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4 Ex exam 4    4/12

We now have an official Exam Procedure page. Check it out and know what to expect on Thursday.

Old Quest HW from 2013

Use the pdfs below to further study / train for Exam 4 on Kinetics. It is broken into two parts.

Kinetics - part 1 | KEY

Kinetics - part 2 | KEY


Coverage for Exam 4: Exam 4 covers all the material that was covered on LE's 24-27 and HW07. The exam covers only Chapter 11 on Kinetics. The extra practice assignment on canvas is number 7 for kinetics.

Not on exam: Nuclear chemistry. Nothing from LE28 and LE29, and nothing from HW08a. Only nuclear would be a simple first order decay problem - which is the same concept as in kinetics.

Length / Time for Exam 4: You should expect about 25 multiple choice questions at 4 points each. Remember that the point values are included with all questions. The exam is given during class time (9:30-10:45, 11-12:15) which is 75 minutes total which includes the handout time.

  Chemical Kinetics

Normalized Rate of Reaction

We can measure the rate of a reaction via any of the species in the over reaction:

\(a {\rm A} + b {\rm B} \rightarrow c {\rm C} + d {\rm D}\)

The rate of the "overall reaction as balanced" means you are measuring the rate of entire reactions as written. So each reactant and product is running at a scaled up version of the overall reaction. The "scaled up" amount is the coefficient for that species. For example, reactant A is running "a" times faster than the overall reaction. So to get ALL species to match up, we normalize the rates to the rate of one mole of reaction (the whole thing).

rate of reaction = \(-{\Delta[{\rm A}]\over a\Delta t} = -{\Delta[{\rm B}]\over b\Delta t} = {\Delta[{\rm C}]\over c\Delta t} = {\Delta[{\rm D}]\over d\Delta t}\)

Make sure you can convert the rate of any one species into the rate of another species. This is really just saying to know how stoichiometry works when dealing with rates.

Rate Laws and "order"

Rates of reactions are dependent on the concentrations of the reactant (and sometimes product) species. This is generalized by showing the rate law for a reaction of A, B, and C going to products.

\({\rm rate\;of\;rxn} = k [{\rm A}]^x[{\rm B}]^y[{\rm C}]^z\cdots \)

\(x\) is the order in A, \(y\) is the order in B, and \(z\) is the order in C. Sum those orders all together and you'll have what is called the overall order. The overall order is important to know and the units for the rate constant, \(k\), depends on the overall order.

Kinetic Rate Formulas for:    A → products

namezero orderfirst ordersecond order
rate law \({\rm rate} = k\) \({\rm rate} = k[{\rm A}]\) \({\rm rate} = k[{\rm A}]^2\)
integrated
rate law
\([{\rm A}]_0 - [{\rm A}] = kt\) \(\ln[{\rm A}]_0 - \ln[{\rm A}] = kt\)

   \(\ln\left({[{\rm A}]_0 \over [{\rm A}]}\right) = kt\)
\({1\over[{\rm A}]} - {1\over[{\rm A}]_0} = kt\)
straight line form
   (\(y = mx + b\))
\([{\rm A}] = -kt + [{\rm A}]_0 \) \(\ln[{\rm A}] = -kt + \ln[{\rm A}]_0 \) \({1\over[{\rm A}]} = kt + {1\over[{\rm A}]_0}\)
half life \(t_{1/2} = {[{\rm A}]_0\over 2k}\) \(t_{1/2} = {\ln 2\over k}\) \(t_{1/2} = {1\over [{\rm A}]_0 k}\)
to actually plot on x,y graph
\(y\) = conc
\(x\) = time
\(y = -kx + {\rm A}_0 \) \(y = {\rm A}_0 e^{-kx} \) \(y = \left(kt + {1\over{\rm A}_0}\right)^{-1}\)

Rate Constant, k, and Temperature, T

Arrhenius Equation:    \(k = A\,e^{-E_{\rm a}/RT} \)

\(E_{\rm a}\) is the activation energy for the reaction and it is always positive. The \(A\) is known as the Arrhenius "pre-exponential factor" and is unique for every reaction - it has the same units as the rate constant, \(k\). The factor can be eliminated by setting a ratio for two values of k at two different temperatures. Dr. McCord calls this the "user friendly" version of the Arrhenius equation.

\[\ln\left({k_2\over k_1}\right) = {E_{\rm a}\over R}\left({1\over T_1} - {1\over T_2}\right)\]

Notice that this is the third time you've seen this basic formula in CH302. The first time, it was the Clausius-Clapeyron equation for vapor pressures at two temperatures. The second time, it was the van't Hoff equation for the equilibrium constant, K, at two temperatures. Now the same set up works again but for rate constants. You should now be a "pro" at using this type of formula.

