Introduction to Rate Law - AP Chemistry

1. Identify $m$ if doubling $[A]$ makes the rate quadruple (with other reactants constant).

   $m = 2$. Rate quadruples means $(2)^m = 4$, so $m = 2$.

2. Identify $m$ if tripling $[A]$ makes the rate triple (with other reactants constant).

   $m = 1$. Rate triples means $(3)^m = 3$, so $m = 1$.

3. What are the units of reaction rate when concentration is in $\text{M}$ and time is in seconds?

   $\text{M}\,\text{s}^{-1}$. Rate is change in concentration per unit time.

4. What are the units of $k$ for a zero-order rate law $\text{rate} = k$?

   $\text{M}\,\text{s}^{-1}$. Units: $k = \text{rate}$ since no concentration dependence.

5. Identify $m$ if doubling $[A]$ makes the rate unchanged (with other reactants constant).

   $m = 0$. Rate unchanged means $(2)^m = 1$, so $m = 0$.

6. What are the units of rate for concentration in $\text{mol}\,\text{L}^{-1}$ and time in seconds?

   $\text{mol}\,\text{L}^{-1}\,\text{s}^{-1}$. Rate measures concentration change per unit time.

7. What is the general form of the rate law for $aA + bB \to$ products?

   $\text{rate} = k[A]^m[B]^n$. Exponents $m$ and $n$ are reaction orders, not stoichiometric coefficients.

8. What are the units of $k$ for a first-order rate law $\text{rate}=k[A]$?

   $\text{s}^{-1}$. First-order $k$ has time inverse units only.

9. What is the rate law for a second-order reactant $A$ (dependence on $[A]$ only)?

   $\text{rate} = k[A]^2$. Second-order means rate is proportional to $[A]^2$.

10. Which option states how reaction orders $m$ and $n$ are determined for most reactions?

    Experimentally, not from balanced equation coefficients. Orders must be found from kinetic data, not stoichiometry.

11. What is the general form of a rate law for $aA+bB\rightarrow$ products using orders $m$ and $n$?

    $\text{rate}=k[A]^m[B]^n$. Shows how rate depends on concentrations raised to experimental powers.

12. What is the overall reaction order for $\text{rate}=k[A]^m[B]^n$?

    $m+n$. Sum of all individual reaction orders gives overall order.

13. What is the rate ratio $\frac{\text{rate}_2}{\text{rate}_1}$ when only $[A]$ changes for $\text{rate}=k[A]^m$?

    $\frac{\text{rate}_2}{\text{rate}_1} = \left(\frac{[A]_2}{[A]_1}\right)^m$. Ratio of rates equals concentration ratio raised to order $m$.

14. What are the units of $k$ for a first-order rate law $\text{rate} = k[A]$?

    $\text{s}^{-1}$. Units: $\frac{\text{M}\,\text{s}^{-1}}{\text{M}} = \text{s}^{-1}$.

15. What is the rate law for an elementary step $2A\rightarrow$ products?

    $\text{rate}=k[A]^2$. Two identical molecules reacting gives second-order dependence.

16. What is the rate law for an elementary termolecular step $A+B+C\rightarrow$ products?

    $\text{rate}=k[A][B][C]$. Three-molecule collisions give third-order rate law.

17. Identify the overall order for $\text{rate}=k[A]^{\frac{1}{2}}[B]^{\frac{3}{2}}$.

    $2$. Add exponents: $\frac{1}{2} + \frac{3}{2} = 2$.

18. What is the definition of rate in terms of concentration change for reactant $A$ in $aA\rightarrow$ products?

    $\text{rate}=-\frac{1}{a}\frac{d[A]}{dt}$. Negative sign shows reactant concentration decreases over time.

19. What is the rate law for a zero-order reactant $A$ (dependence on $[A]$ only)?

    $\text{rate} = k[A]^0 = k$. Zero-order means rate is independent of concentration.

