# Chemical reaction rate

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The chemical reaction rate for a reactant or product in a particular chemical reaction is defined as the amount of the chemical that is formed or removed (in moles or mass units) per unit time per unit volume. Knowledge of these rates is essential in, among other disciplines, chemical engineering and environmental engineering. Chemical kinetics is the part of physical chemistry which studies reaction rates.

## Factors influencing rate of reaction

There are several factors that affect the rate of reaction:

• Temperature: Conducting a reaction at a higher temperature puts more energy into the system and increases the reaction rate. The influence of temperature is described by the Arrhenius equation, whose result is factored into the equation by k. As a rule of thumb, the reaction rate doubles for every 10 degrees Celsius increase in temperature.
• Concentration: As reactant concentration increases, the frequency of collision increases and so therefore does the frequency of collisions having sufficient energy to cause reaction.
• Pressure: The rate of gaseous reactions usually increases with an increase in pressure. Increase in pressure in fact is equivalent to an increase in concentration of the gas.
• Electromagnetic Radiation: Electromagnetic radiation is a form of energy. It may affect the rate or even cause a reaction. For example when methane reacts with chlorine in the dark, the reaction rate is very low. It can be sped up when the mixture is put under diffused light. In bright sunlight, the reaction is explosive.
• Order: The order of the reaction has a major effect on its rate. The order of a reaction is found experimentally, and, for most basic reactions, is an integer value.
• A catalyst: 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.
• The complexity of the reaction: If a reaction involves the breaking and reforming of bonds (complex) compared to just the forming of bonds (simple) then it generally takes longer. The reactants position in the reactivity series also affects reaction rate.
• Surface Area: In reactions on surfaces, which take place during heterogeneous catalysis, the rate of reaction increases as the surface area does. This is because the more surface area you have, the more reactant you are able to react at any given time. The larger the surface area compared to the volume, the faster a reaction can take place, as more simultaneous reactions can occur.

## Rate law

For a chemical reaction n A + m B → C + D, the rate equation or rate law is a mathematical expression used in chemical kinetics to link the rate of a reaction (e.g. "rC", i.e. how fast substance C is formed) to the concentration of each reactant and their various orders.

${\displaystyle \,r_{C}=k(T)[A]^{n'}[B]^{m'}}$

By combining the rate law with a 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

${\displaystyle {\frac {d[C]}{dt}}=k(T)[A]^{n'}[B]^{m'}}$

To be more accurate, it is the activities for each species that matters (written {A} rather than [A]), but in diluted solutions this is essentially the same as concentration. For a reaction taking place at a boundary, however, the activity is related to moles of X per area. For gases the rate law can also be expressed in pressure units using e.g. the ideal gas law.

In this equation k(T) is the reaction rate coefficient or rate constant, although it is not really a constant, because it includes everything that affects reaction rate outside concentration: mainly temperature (see the Arrhenius equation) but also ionic strength or light irradiation.

The exponents n and m are called orders and depend on the reaction mechanism.

## Temperature dependence

Each reaction rate coefficient k (i.e., k1 and k2) has a temperature dependency, which is usually given by the Arrhenius equation:

${\displaystyle k=Ae^{-{\frac {E_{a}}{RT}}}}$

Ea is the activation energy and R is the Gas constant. 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 ${\displaystyle e^{\frac {-E_{a}}{RT}}}$. A is the pre-exponential factor or frequency factor.

The values for A and Ea are dependent on the reaction (so, for example, they may differ between k1 and k2). There are also more complex equations possible, which describe temperature dependence of other rate constants which do not follow this pattern.

## Example

For the reaction

${\displaystyle 2H_{2}(g)+2NO(g)\rightarrow N_{2}(g)+2H_{2}O(g)}$

The rate equation is:

${\displaystyle r=k[H_{2}][NO]^{2}\,}$

The reaction is first order in H2, as the hydrogen concentration is raised to the power of 1; it is second order in NO, according to the index.

As can be seen, the rate equation does not simply reflect the reactants - In kinetics the overall reaction can be proposed to occur through a number of elementary steps as follows, all the steps of a proposed mechanism (elemetary steps accounting for the overall equation) must be looked at, this reaction has three proposed mechanisms as follow:

1. ${\displaystyle 2NO\ {\overrightarrow {\longleftarrow }}\ N_{2}O_{2}}$ (fast equilibrium)
2. ${\displaystyle N_{2}O_{2}+H_{2}\rightarrow N_{2}O+H_{2}O}$ (slow)
3. ${\displaystyle N_{2}O+H_{2}\rightarrow N_{2}+H_{2}O}$ (fast)

As reactions 1 and 3 are very rapid compared to the second, it is the slowest reaction that is reflected in the rate equation. Because the other steps of the proposed mechanism for the overall reaction are contingent upon this slow step, the rate of reaction must be equal to this slow step. As these steps account for the overall reaction, they show the reaction from a molecular level this is referred to in chemistry as *Molecularity. Molecularity is the illustration of a reaction from the molecular level. Due to the molecularity of these elementary steps, (shown above) we can write the subsequent rates of reaction for each, according to their relative position amongst all the elementary steps with regard to the rate constant, k, and the order of each, based simply on their coefficents. One must fully understand however, that these elementary steps are neither true nor false, they can only be consistent with the overall reaction.