One more thing... the Arrhenius equation can be rewritten to be in a "straight line plot" form, \(y=mx+b\). That form is the following

\(\ln k = {-E_{\rm a}\over R}\left({1\over T}\right) + \ln A \)

So your plot is ln(k) vs 1/T and the slope will be equal to –Ea/R, and the y-intercept is equal to ln(A).

Nuclear Chemistry

Summary of Concepts/Definitions

Binding Energy holds the nucleus together - all those protons are held in place with the help of just as many or even more neutrons. The binding energy will be the energy equivalent of the mass defect in the nucleus. A free protons and neutrons have a slightly greater mass than they due within the nucleus. The difference in mass is called the mass defect... put that change in mass (\(\Delta m\)) into the Einstein equation (\(E=mc^2\)) and you can calculate the binding energy of that nucleus.

Fusion is when two smaller atoms combine to make a larger atom. Fusion is most common with those elements with atomic numbers less than that of iron (26).

Fission is when an unstable large atom (typically Z > 82) splits into to give two new medium sized atoms.

Alpha decay (α) is when the nucleus ejects an α-particle which is the nucleus (no electrons) of a helium atom. The parent atom decreases in mass number by 4 and decreases in atomic number by 2. It has the lowest penetration depth of all the nuclear radiation types - paper / outer layer of skin can stop it.

Beta decay (β) is the ejection of a β-particle (electron) from the nucleus. The mass number stays the same, but the atomic number increases by one. Beta particles penetrate slightly better than alpha rays, but still does not make it far. Wood and normal walls will stop this radiation.

positron emission (β+) is the ejection of a positron (β+) from the nucleus. The mass number stays the same, but the atomic number decreases by one.

Gamma rays/emission (γ) is the only emission that is pure energy and no mass - it is electromagnetic radiation of very high frequency and very short wavelength. It occurs when certain nuclei are in excited nuclear states and then return to nuclear ground state ejecting a gamma photon. This is analogous to excited electrons relaxing to ground state and emitting visible or UV radiation. Gamma emission often accompanies other types of decay as part of the energy release. Gamma rays are the most penetrating radiation there is. The only way to stop it is to use a lot of dense material - like thick lead sheets or other heavy metals.


Learning Outcomes for Chemical Kinetics

Students will be able to...

  1. Understand the concept of rate of change associated with a given chemical reaction and how it can be measured.
  2. Determine rate law of chemical change based on experimental data.
  3. Be able to identify the reaction order for a chemical change.
  4. Understand the concept of pseudo-first order kinetics and when they apply.
  5. Apply integrated rate equations to solve for the concentration of chemical species during a reaction of different orders.
  6. Understand the concept of mechanism and using rate law data predict whether or not a proposed mechanism is viable or not.
  7. Recall and explain why certain factors such as concentration, temperature, medium and the presence of a catalyst will affect the speed of a chemical change.
  8. Interpret a reaction coordinate diagram and determine if such a diagram supports a given single or multistep mechanism, including the concept and depiction of any transition states and reaction intermediates.
  9. Understand the concept of an activation energy in the context of the transition state and be able to calculate the activation energy given some experimental data.
  10. Recall, manipulate and properly employ the Arrhenius Law.
  11. Explain the function and purpose of a catalyst.

Learning Outcomes for Nuclear Chemistry

Students will be able to...

  1. Explain the macroscopic observables associated with nuclear change and the microscopic or chemists view of nuclear change.
  2. Identify and define various types of nuclear transmutation including fission, fusion and decay reactions.
  3. Use proper isotopic notation to write down and balance a nuclear reaction.
  4. State and compare the differences and similarities between a nuclear change and a chemical change.
  5. Recall and properly use Einstein’s theory of relativity equation, E = mc2, to calculate the amount of energy released upon a nuclear change.
  6. Define binding energy and mass defect and be able to calculate each for a given nucleus.
  7. Understand and explain the concept of ionizing radiation and distinguish between the three different types of radiation.
  8. Understand and explain the concept of isotopic stability including the band of stability.
  9. Be familiar with the units used to quantify nuclear decay
  10. Understand the concept of rate of change and half life in the context of nuclear decay.
  11. Understand the basics of nuclear chemistry applications: nuclear power, medical treatment, isotopic labeling, and carbon dating.

No Nuclear Chemistry on Exam 4!

please fully study kinetics - Dr. McCord added Nuclear back to this study guide AFTER the semester ended (as a reference guide)

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