12.4 Integrated Rate Laws

12.4 Integrated Rate Laws

• The table shows the rate constant units for reaction orders.

• Depending on the situation, units of time other than the second may be used.

• The rate laws relate the rate to the concentrations of reactants.
• There is a second form of each rate law that relates the concentrations of reactants and time.

• An integrated rate law can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent.
• An integrated rate law can be used to determine the length of time a radioactive material needs to be stored.

• The differential rate law for a chemical reaction can be used to calculate an equation that relates the amount of reactant or product present in a reaction mixture to the elapsed time.

• Depending on the complexity of the differential rate law, this process can be very straightforward or very complex.
• The resulting rate laws for first-, second-, and zero-order reactions will be the focus of the discussion.

• If we know three of the four variables, we can determine the fourth.

• Iodine-131 is used to diagnose and treat some forms of cancer.

• The rate constant is 0.138 d-1.
• The radioactive decay is first order.

• To determine the order and rate constant of a reaction, we can use integrated rate laws with experimental data.

• The relationship between time and ln[H2O2] shows that hydrogen peroxide is a first-order reaction.

• The plot of ln[H2O2] versus time is linear, thus we have verified that the reaction may be described by a first-order rate law.

• The rate constant of second-order reactions and the concentrations of reactants are complicated equations.

• The integrated form of the rate law is used to answer questions.

• The data should show if the dimerization of C4H6 is a first- or second-order reaction.

• The values are needed for the plots.

• The first and second-order plots are for the dimerization of C4H6.
• The reaction is not first order since the first-order plot is not linear.
• The secondorder plot shows that the reaction follows second-order kinetics.

• A zero-order reaction has a constant reaction rate regardless of the concentration of its reactants.

• The plot is straight and the NH3 decomposition is zero order.
• The first order of the NH3 decomposition is not zero order.

• The reaction on a W surface is zero-order, whereas the reaction on a SiO2 surface is first order.

• Half of the remaining concentration is consumed in each succeeding half-life.
• The half-life of a first-order reaction is unaffected by the concentration of the reactant.
• Half-lives of reactions with other orders depend on concentrations of reactants.

• The 2H2 O + O2) is illustrated.
• The intensity of the color shows the concentration of H2O2 at certain times.

• 1/2 is proportional to the concentration of the reactant and the half-life increases as the reaction proceeds.
• The half-life concept is more complex for second-order reactions than for first-order reactions.
• The rate constant of a second-order reaction cannot be calculated directly from the half-life unless the initial concentration is known.