Concentration Changes Over Time - AP Chemistry

1. What is the half-life formula for a second-order reaction?

   $t_{1/2} = \frac{1}{k[\text{A}]_0}$. Half-life inversely proportional to initial concentration.

2. What is the effect of a catalyst on the rate of reaction?

   Increases the reaction rate. Lowers activation energy without being consumed.

3. What does the slope of a second-order reaction plot $\frac{1}{[\text{A}]}$ vs. time represent?

   Rate constant $k$. Slope of reciprocal concentration vs time plot.

4. How do you determine the reaction order from a concentration vs. time graph?

   Analyze the shape of the plot. Different orders produce characteristic curve shapes.

5. What is the half-life formula for a first-order reaction?

   $t_{1/2} = \frac{\ln(2)}{k}$. Constant half-life independent of initial concentration.

6. Determine the reaction order: Rate is independent of $[\text{A}]$ concentration.

   Zero-order reaction. Rate independent of concentration changes.

7. Which factor does NOT affect the rate constant $k$?

   Concentration of reactants. Rate constant depends only on temperature and catalyst.

8. What is the half-life formula for a second-order reaction?

   $t_{1/2} = \frac{1}{k[\text{A}]_0}$. Half-life inversely proportional to initial concentration.

9. What is the rate law expression for a reaction $aA + bB \rightarrow cC$?

   $\text{rate} = k[A]^m[B]^n$. Rate depends on concentrations raised to their respective orders.

10. State the integrated rate law for a first-order reaction.

    $[\text{A}]_t = [\text{A}]_0 e^{-kt}$. Exponential decay relationship for first-order kinetics.

11. What does the slope of a second-order reaction plot $\frac{1}{[\text{A}]}$ vs. time represent?

    Rate constant $k$. Slope of reciprocal concentration vs time plot.

12. Identify the graph shape for a first-order reaction concentration vs. time plot.

    Exponential decay curve. Rate proportional to concentration creates exponential decay.

13. Determine the reaction order: Rate is independent of $[\text{A}]$ concentration.

    Zero-order reaction. Rate independent of concentration changes.

14. Which order of reaction has a constant half-life regardless of initial concentration?

    First-order reaction. Constant half-life is characteristic of first-order kinetics.

15. State the integrated rate law for a zero-order reaction.

    $[\text{A}]_t = [\text{A}]_0 - kt$. Linear decrease with time for zero-order kinetics.

16. What is the role of the frequency factor $A$ in the Arrhenius equation?

    Represents collision frequency factor. Pre-exponential factor in Arrhenius equation.

17. State the Arrhenius equation.

    $k = A e^{-\frac{E_a}{RT}}$. Exponential relationship between rate constant and temperature.

18. Identify the graph shape for a second-order reaction concentration vs. time plot.

    Inversely proportional curve. Rate proportional to concentration squared.

19. How does the concentration of reactants change over time in a second-order reaction?

    Decreases more steeply than first-order. Rate proportional to concentration squared.

20. State the integrated rate law for a zero-order reaction.

    $[\text{A}]_t = [\text{A}]_0 - kt$. Linear decrease with time for zero-order kinetics.

21. What is the effect of concentration on the rate for a zero-order reaction?

    Rate is independent of concentration. Rate remains constant regardless of concentration.

22. Which factor does NOT affect the rate constant $k$?

    Concentration of reactants. Rate constant depends only on temperature and catalyst.

23. What is the effect of a catalyst on activation energy $E_a$?

    Decreases activation energy $E_a$. Provides alternative pathway with lower energy barrier.

24. How does the concentration of reactants change over time in a first-order reaction?

    Decreases exponentially. Rate proportional to remaining concentration.

25. What is the relationship between reaction rate and concentration for a first-order reaction?

    Rate is directly proportional to concentration. Rate equals rate constant times concentration.

26. Which order of reaction has a constant half-life regardless of initial concentration?

    First-order reaction. Constant half-life is characteristic of first-order kinetics.

27. What is the effect of a catalyst on the overall reaction rate?

    Increases overall reaction rate. Provides faster pathway without changing equilibrium.

28. Identify the units of the rate constant $k$ for a first-order reaction.

    Units: $\text{s}^{-1}$. First-order rate constant has units of reciprocal time.

29. State the integrated rate law for a zero-order reaction.

    $[\text{A}]_t = [\text{A}]_0 - kt$. Linear decrease with time for zero-order kinetics.

30. What is the effect of a catalyst on the overall reaction rate?

    Increases overall reaction rate. Provides faster pathway without changing equilibrium.

31. Calculate the rate if $k = 0.5 \text{s}^{-1}$ and $[\text{A}] = 2 \text{M}$ for a first-order reaction.

    Rate = $1 \text{M} \text{s}^{-1}$. Rate equals $k$ times concentration for first-order.

32. Determine the reaction order: Doubling $[\text{A}]$ quadruples the reaction rate.

    Second-order reaction. Rate proportional to concentration squared.

33. Identify the units of the rate constant $k$ for a second-order reaction.

    Units: $\text{M}^{-1} \text{s}^{-1}$. Second-order rate constant has units of reciprocal concentration-time.

34. What is the relationship between reaction rate and concentration for a first-order reaction?

    Rate is directly proportional to concentration. Rate equals rate constant times concentration.

