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Rate law expressions: For a reaction The rate of reaction according to the rate law expression
Where: K= specific rate constant or velocity constant And need to necessarily be equal to the stoichiometric coefficients.
For a reaction Step1: Step2: Rate of reaction But (from laws of chemical equilibrium) Hence rate of reaction is Order of a reaction: If the rate of reaction is Then the order of the reaction is Modification of Rate Law Expression: For a reaction Rate of reaction is Order of the reaction is But if one of the reactants, say, ; is taken in large quantity then its concentration is eliminated from the rate law expression (owing to the fact that the reaction will proceed only to that extent to which is available) Hence the rate of reaction can be written as And the NEW Order of the reaction would Integrated rate equations: 1) Zero order reaction:
Where = concentration of the reactant at the beginning of the reaction = concentration of the reactant at time t When we plot a graph of vs t, we would get a straight line with and intercept= 2) 1^{st} order reactions:
3) Half life of a reaction:
Hence half life of a first order reaction would be:
For an order reaction:
Where: is the initial concentration of the reactant and n is the order of the reaction. Amount of reactant left after nth half life periods for a 1^{st} order reaction: Amount of reactant left= Where: n is the number of halflives.
Some examples of 1^{st} order reactions are as follows:
DETERMINATION OF ORDER OF REACTION:
Molecular collisions are effective only when the following conditions are satisfied:
ARRHENIUS EQUATION: This relates the effect of temperature to the rate of reaction.
The value of temperature coefficient is usually 23 The effect of change in temperature on the rate of reaction is given by: Where: = activation energy A= frequency factor K= velocity constant R= molar gas constant T= temperature in Kelvin This implies that
Sample Questions
QuestionA first order reaction has a rate constant of . What is the half life of the reaction? SolutionFor a first order reaction, and for a first order reaction only, the half life is a constant and is proportional to the inverse of the rate constant. By definition, at the time , the concentration is equal to exactly one half of what it was when you started, i.e. Thus, the relationship between the half life and the rate constant of a reaction can easilty be derived for any type of rate law. In this case we have a first order reaction. Remembering the integrated rate law for a first order reaction:
Then
taking the ln of both sides ln or
Thus, the halflife of the reaction is seconds or
QuestionAn elementary reaction, , is second order in A and first order in C. The rate of this reaction is M/s when the concentrations of A, C, and D are all . What is the rate constant for the reaction? SolutionThe rate law for the reaction is rate = Since we know the instantaneous rate of the reaction at known concentrations, we can directly evaluate the rate constant
This is the appropriate units of a rate constant for a reaction that is third order overall.
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