# Chemical Kinetics Part 2 - PowerPoint PPT Presentation

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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

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## 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)

• 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:

• Zero-Order Reactions (or zeroth order)

• We rearrange this equation:

• We then integrate:

• 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:

• 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.

First-Order Reactions

• 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.

The Change of Concentration with Time

Half-Life

• 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

• 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

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?

Temperature and Rate

• 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.

The Collision Model

The Collision Model

• 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.

Orientation Factor in Effective Collisions

• 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

• 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

• 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.

• Arrhenius Equation

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