Integrated Rate Equations

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chemistry 12th class cbse notes

Integrated Rate Equations

The integrated rate equations are different for the reactions of different reaction orders. We shall determine these equations only for zero and first order chemical reactions.

Zero Order Reaction

The rate of the reaction is proportional to zero power of the concentration of reactants.

Zero Order Reaction

Zero Order Reaction

As any quantity raised to power zero is unity

Zero Order Reaction

Integrating both sides

Zero Order Reaction

Where, I is the constant of integration.

At t = 0, the concentration of the reaction R = [R]0 , where [R]0 is initial concentration of the reaction.

Substituting in equation,

Zero Order Reaction

Substituting the value of I

Zero Order Reaction

Zero Order Reaction

Zero Order Reaction

Example:

  • The decomposition of gaseous ammonia on a hot platinum surface at high pressure.

Zero Order Reaction

Zero Order Reaction

  • Thermal decomposition of HI on a gold surface.

First Order Reaction

The rate of the reaction is proportional to the first power of the concentration of the reactant R.

First Order Reaction

Integrating this equation, we get

First Order Reaction

Again, I is the constant of integration and its value can be determined easily.

When t= 0, R= [R]0, where [R]0 is the initial concentration of the reactant.

Therefore, equation can be written as

First Order Reaction

Substituting the value of I in equation

First Order Reaction

Rearranging this equation

First Order Reaction

At time t1 from above eq.

First Order Reaction

Where, [R]1 and [R]2 are the concentrations of the reactants at time t1 and t2 respectively.

Subtracting

First Order Reaction

Comparing equation (2) with y = mx +c, if we plot In[R] against t, we get a straight line with slope = -k and intercept equal to ln[R]0

First Order Reaction

The first order rate equation (3) can also be written in the form

First Order Reaction

First Order Reaction

Example:

  • Hydrogenation of ethane,

First Order Reaction

  • Decomposition of N2O5 and N2O

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