35. Determine the reaction order: $[\text{A}]$ halves every 20 seconds regardless of initial concentration.

    First-order reaction. Constant half-life indicates first-order kinetics.

36. Determine the reaction order: Doubling $[\text{A}]$ quadruples the reaction rate.

    Second-order reaction. Rate proportional to concentration squared.

37. How does the concentration of reactants change over time in a second-order reaction?

    Decreases more steeply than first-order. Rate proportional to concentration squared.

38. How is the rate constant $k$ affected by temperature increase?

    The rate constant $k$ increases. Higher temperature provides more kinetic energy for reactions.

39. What is the half-life formula for a zero-order reaction?

    $t_{1/2} = \frac{ { [ \text{A} ] } _0 }{2k}$. Half-life depends on initial concentration for zero-order.

40. How does temperature affect reaction rate?

    Higher temperature increases reaction rate. More molecular collisions occur at higher temperatures.

41. How does the concentration of reactants change over time in a first-order reaction?

    Decreases exponentially. Rate proportional to remaining concentration.

42. How is the rate constant $k$ affected by temperature increase?

    The rate constant $k$ increases. Higher temperature provides more kinetic energy for reactions.

43. Identify the units of the rate constant $k$ for a first-order reaction.

    Units: $\text{s}^{-1}$. First-order rate constant has units of reciprocal time.

44. Identify the units of the rate constant $k$ for a zero-order reaction.

    Units: $\text{M} \text{s}^{-1}$. Zero-order reactions have rate units of concentration per time.

45. What is the half-life formula for a zero-order reaction?

    $t_{1/2} = \frac{[\text{A}]_0}{2k}$. Half-life depends on initial concentration for zero-order.

46. Calculate the half-life if $k = 0.693 \text{s}^{-1}$ for a first-order reaction.

    $t_{1/2} = 1 \text{s}$. Using $t_{1/2} = \frac{\ln(2)}{k}$ formula.

47. State the integrated rate law for a second-order reaction.

    $\frac{1}{[\text{A}]_t} = \frac{1}{[\text{A}]_0} + kt$. Reciprocal concentration increases linearly with time.

48. How does the concentration of reactants change over time in a second-order reaction?

    Decreases more steeply than first-order. Rate proportional to concentration squared.

49. How does temperature affect reaction rate?

    Higher temperature increases reaction rate. More molecular collisions occur at higher temperatures.

50. Identify the graph shape for a zero-order reaction concentration vs. time plot.

    Straight line downward. Constant rate produces linear concentration decrease.

51. Determine the reaction order: $[\text{A}]$ halves every 20 seconds regardless of initial concentration.

    First-order reaction. Constant half-life indicates first-order kinetics.

52. Calculate the half-life if $k = 0.693 \text{s}^{-1}$ for a first-order reaction.

    $t_{1/2} = 1 \text{s}$. Using $t_{1/2} = \frac{\ln(2)}{k}$ formula.

53. What is the Arrhenius equation used for?

    Calculating the temperature dependence of the rate constant. Relates rate constant to temperature and activation energy.

54. How do you determine the reaction order from a concentration vs. time graph?

    Analyze the shape of the plot. Different orders produce characteristic curve shapes.

55. What is the half-life formula for a zero-order reaction?

    $t_{1/2} = \frac{[\text{A}]_0}{2k}$. Half-life depends on initial concentration for zero-order.

56. What is the rate law expression for a reaction $aA + bB \rightarrow cC$?

    $\text{rate} = k[A]^m[B]^n$. Rate depends on concentrations raised to their respective orders.

57. What does the slope of a first-order reaction plot $[\text{ln[A]}]$ vs. time represent?

    Negative rate constant $-k$. Slope of $\ln[A]$ vs time plot.

58. Calculate the rate if $k = 0.5 \text{s}^{-1}$ and $[\text{A}] = 2 \text{M}$ for a first-order reaction.

    Rate = $1 \text{M} \text{s}^{-1}$. Rate equals $k$ times concentration for first-order.

59. What is the role of the frequency factor $A$ in the Arrhenius equation?

    Represents collision frequency factor. Pre-exponential factor in Arrhenius equation.

60. Identify the graph shape for a zero-order reaction concentration vs. time plot.

    Straight line downward. Constant rate produces linear concentration decrease.

61. Identify the units of the rate constant $k$ for a second-order reaction.

    Units: $\text{M}^{-1} \text{s}^{-1}$. Second-order rate constant has units of reciprocal concentration-time.

62. State the Arrhenius equation.

    $k = A e^{-\frac{E_a}{RT}}$. Exponential relationship between rate constant and temperature.

63. Which order of reaction has a constant half-life regardless of initial concentration?

    First-order reaction. Constant half-life is characteristic of first-order kinetics.

64. Identify the units of the rate constant $k$ for a zero-order reaction.

    Units: $\text{M} \text{s}^{-1}$. Zero-order reactions have rate units of concentration per time.

65. How does the concentration of reactants change over time in a first-order reaction?

    Decreases exponentially. Rate proportional to remaining concentration.

66. What happens to the concentration of reactants over time in a zero-order reaction?

    Decreases linearly over time. Constant rate independent of remaining concentration.

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