Reaction rate
Reaction rate | |
---|---|
Common symbols | ν |
SI unit | mol⋅L-1⋅s-1 |
In SI base units | mol⋅m-3⋅s-1 |
Dimension | L-3⋅T-1⋅N |
The reaction rate or rate of reaction is the speed at which a
Formal definition
Consider a typical balanced chemical reaction:
The lowercase letters (a, b, p, and q) represent
According to
where [X] denotes the concentration of the substance X (= A, B, P or Q). The reaction rate thus defined has the units of mol/L/s.
The rate of a reaction is always positive. A
The above definition is only valid for a single reaction, in a closed system of constant volume. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
For an open system, the full mass balance must be taken into account:
- FA0 is the inflow rate of A in molecules per second;
- FA the outflow;
- v is the instantaneous reaction rate of A (in number concentrationrather than molar) in a given differential volume, integrated over the entire system volume V at a given moment.
When applied to the closed system at constant volume considered previously, this equation reduces to:
For a single reaction in a closed system of varying volume the so-called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time.
Here νi is the stoichiometric coefficient for substance i, equal to a, b, p, and q in the typical reaction above. Also V is the volume of reaction and Ci is the concentration of substance i.
When side products or reaction intermediates are formed, the IUPAC[8] recommends the use of the terms the rate of increase of concentration and rate of the decrease of concentration for products and reactants, properly.
Reaction rates may also be defined on a basis that is not the volume of the reactor. When a
Influencing factors
Factors that influence the reaction rate are the nature of the reaction, concentration,
Reaction rate increases with concentration, as described by the
The order of the reaction controls how the reactant concentration (or pressure) affects the reaction rate.
Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles, as explained by collision theory. However, the main reason that temperature increases the rate of reaction is that more of the colliding particles will have the necessary activation energy resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the
.Reaction rates can be independent of temperature (non-Arrhenius) or decrease with increasing temperature (anti-Arrhenius). Reactions without an activation barrier (for example, some radical reactions), tend to have anti-Arrhenius temperature dependence: the rate constant decreases with increasing temperature.
Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength also has an effect on the reaction rate.
Electromagnetic radiation is a form of energy. As such, it may speed up the rate or even make a reaction spontaneous as it provides the particles of the reactants with more energy.[citation needed] This energy is in one way or another stored in the reacting particles (it may break bonds, and promote molecules to electronically or vibrationally excited states...) creating intermediate species that react easily. As the intensity of light increases, the particles absorb more energy and hence the rate of reaction increases. For example, when methane reacts with chlorine in the dark, the reaction rate is slow. It can be sped up when the mixture is put under diffused light. In bright sunlight, the reaction is explosive.
The presence of a catalyst increases the reaction rate (in both the forward and reverse reactions) by providing an alternative pathway with a lower activation energy. For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature.
The kinetic isotope effect consists of a different reaction rate for the same molecule if it has different isotopes, usually hydrogen isotopes, because of the relative mass difference between hydrogen and deuterium. In reactions on surfaces, which take place, for example, during heterogeneous catalysis, the rate of reaction increases as the surface area does. That is because more particles of the solid are exposed and can be hit by reactant molecules.
Stirring can have a strong effect on the rate of reaction for
Some reactions are limited by diffusion. All the factors that affect a reaction rate, except for concentration and reaction order, are taken into account in the reaction
Rate equation
For a chemical reaction aA + bB → pP + qQ, the rate equation or rate law is a
For reactions that go to completion (which implies very small kr), or if only the initial rate is analyzed (with initial vanishing product concentrations), this simplifies to the commonly quoted form
For gas phase reaction the rate equation is often alternatively expressed in terms of partial pressures.
In these equations k(T) is the reaction rate coefficient or rate constant, although it is not really a constant, because it includes all the parameters that affect reaction rate, except for time and concentration. Of all the parameters influencing reaction rates, temperature is normally the most important one and is accounted for by the Arrhenius equation.
