Chemical Kinetics flash cards

1. 1.What does chemical kinetics study?

   The rate (speed) of chemical reactions, the factors affecting them, and the mechanism by which reactions occur.

   Hint: Speed + how, not how far.

2. 2.Define the rate of a reaction.

   The change in concentration of a reactant or product per unit time. For a species, rate $= \pm \dfrac{\Delta[X]}{\Delta t}$ (minus for reactants, plus for products).

   Hint: Concentration change over time.

3. 3.Distinguish average rate from instantaneous rate.

   Average rate $= \dfrac{\Delta[X]}{\Delta t}$ over a finite interval; instantaneous rate $= \dfrac{d[X]}{dt}$ at a specific instant (limit as $\Delta t \to 0$).

   Hint: Finite interval vs a single instant.

4. 4.For $aA + bB \to cC + dD$, write the unique rate of reaction.

   Rate $= -\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt} = +\dfrac{1}{c}\dfrac{d[C]}{dt} = +\dfrac{1}{d}\dfrac{d[D]}{dt}$.

   Hint: Divide each by its stoichiometric coefficient.

5. 5.Why divide by stoichiometric coefficients when writing the rate?

   So the rate has a single unique value regardless of which species is monitored; species are consumed/formed at different numerical rates set by their coefficients.

   Hint: One rate for the whole reaction.

6. 6.What are the common units of rate of reaction?

   $\text{mol L}^{-1}\text{ s}^{-1}$ (concentration per time). For gases sometimes $\text{atm s}^{-1}$.

   Hint: Concentration/time.

7. 7.List the main factors affecting reaction rate.

   Concentration (pressure for gases), temperature, presence of a catalyst, surface area of reactants, and nature of reactants (and radiation for photochemical reactions).

   Hint: Conc, temp, catalyst, area, nature.

8. 8.State the rate law (rate equation) in general form.

   For $aA + bB \to$ products, Rate $= k[A]^x[B]^y$, where $x,y$ are experimentally determined orders (not necessarily $a,b$).

   Hint: Rate $=k[A]^x[B]^y$; exponents from experiment.

9. 9.Define the rate constant $k$.

   The proportionality constant in the rate law; numerically equal to the rate when all reactant concentrations are unity. Also called specific reaction rate.

   Hint: Rate when all concentrations = 1 M.

10. 10.Why can't the rate law generally be written from the balanced equation?

    Because it depends on the reaction mechanism, not stoichiometry. Orders must be found experimentally; they equal coefficients only for a single-step (elementary) reaction.

    Hint: Mechanism, not the balanced equation.

11. 11.Define order of a reaction.

    The sum of the powers of the concentration terms in the experimentally determined rate law. For Rate $=k[A]^x[B]^y$, order $=x+y$.

    Hint: Sum of exponents in the rate law.

12. 12.Can order be zero, fractional, or negative?

    Yes. Order is experimental, so it can be $0$, integer, fractional, or even negative, unlike molecularity.

    Hint: Order is flexible; molecularity is not.

13. 13.Define molecularity of a reaction.

    The number of reacting species (atoms, ions, molecules) that collide simultaneously in an elementary step to bring about the reaction.

    Hint: Molecules colliding in one elementary step.

14. 14.Give the range of allowed values for molecularity.

    A positive integer, generally $1$, $2$, or rarely $3$. It is never zero, fractional, or negative.

    Hint: 1, 2, or 3 only.

15. 15.Contrast order and molecularity.

    Order: experimental, for overall reaction, can be $0$/fractional/negative. Molecularity: theoretical, only for elementary steps, small positive integer only.

    Hint: Experimental & flexible vs theoretical & integer.

16. 16.What is the rate-determining step?

    The slowest step in a multi-step reaction mechanism; it governs the overall rate and hence the observed rate law.

    Hint: The slowest step controls the speed.

17. 17.For a complex reaction, is molecularity meaningful?

    No. Molecularity is defined only for elementary steps. A complex reaction has an overall order but no overall molecularity.

    Hint: Molecularity: elementary steps only.

18. 18.Give the units of the rate constant for an $n$th-order reaction.

    $k$ has units $(\text{mol L}^{-1})^{1-n}\,\text{s}^{-1}$, i.e. $\text{mol}^{1-n}\,\text{L}^{n-1}\,\text{s}^{-1}$.

    Hint: Depends on order: $\text{conc}^{1-n}\text{time}^{-1}$.

19. 19.Units of $k$ for a zero-order reaction?

    $\text{mol L}^{-1}\text{s}^{-1}$ (same as rate), since $n=0$ gives $(\text{mol L}^{-1})^{1}\text{s}^{-1}$.

    Hint: Same as the rate itself.

20. 20.Units of $k$ for a first-order reaction?

    $\text{s}^{-1}$ (or $\text{time}^{-1}$), because $n=1$ gives $(\text{mol L}^{-1})^{0}\text{s}^{-1}$.

    Hint: Just inverse time.

21. 21.Units of $k$ for a second-order reaction?

    $\text{L mol}^{-1}\text{s}^{-1}$ (i.e. $\text{mol}^{-1}\text{L s}^{-1}$), since $n=2$.

    Hint: $\text{L mol}^{-1}\text{s}^{-1}$.

22. 22.Write the differential rate law for a zero-order reaction.

    $-\dfrac{d[R]}{dt} = k$; the rate is independent of the concentration of the reactant.

    Hint: Rate constant, no concentration term.

23. 23.Write the integrated rate law for a zero-order reaction.

    $[R] = [R]_0 - kt$, or $k = \dfrac{[R]_0 - [R]}{t}$.

    Hint: Linear decrease in concentration with time.

24. 24.For a zero-order reaction, what does a plot of $[R]$ vs $t$ look like?

    A straight line with slope $-k$ and intercept $[R]_0$.

    Hint: Straight line, slope $=-k$.

25. 25.Give examples of zero-order reactions.

    Decomposition of gaseous $NH_3$ on a hot platinum surface, decomposition of $HI$ on gold, and enzyme reactions at high substrate (metal-surface-catalysed reactions).

    Hint: Reactions on metal surfaces.

26. 26.Write the differential rate law for a first-order reaction.

    $-\dfrac{d[R]}{dt} = k[R]$; rate is directly proportional to reactant concentration.

    Hint: Rate $\propto$ concentration.

27. 27.Write the integrated rate law for a first-order reaction.

    $k = \dfrac{2.303}{t}\log\dfrac{[R]_0}{[R]}$, equivalently $\ln[R] = \ln[R]_0 - kt$ or $[R]=[R]_0 e^{-kt}$.

    Hint: $k=\frac{2.303}{t}\log\frac{[R]_0}{[R]}$.

28. 28.For a first-order reaction, which plot gives a straight line?

    $\ln[R]$ vs $t$ (slope $=-k$), or $\log[R]$ vs $t$ (slope $=-k/2.303$).

    Hint: Log of concentration is linear in time.

29. 29.Give the first-order rate constant in terms of amounts $a$ and $a-x$.

    $k = \dfrac{2.303}{t}\log\dfrac{a}{a-x}$, where $a$ is initial amount and $x$ is amount reacted in time $t$.

    Hint: $a$ = initial, $a-x$ = remaining.

30. 30.Name two important classes of first-order processes.

    All radioactive decays are first order; many gas-phase decompositions and hydrolyses (e.g. $N_2O_5$ decomposition) are first order.

    Hint: Radioactive decay is the classic case.

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