20. What is the rate law for a first-order reactant $A$ (dependence on $[A]$ only)?

    $\text{rate} = k[A]^1$. First-order means rate is directly proportional to $[A]$.

21. Which statement is correct: reaction orders come from stoichiometric coefficients or from experiment?

    From experiment (not from overall stoichiometric coefficients). Orders must be determined experimentally, not from balanced equation.

22. What does the rate constant $k$ represent in a rate law?

    Proportionality constant relating rate to reactant concentrations. Links reaction rate to concentrations; temperature-dependent.

23. What does it mean if a reactant is second order in the rate law?

    Doubling its concentration quadruples the rate. Second power means rate changes with concentration squared.

24. What is the rate law for an elementary step $A+B\rightarrow$ products?

    $\text{rate}=k[A][B]$. Elementary steps use stoichiometric coefficients as orders.

25. Identify the rate factor change if $[A]$ is halved in $\text{rate}=k[A]^2$.

    $\frac{1}{4}\times$. Rate multiplies by $(\frac{1}{2})^2 = \frac{1}{4}$ when concentration halves.

26. What is the overall reaction order for $\text{rate} = k[A]^2[B]^1$?

    $3$. Sum all exponents: $2 + 1 = 3$.

27. What is the method called that uses two trials to solve for reaction orders from rate data?

    Method of initial rates. Compares initial rates at different concentrations to find orders.

28. What does it mean if a reactant is first order in the rate law?

    Doubling its concentration doubles the rate. First power means rate changes proportionally with concentration.

29. What does it mean if a reactant is zero order in the rate law?

    Rate is independent of that reactant's concentration. Zero power means concentration changes don't affect rate.

30. What are the units of $k$ for a second-order rate law $\text{rate}=k[A]^2$?

    $\text{L}\,\text{mol}^{-1}\,\text{s}^{-1}$. Second-order $k$ needs inverse concentration and time units.

31. What is the order with respect to $A$ in $\text{rate} = k[A]^{\frac{1}{2}}[B]^2$?

    $\frac{1}{2}$. The exponent on $[A]$ is the order with respect to $A$.

32. What is the rate law for an elementary unimolecular step $A\rightarrow$ products?

    $\text{rate}=k[A]$. Single molecule reactions are first order in that reactant.

33. What are the units of $k$ for a second-order rate law $\text{rate} = k[A]^2$?

    $\text{M}^{-1}\,\text{s}^{-1}$. Units: $\frac{\text{M}\,\text{s}^{-1}}{\text{M}^2} = \text{M}^{-1}\,\text{s}^{-1}$.

34. Identify $m$ if doubling $[A]$ makes the rate double (with other reactants constant).

    $m = 1$. Rate doubles means $(2)^m = 2$, so $m = 1$.

35. Identify the rate change if $[B]$ triples for $\text{rate} = k[A][B]^0$ (all else constant).

    No change; factor of $1$. $[B]^0 = 1$, so changing $[B]$ doesn't affect rate.

36. Identify the rate factor change if $[A]$ is doubled in $\text{rate}=k[A]^3$.

    $8\times$. Rate multiplies by $2^3 = 8$ when concentration doubles.

37. What are the units of $k$ for a zero-order rate law $\text{rate}=k$?

    $\text{mol}\,\text{L}^{-1}\,\text{s}^{-1}$. Zero-order $k$ has same units as rate itself.

38. Identify the rate change if $[A]$ doubles for $\text{rate} = k[A]^2$ (all else constant).

    Rate increases by a factor of $4$. When $[A]$ doubles: $(2)^2 = 4$ times faster.

39. What is the definition of rate in terms of concentration change for product $P$ in $\rightarrow pP$?

    $\text{rate}=\frac{1}{p}\frac{d[P]}{dt}$. Positive derivative shows product concentration increases over time.

40. What does the rate constant $k$ represent in a rate law?

    Proportionality constant relating rate to reactant concentrations. Links reaction rate to concentrations through multiplication.

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