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### Chemical KineticsPart 2

Chapter 13

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:

- 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 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.

- 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.

- 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).

- 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.

- 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.

- 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?

- 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 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.

- 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.

- 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.

- 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!

- 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?

- 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.

- 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:

- 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 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.

- 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

- 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!

- 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:

- 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.

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

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