Gavin Howe
Rate expression and rate law are two important concepts in chemistry that describe the rate of a chemical reaction. The rate expression gives the rate of appearance or disappearance of products or reactants, whereas the rate law gives the relationship between the rate of the reaction and the concentration or pressure of reactants. The rate law is the mathematical expression of the rate of a reaction, which can be determined experimentally.
| Characteristics | Values |
|---|---|
| Rate Expression | Gives the rate of appearance or disappearance of products or reactants |
| Rate Law | Gives the relationship between rate and concentration or pressure of reactants |
| Rate Expression | Provides a way of representing the change in reactant concentration over the time of reaction |
| Rate Law | Provides a mathematical expression of the rate of a reaction |
| Rate Expression | Independent of the mechanism of the reaction |
| Rate Law | Dependent on the mechanism of the reaction |
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What You'll Learn
Rate Expression: Change in reactant concentration over time
The rate expression is a way of representing the change in reactant concentration over the time of reaction. It gives the rate of appearance or disappearance of products or reactants. It is a mathematical equation that shows the dependence of the reaction rate on the rate constant and the concentration of one or more reactants.
The rate expression can be written in the form:
Reaction rate = k x [Concentration of A] x [Concentration of B] y
Here, 'k' is the rate constant, and 'x' and 'y' are the partial orders of reactants A and B, respectively. The overall order of the reaction is the sum of these partial orders. The rate expression can also be expressed as:
Reaction rate = -[Concentration of A] / a x change in time
Where 'a' is the coefficient of reactant A. This form of the equation shows how the rate of appearance or disappearance of products and reactants is related to one another. It also tells us how the rate of a reaction is related to the concentration or pressure of reactants.
The rate expression is a useful tool when studying reaction kinetics, as it helps to relate the rates of appearance and disappearance of species present in the reaction. It is important to note that the rate expression is independent of the mechanism of the reaction and is based on stoichiometry.
The rate law, on the other hand, gives the relationship between the rate of a reaction and the concentration or pressure of reactants. It is the mathematical expression of the rate of a reaction and can be determined experimentally. The rate law can be written in two major ways: the differential rate law and the integrated rate law. The differential rate law expresses the reaction rate using the change in concentration of one or more reactants over a specific period of time. The integrated rate law, on the other hand, expresses the reaction rate as a function of time.
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Rate Law: Relationship between rate and concentration
Rate laws provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. The rate law gives the relationship between the rate of a reaction and the concentration or pressure of reactants. It is the mathematical expression of the rate of a reaction, which includes the relationship between reactants' rates and products' rates.
The rate law can be determined experimentally and can be expressed in two major ways: differential rate law and integrated rate law. The differential rate law expresses the reaction rate using the change in concentration of one or more reactants over a specific period of time. The integrated rate law, on the other hand, expresses the reaction rate as a function of time and can be obtained through the integration of the differential rate law.
The rate law equation can be expressed as:
Rate = k[A]x[B]y
Where k is the rate constant, and x and y are the partial orders of reactants A and B, respectively. The sum of these partial orders gives the overall order of the reaction. For example, if the reaction is of the first order, doubling the reactant concentration will double the reaction rate.
The rate expression, on the other hand, gives the rate of appearance or disappearance of products or reactants. It describes the reaction in terms of the change in reactant or product concentrations over time. The rate expression is of the form:
Reaction rate = k [A]^m[B]^n
Where k is the rate constant, and m and n are the reaction orders for A and B, respectively. The rate expression helps to relate the rates of appearance or disappearance of the species present in the reaction.
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Rate Expression: Independent of reaction mechanism
The rate expression is a way of representing the change in reactant concentration over the time of reaction. It gives the rate of appearance or disappearance of products or reactants. The rate expression is independent of the reaction mechanism and is based on stoichiometry. For example, for the reaction:
$$\ce{aA + bB -> cC + dD}$$
The rate expressions are:
- Rate = - [A]/a x change in time
- Rate = - [B]/b x change in time
- Rate = [C]/c x change in time
- Rate = [D]/d x change in time
Here, the minus signs represent the decrease of reactants, and no sign represents the increase of products over some time period. The rate expression is also known as the rate relationship. It helps relate the rates of appearance or disappearance of the species present. For instance, for the reaction:
$$\ce{H2 + I2 -> 2HI}$$
The rate expression is:
$$-\frac{1}{1}\frac{\Delta \left [ \ce{H2} \right]}{\Delta t}\; = \; -\frac{1}{1}\frac{\Delta \left [ \ce{I2} \right]}{\Delta t}\; =\; \frac{1}{2}\frac{\Delta \left [ \ce{HI} \right]}{\Delta t}$$
The rate expression is modified by the inverse of the stoichiometric coefficient. The rate expression is independent of the reaction mechanism, meaning it is not concerned with how the reaction occurs, but rather with the relationship between the rates of appearance and disappearance of products and reactants.
