface area, temperature, concentration, and catalysts.
The reaction order is the relationship between the concentrations of species and the rate of a reaction. The rate law equation is written in the form of reaction rate = rate constant x concentrations of reactants^reaction orders.
