# Rate Equations

Understanding Rate Equations

• A rate equation shows how the rate of a reaction depends on the concentration of the reactants.
• General form of a rate equation is rate = k[A]^m[B]^n where k is the rate constant, and m and n are the orders of reaction with respect to A and B.
• The sum of m and n gives the overall order of the reaction.

Defining Order of Reaction

• Zero order: The rate of reaction is unaffected by the concentration of the reactant. The graph of concentration against time is a straight line with a negative slope.
• First order: The rate of reaction is proportional to the concentration of the reactant. The graph of concentration against time follows an exponential decay curve.
• Second order: The rate of reaction is proportional to the square of the concentration of the reactant.

Determining Rate Equations

• Experimental data for variation of rate of reaction with changing concentrations is used to determine the rate equation.
• Various methods like initial rates method, graphical method etc., are used to identify the order of reaction and rate constant.
• For reactions involving more than one reactant, each reactant’s order is determined individually by changing its concentration and keeping others constant.

Rate Constants and Temperature

• The rate constant k depends on the temperature of the reaction system.
• As the temperature increases, the rate constant usually increases, demonstrating the specificity of reactions at different temperatures.
• The Arrhenius equation relates the rate constant to the temperature and activation energy of a reaction.

Applications of Rate Equations

• Rate equations can be used to predict the behaviour of a reaction over time.
• Chemical engineers and chemists use rate equations to design and optimise chemical processes.
• By controlling variables linked to the rate equation (such as temperature and reactant concentrations), production rates can be maximised, and energy and waste minimised.

Safety Considerations for Rate Equations

• Exothermic reactions, which release heat, may cause temperature increases that can significantly speed up reactions; understanding the rate equation can help control these reactions.
• If an industrial process is happening too quickly due to high reactant concentrations, it can be slowed down by diluting the reactants or lowering the temperature.
• Knowing a process’s rate equation and the factors affecting the rate allows for forecasts on potential hazards, helping to establish safe operating parameters.