The exponents n and m are called reaction
For elementary reactions or reaction steps, the order and stoichiometric coefficient are both equal to the molecularity or number of molecules participating. For a unimolecular reaction or step, the rate is proportional to the concentration of molecules of reactant, so the rate law is first order. For a bimolecular reaction or step, the number of collisions is proportional to the product of the two reactant concentrations, or second order. A termolecular step is predicted to be third order, but also very slow as simultaneous collisions of three molecules are rare.
By using the mass balance for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. For a closed system with constant volume, such an expression can look like
Example of a complex reaction: hydrogen and nitric oxide
For the reaction
the observed rate equation (or rate expression) is:
As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is
In chemical kinetics, the overall reaction rate is often explained using a mechanism consisting of a number of elementary steps. Not all of these steps affect the rate of reaction; normally the slowest elementary step controls the reaction rate. For this example, a possible mechanism is:
Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate-determining step. This is a
However N2O2 is an unstable intermediate whose concentration is determined by the fact that the first step is in equilibrium, so that where K1 is the equilibrium constant of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants
This agrees with the form of the observed rate equation if it is assumed that k = k2K1. In practice the rate equation is used to suggest possible mechanisms which predict a rate equation in agreement with experiment.
The second molecule of H2 does not appear in the rate equation because it reacts in the third step, which is a rapid step after the rate-determining step, so that it does not affect the overall reaction rate.
Temperature dependence
Each reaction rate coefficient k has a temperature dependency, which is usually given by the Arrhenius equation:
where
- Ea is the activation energy;
- R is the gas constant;
- exp is the exponential function.
Since at temperature T the molecules have energies given by a Boltzmann distribution, one can expect the number of collisions with energy greater than Ea to be proportional to The coefficient, A, is the pre-exponential factor or
The values for A and Ea are dependent on the reaction. There are also more complex equations possible, which describe the temperature dependence of other rate constants that do not follow this pattern.
Temperature is a measure of the average kinetic energy of the reactants. As temperature increases, the kinetic energy of the reactants increases. That is, the particles move faster. With the reactants moving faster this allows more collisions to take place at a greater speed, so the chance of reactants forming into products increases, which in turn results in the rate of reaction increasing. A rise of ten degrees Celsius results in approximately twice the reaction rate.
The minimum kinetic energy required for a reaction to occur is called the activation energy and is denoted by Ea or ΔG‡. The transition state or activated complex shown on the diagram is the energy barrier that must be overcome when changing reactants into products. The molecules with an energy greater than this barrier have enough energy to react.
For a successful collision to take place, the collision geometry must be right, meaning the reactant molecules must face the right way so the activated complex can be formed.
A chemical reaction takes place only when the reacting particles collide. However, not all collisions are effective in causing the reaction. Products are formed only when the colliding particles possess a certain minimum energy called threshold energy. As a rule of thumb, reaction rates for many reactions double for every ten degrees Celsius increase in temperature.[11] For a given reaction, the ratio of its rate constant at a higher temperature to its rate constant at a lower temperature is known as its temperature coefficient, (Q). Q10 is commonly used as the ratio of rate constants that are ten degrees Celsius apart.
Pressure dependence
The pressure dependence of the rate constant for condensed-phase reactions (that is, when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice.
The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex:
the activation volume, ΔV ‡, is:
where V̄ denotes the
For the above reaction, one can expect the change of the reaction rate constant (based either on mole fraction or on molar concentration) with pressure at constant temperature to be:[9]: 390
In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure.
Reactions can increase or decrease their rates with pressure, depending on the value of ΔV ‡. As an example of the possible magnitude of the pressure effect, some organic reactions were shown to double the reaction rate when the pressure was increased from atmospheric (0.1 MPa) to 50 MPa (which gives ΔV ‡ = −0.025 L/mol).[12]
See also
- Diffusion-controlled reaction
- Dilution (equation)
- Isothermal microcalorimetry
- Rate of solution
- Steady state approximation
Notes
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