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Chemical Kinetics Part 2. Chapter 13. The Change of Concentration with Time. Zero-Order Reactions (or zeroth order) Goal: convert rate law into a convenient equation to give concentrations as a function of time.

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slide2

The Change of

Concentration with Time

slide3

Zero-Order Reactions (or zeroth order)

  • Goal: convert rate law into a convenient equation to give concentrations as a function of time.
  • For a zero order rxn, the rate is unchanged or is independent of the concentration of a reactant.
  • However, you must have some of the reactant for the rxn to occur!
slide4

Zero-Order Reactions (or zeroth order)

  • One example of a rxn which is 0 order is:
  • 2HI(g) H2(g) + I2(g)
  • The rate law for this rxn has been determined experimentally and is:
  • rate = k[HI]0 = k or rate = k
  • What are the k units?
  • Rate = M/s so k units are M/s or M•s-1
slide5

Zero-Order Reactions (or zeroth order)

  • But the rate is also equal to the change in [reactant] over the change in time:
  • But if rate = k, this means that this is true:
slide6

Zero-Order Reactions (or zeroth order)

  • We rearrange this equation:
  • We then integrate:
slide7

Zero-Order Reactions (or zeroth order)

  • This eq. means that a graph of [HI] vs. time is a straight line with a slope of -k and a y-intercept of [HI]0.
  • Here are typical 0-order graphs:
slide8

Zero-Order Reactions (or zeroth order)

  • We can find the half-life, t1/2, for a 0-order rxn.
  • The t1/2 is defined as the time it takes for half of the reactant to disappear.
  • But this is the time required for [A] to reach
  • 0.5[A]0
  • Mathematically, this is:
slide9

First-Order Reactions

  • For a first order rxn, the rate doubles as the concentration of a reactant doubles.
  • We can show that
  • A plot of ln[A]t versus t is a straight line with slope -k and y-intercept ln[A]0.
  • In the above we use the natural logarithm, ln, which is log to the base e.
slide11

Half-Life for 1st-Order Rxns

  • Half-life is the time taken for the concentration of a reactant to drop to half its original value.
  • That is, half life, t1/2 is the time taken for [A]0 to reach ½[A]0.
  • Mathematically,
  • Note the half-life is independent of the [reactant]0.
slide13

Second-Order Reactions

  • For a second order reaction with just one reactant
  • A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0
  • For a second order reaction, a plot of ln[A]t vs. t is not linear.
slide15

Second-Order Reactions

  • We can show that the half life is:
  • The half-life of a 2nd-order rxn changes as the rxn progresses.
  • Each half-life is twice as long as the one before!
  • This makes these problems harder (and less common).
slide16

Second-Order Reactions

  • A reaction can also have a rate constant expression of the form:
  • rate = k[A][B]
  • This is second order overall, but has first order dependence on A and B.
  • This is more complicated and you won’t have to solve for half-lives of these rxns.
slide18

Temperature and Rate

  • Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.)
  • When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice.
  • The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.
  • As temperature increases, the rate increases.
slide19

Temperature and Rate

  • As temperature increases, the rate increases.
  • Since the rate law has no temperature term in it, the rate constant must depend on temperature.
  • Consider the first order reaction CH3NC→CH3CN.
    • As temperature increases from 190°C to 250°C the rate constant increases from 2.52x10-5 s-1 to 3.16x10-3 s-1.
  • A rule of thumb is that for every 10°C increase in temperature, the rate doubles!
  • The temperature effect is quite dramatic. Why?
slide21

The Collision Model

  • Observations: rates of reactions are affected by concentration and temperature.
  • Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases.
  • The collision model: in order for molecules to react they must collide.
  • The greater the number of collisions the faster the rate.
slide22

The Collision Model

  • The more molecules present, the greater the probability of collision and the faster the rate.
  • The higher the temperature, the more energy available to the molecules and the faster the rate.
  • However, not all collisions lead to products. In fact, only a small fraction of collisions lead to product.
  • In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.
  • These are called effective collisions.
slide25

