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Ch 14.5 Temperature and Rate

Ch 14.5 Temperature and Rate. Generally, as temperature increases, so does the reaction rate. This is because k is temperature dependent. The Collision Model. In a chemical reaction, bonds are broken and new bonds are formed. Molecules can only react if they collide with each other.

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Ch 14.5 Temperature and Rate

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  1. Ch 14.5 Temperature and Rate • Generally, as temperature increases, so does the reaction rate. • This is because k is temperature dependent.

  2. The Collision Model • In a chemical reaction, bonds are broken and new bonds are formed. • Molecules can only react if they collide with each other. • Molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation. • In some reactions only about 1 in 1013 collisions will produce a product molecule. Why?

  3. The Orientation Factor • Molecules must be oriented in a certain way during collisions in order for a reaction to occur. • The diagrams below show how orientation affects the formation of the product. Even if molecules collide with enough energy, if their orientation is not correct a product will not be formed. Cl + NOCl  Cl2 + NO

  4. Activation Energy • Assuming molecules collide with the proper orientation, there is a minimum amount of energy required for a reaction: the activation energy, Ea. • Just as a ball cannot get over a hill if it does not roll up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation energy barrier.

  5. It is helpful to visualize energy changes throughout a process on a reaction coordinate diagram like this one for the rearrangement of methyl isonitrile.

  6. The energy gap between the reactants and the activated complex is the activation energy (Ea) barrier. • The high point on the diagram is the activated complex or transition state. • The energy barrier represents the energy necessary to force the molecule through the unstable intermediate state to the final product.

  7. Maxwell–Boltzmann Distribution • A Maxwell-Boltzman distribution curve (below) shows the distribution of molecular energies for a confined gas. • Temperature is defined as a measure of the average kinetic energy of the molecules in a sample. • As the temperature increases the peak of the line moves lower and to the right: from the lower temperature to the higher temperature. • The area under the graph represents the total number of particles and stays the same whatever the temperature. • At higher temperatures a larger number of molecules at any instant will have the minimum energy required for reaction.

  8. If the dotted line represents the activation energy, as the temperature increases, so does the fraction of molecules that can overcome the activation energy barrier. • This fraction of molecules can be found through the expression where R is the gas constant and T is the Kelvin temperature. f = e−Ea/RT

  9. The Arrhenius Equation • Svante Arrhenius (c.1888) noted that for most reactions the increase in rate with temperature is nonlinear. • He developed a mathematical relationship between k (the rate constant) and Ea(the activation energy): k = Ae−Ea/RT • A is the frequency factor, a number that represents the likelihood that collisions would occur with the proper orientation for reaction.

  10. -Ea RT • Taking the natural logarithm of both sides, the equation becomes ln k = ( ) + ln A y = mx + b • Therefore, if k is determined experimentally at several temperatures, Eacan be calculated from the slope of a plot of ln k vs. 1/T. (See Ex 14.11) • Ea can also be calculated a nongraphical way if we know the rate constants of a reaction at two different temperatures. Also, knowing Ea, the rate constant can be determined at some other temperature. (See equation 14.21)

  11. 14.6 Reaction Mechanisms • The sequence of events that describes the actual process by which reactants become products is called the reaction mechanism. • Reactions occur in a single step or event. • Each of these processes is known as an elementary reaction or elementary process. Elementary Reactions

  12. Rate Laws for Elementary Reactions • The molecularity of a process tells how many molecules are involved in the process.

  13. Multistep Mechanisms • In a multistep process, one of the steps will be slower than all others. • The overall reaction cannot occur faster than this slowest, rate-determining step.

  14. Mechanism with Slow Initial Step Ex: NO2 (g) + CO (g)  NO (g) + CO2 (g) • The rate law for this reaction is found experimentally to be Rate = k [NO2]2 • A proposed mechanism for this reaction is Step 1: NO2 + NO2 NO3 + NO (slow) Step 2: NO3 + CO  NO2 + CO2 (fast) • The NO3 intermediate, produced slowly, is consumed in the second step which is very fast. • As CO is not involved in the slow, rate-determining step, it does not appear in the rate law. k1 k2

  15. Mechanism with Fast Initial Step Ex: 2 NO (g) + Br2(g) 2 NOBr (g) • The rate law for this reaction is found to be Rate = k [NO]2 [Br2] • Because termolecular processes are rare, this rate law suggests a two-step mechanism.

  16. Step 1: NO + Br2 NOBr2 (fast) Step 2: NOBr2 + NO  2 NOBr (slow) • A proposed mechanism is • Step 1 includes the forward and reverse reactions. • The rate of the overall reaction depends upon the rate of the slow step. • The rate law for that step would be Rate = k2 [NOBr2] [NO] • But how can we find [NOBr2]?

  17. NOBr2 can react two ways: • With NO to form NOBr • By decomposition to reform NO and Br2 • The reactants and products of the first step are in equilibrium with each other. • Therefore, Ratef = Rater

  18. k1 k−1 [NO] [Br2] = [NOBr2] • Because Ratef = Rater , k1 [NO] [Br2] = k−1 [NOBr2] • Solving for [NOBr2] gives us

  19. k2k1 k−1 [NO] [Br2] [NO] Rate = • Substituting this expression for [NOBr2] in the rate law for the rate-determining step gives = k [NO]2 [Br2]

  20. 14.7 Catalysis • Catalysts increase the rate of a reaction by decreasing the activation energy of the reaction. • Catalysts change the mechanism by which the process occurs. • Catalysts are not consumed in the reaction.

  21. Homogeneous Catalysis • A catalyst present in the same phase (gas or solution) as the reacting molecules is called a homogeneous catalyst. • Ex: 2 H2O2(aq)  2 H2O(l)+ O2(g) • See Fig 14.19 • H2O2 decomposes slowly, but when NaBr is added to H2O2 in acidic solution the bromide ion reacts with the H2O2 to form aqueous bromine and water. • The brown color in fig 14.19 indicates formation of Br2(aq) • H2O2 also reacts with Br2(aq) to generate O2(g) • The Br- ions present at the start of the reaction are also present at the end.

  22. Heterogeneous Catalysis • A heterogeneous catalyst exists in a different phase from the reactant molecules, such as a solid catalyst in contact with gaseous or aqueous reactants. • One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break. • Ex: C2H4(g) + H2(g) C2H6(g) • The above reaction is exothermic but still occurs slowly. • A finely powdered metal, such as nickel, palladium, or platinum, allows the reaction to occur rapidly at room temperatures.

  23. The catalyst speeds up the reaction by holding the reactants together and helping bonds to break. • H2 and C2H4 are adsorbed at metal surface. The H—H bond is broken to give adsorbed H atoms which migrate to the adsorbed ethylene and bond to the carbon atoms. The adsorption of ethane to the metal surface is decreased and ethane is released.

  24. Enzymes • Enzymes are catalysts in biological systems. • Most are large protein molecules from about 10,000 to 1 million amu. • They are very selective in the reactions they catalyze. • Ex: decomposition of H2O2 produced in cells by catalase. • The substrate fits into the active site of the enzyme much like a key fits into a lock. • Active sites are actually flexible, not rigid. Binding occurs through various intermolecular forces (H-bonding, dipole-dipole attractions, London dispersion forces). • Substrate molecules are activated for quick reaction at active site by withdrawal or donation of electron density at a particular bond.

  25. Substrate molecules can also be distorted at the active site making them more reactive. • Enzyme inhibitors are substances that can bind at or distort the active site of an enzyme and prevent substrates from being able to bind. • The number of individual catalyzed reactions at a particular active site (turnover number) in generally in the range of 103 to 107 reactions per second.

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