# Reaction kinetics

There are two fundamental areas of chemistry that deal with how and why chemical reactions occur: thermodynamics and kinetics. Thermodynamics allows one to predict which chemical reactions will occur spontaneously but it provides no information on how fast the reaction will occur. Note spontaneous does not mean fast. Thermodynamics is concerned only with the reactants and products. Thermodynamics is not concerned with the pathway in which the reactants change into products or how fast the reaction occurs. This is the area of kinetics.

Thermodynamics says that the reaction C(diamond) C(graphite) is spontaneous but the reaction rate is so slow that one does not worry about their diamonds turning into pencil lead. Kinetics also deals with the pathway by which the reaction proceeds (the reaction mechanism). The reaction 2H2(g) + O2(g) 2H2O(l) is spontaneous. When H2(g) and O2(g) are mixed nothing much happens until there is a spark then the reaction proceeds explosively.

Sometime it is desirable to have a fast reaction such as to inflate the air bags in a car. Sometimes one wants to slow down the reaction such as the corrosion of steel. Some chemical reactions can produce more than one product. Conditions can be chosen so that the amount of the preferred product is maximized while the amount of side product is minimized. One of the main goals is to understand the mechanism of the reaction. With this knowledge, one can postulate ways to control the reaction, making it either faster or slower.

How fast a reaction is proceeding is its reaction rate. The rate of travel by a car, its speed, is given by the distance travel divided by the amount of time. Similarly the reaction rate is the amount of product formed (or the amount of reactant used) divided by the time period.

Where ∆ means change in.

So ∆product = (amount of product at time, t2) - (amount of product at time, t1) and ∆t = t2 – t1.

Note the minus sign for the change in reactants; this is because the amount of reactant decreases as the reaction proceeds.

Relative rates of the disappearance of reactants and appearance of products are not required to be equal. But the rates are related by the reaction stoichiometry, or by the coefficients in the balanced equation. For example, consider for example the combustion of propane, C3H8, in your barbeque. The balanced chemical reaction is

C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g)

In this case:

O2 consumed is 5x faster than propane
CO2 is formed 3x faster than propane.
H2O is formed 4x faster than propane.

$Rate\ of\ C_3H_8\ consumption = \left(\frac{1}{5}\right)\left(Rate\ of\ O_2\ consumption\right)$ $= \left(\frac{1}{3}\right)\left(Rate\ of\ CO_2\ production\right) = \left(\frac{1}{4}\right)\left(Rate\ of\ H_2O\ production\right)$

$-\frac{\Delta C_3H_8}{\Delta t} = -\left(\frac{1}{5}\right)\left(\frac{\Delta O_2}{\Delta t}\right) = \left(\frac{1}{3}\right)\left(\frac{\Delta CO_2}{\Delta t}\right) = \left(\frac{1}{4}\right)\left(\frac{\Delta H_2O}{\Delta t}\right)$

In general, consider the following reaction occurring in a fixed volume

a A + b B c C + d D
 Rate of Reaction = rate of consumption of reactants $=-\left(\frac{1}{a}\right)\left(\frac{\Delta [A]}{\Delta t}\right) =-\left(\frac{1}{b}\right)\left(\frac{\Delta [B]}{\Delta t}\right)$ = rate of production of products $=\left(\frac{1}{c}\right)\left(\frac{\Delta [C]}{\Delta t}\right) =\left(\frac{1}{d}\right)\left(\frac{\Delta [D]}{\Delta t}\right)$