Orientation Factor in Effective Collisions

  • The orientation of a molecule during collisions is critical in whether a rxn takes place.
  • Consider the reaction between Cl and NOCl:
  • Cl + NOCl→NO + Cl2
  • If the Cl collides with the Cl of NOCl then the products are Cl2 and NO.
  • If the Cl collided with the O of NOCl then no products are formed.
slide27

Activation Energy

  • Arrhenius: molecules must possess a minimum amount of energy to react. Why?
    • In order to form products, bonds must be broken in the reactants.
    • Breaking bonds always requires energy.
  • Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.
  • It is also called the Energy of Activation.
slide29

Activation Energy

  • Consider the rearrangement of methyl isonitrile to form acetonitrile:
    • In H3C-N≡C, the C-N≡C bond bends until the C-N bond breaks and the N≡C portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state.
    • The energy required for the above twist and break is the activation energy, Ea.
    • Once the C-N bond is broken, the N≡C portion can continue to rotate forming a C-C≡N bond.
slide31

Activation Energy

  • The change in energy for the reaction is the difference in energy between CH3NC and CH3CN.
  • The activation energy is the difference in energy between reactants, CH3NC and transition state.
  • The rate depends on Ea.
  • The higher the Ea, the slower the rate!
slide32

Activation Energy

  • Notice that if a forward reaction is exothermic (CH3NC→CH3CN), then the reverse reaction is endothermic (CH3CN→CH3NC).
  • What is theΔH and the Ea for the reverse rxn?
  • Is Ea revjust -Ea?
slide34

Activation Energy

  • How does the Ea relate to temperature?
  • At any particular temperature, the molecules (or atoms) have an average kinetic energy.
  • However, somemolecules have less energy while others have more energy than the average value.
  • This gives us an energy distribution curve where we plot the fraction of molecules with a given energy.
  • We can graph this for different temperatures as well.
slide36

Activation Energy

  • We can see on the graph that some molecules do have enough kinetic energy to react.
  • This is called f, the fraction of molecules with an energy ≥ Ea.
  • The equation for f is:
slide37

Activation Energy

  • Molecules with an energy ≥ Ea have sufficient energy to react.
  • What happens to the kinetic energy as we increase the temperature?
  • It increases!
  • So, as we increase the temperature, more molecules have an energy ≥ Ea.
  • So more molecules react per unit time, and the rate increases.
slide38

Arrhenius Equation

  • Arrhenius discovered that most rxn-rate data obeyed an equation based on 3 factors:
  • The number of collisions per unit time.
  • The fraction of collisions that occur with the correct orientation.
  • f, the fraction of colliding molecules with an energy ≥ Ea.
  • From this, he developed the Arrhenius Equation.
slide39

Arrhenius Equation

  • In the above, k is the rate constant: it depends on temperature!
  • R is the Ideal Gas Constant, 8.314J/mol•K
  • Ea is the Energy of Activation in J
  • T is the temperature in Kelvin
  • A is the frequency factor
slide40

Arrhenius Equation

  • A is related to the frequency of collisions & the probability that a collision occurs with the correct orientation.
  • This is related to the molecular size, mass, and shape.
  • Usually the larger or more complicated the shape, the lower A is.
  • Important: Both Ea and A are rxn-specific!
slide41

Arrhenius Equation

  • How do we find Ea and A? By experiments!
  • You will do this in the lab!
  • If we have data from 2 different temperatures, we can find Ea mathematically:
slide42

Arrhenius Equation

  • But we can’t find A with only 2 temperatures.
  • If we have data from 3 or more different temperatures, we can find Ea and A graphically.
  • According to the Arrhenius Equation:
  • If we graph lnk vs. 1/T, we get a straight line with a slope of -Ea/R and a y-intercept of lnA.
slide43

Arrhenius Equation

  • Here’s a typical graph of the Arrhenius Equation.
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