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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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Chemical kinetics part 2

Chemical KineticsPart 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.

  • 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!

  • 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

  • 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:

  • 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.

  • 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.

  • 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.

  • 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).

  • 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.

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.

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?

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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!

  • 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?

  • 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.

  • 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:

  • 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.

  • 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.

  • 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

  • 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!

  • 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:

  • 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.