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Rate Law: Dependent on reaction mechanism
The rate law is dependent on the mechanism of the reaction. It is the mathematical expression of the rate of a reaction, detailing the relationship between the reactants' rate and the product's rate. The rate law can be determined experimentally, and the relationship can be verified. There are two types of rate laws: differential rate law and integrated rate law.
The differential rate law expresses the reaction rate using the change in concentration of one or more reactants over a specific period of time. For example, for the reaction in which reactant "A" decomposes to give products, the rate law equation is as follows:
> −Δ [A]/Δt = k⋅ [A]^n
Where k is the rate constant, and n is the order of the reaction.
The integrated rate law, on the other hand, expresses the reaction rate as a function of time. It can be obtained by integrating the differential rate law. For example, for the reaction A → products, the integrated rate law is as follows:
> ln [A] = −kt + ln [A]0
Where [A]0 is the initial concentration of reactant A.
The order of a reaction is essential in understanding how changes in reactant concentration affect the rate of reaction. For instance, in a zero-order reaction, doubling the reactant concentration has no impact on the reaction rate. In contrast, for a first-order reaction, doubling the reactant concentration leads to a proportional increase in the reaction rate.
Rate laws are crucial in the field of kinetics, where the constant of proportionality is referred to as the rate constant. This rate constant, denoted as "k," is determined by the rate law and represents the relationship between the rate of the reaction and the concentrations of the reactants.
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Rate Law: Mathematically determined
Rate laws provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. The rate law is the mathematical expression of the rate of a reaction, which includes the relationship between reactants' rates and products' rates.
The rate law can be determined experimentally and can be expressed in two major ways: differential rate law and integrated rate law. The differential rate law expresses the reaction rate using the change in concentration of one or more reactants over a specific period of time. The integrated rate law, on the other hand, expresses the reaction rate as a function of time and can be obtained through the integration of the differential rate law.
For example, consider the reaction:
$$\ce{aA + bB -> cC + dD}$$
The rate expressions for this reaction would be:
$$\co: 7,19,21>\text{rate} = -\frac{1}{a} \frac{[A]}{\Delta t} = -\frac{1}{b} \frac{[B]}{\Delta t} = \frac{1}{c} \frac{[C]}{\Delta t} = \frac{1}{d} \frac{[D]}{\Delta t}$$
The negative signs represent the decrease of reactants, and the absence of a sign represents the increase of products over time. The differential rate law for this reaction would be:
$$\co: 7>\text{rate} = k[A]^m[B]^n$$
Where k is the rate constant, and m and n are the reaction orders for A and B, respectively.
The integrated rate law for this reaction would be:
$$\co: 14>\text{rate} = k[A]^a[B]^b$$
Where k is the rate constant, and a and b are the exponents.
The rate law provides a mathematical framework to understand the relationship between the rate of a reaction and the concentration or pressure of reactants. By manipulating the rate law equation, the value of the rate constant, k, can be determined. The units for k will depend on the concentration units to ensure the rate is in the appropriate units.
In summary, the rate law mathematically expresses the rate of a reaction by relating the rate to the concentration or pressure of reactants. This relationship can be determined experimentally, and the rate law can be expressed in differential or integrated forms.
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Frequently asked questions
A rate expression is a way of representing the change in reactant concentration over the time of reaction. It gives the rate of appearance or disappearance of products or reactants.
A rate law gives the relationship between the rate and concentration or pressure of reactants. It is the mathematical expression of the rate of a reaction.
Rate laws are determined experimentally. The rate law for a reaction can be determined by selecting two sets of rate data that differ in the concentration of only one reactant and setting up a ratio of the two rates and the two rate laws.
A rate expression expresses or defines what the rate is, whereas a rate law gives the relationship between the rate and concentration or pressure of reactants.
