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## 4.1 Rate Equation, stoichiometrt And Rate Laws:

### Rate Equation:

The rate law or rate equation is an equation which relates the rate of reaction with concentrations or pressures of reactants and constant parameters. The rate equation for a particular system is determined by combining the reaction rate with a mass balance for the system. For reaction A + B → C the simple rate equation is of the form:

r = k[A]m[B]n In this equation, [ ] expresses the concentration, the k is the reaction rate coefficient or rate constant and it includes everything that affects reaction rate outside concentration such as temperature, ionic strength, surface area of the adsorbent or light irradiation.

The exponents’ n and m are order of reaction and depend on the mechanism of reaction. The stoichiometric coefficients and the reaction orders are very often equal in reactions of one step, number of molecules or atoms actually colliding or molecularity, stoichiometry and reaction order must be the same.

Zeroth order reaction: m = n = 0

First order reaction: m = 1, n = 0

Second order reaction: m = 2, n = 0 or m = n = 1

Order of reaction is decided by value of (m + n)

Various types of reactions are:

Pseudo first order reactions

Equilibrium or opposed reactions

Consecutive reactions

Parallel or competitive reactions

### Stoichiometry:

Stoichiometry or reaction stoichiometry is different from composition stoichiometry and is the calculation of measurable quantitative relationships of the products with reactants in a balanced reaction. It can be used for calculating quantities such as the amount of products that can be produced with the given reactants and percent yield.

Stoichiometry rests upon the law of mass conservation, the law of constant composition and the law of multiple proportion. Chemical reactions combine in definite ratios of chemicals in general. As chemical reactions can neither create nor destroy matter, nor one element is transmuted into another, the amount of each element must be the same throughout the overall reaction. For example, the amount of element A on the reactant side must equal the amount of element A on the product side and vice-versa.

Gas stoichiometry is the quantitative relationship between reactants and products when it is employed for reactions where the product is a gas. Gas stoichiometry applies when the gases produced are assumed to follow ideal gas laws for calculations, and the temperature, pressure, and volume of the gases are all known. Often, but not always, the STPs are taken as 0°C and 1 bar and used as the conditions for gas stoichiometric calculations.

### Rate Laws:

There are two general methods to determine the rate law by the given experimental data. The first is the method of initial rates which is appropriate when the reaction is relatively slow so that the initial rate may be determined as a function of initial concentrations and the second method, which makes use of integrated rate equations, is applicable when the reaction is sufficiently fast so that concentration versus time data may be collected over several half-lives. The half life of a substance is the time needed for its concentration to fall to one-half its initial concentrations and it can be used for several purposes.

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