Kinetics — Hard Practice Quiz

A Chemistry cheat sheet for Kinetics — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Reaction Rate: Relates the rates of disappearance of reactants and appearance of products for \(aA + bB \rightarrow cC + dD\).

$$\text{Rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = \frac{1}{c}\frac{\Delta[C]}{\Delta t} = \frac{1}{d}\frac{\Delta[D]}{\Delta t}$$

Where: \(a,b,c,d\) = stoichiometric coefficients

Rate Law: Relates reaction rate to rate constant and concentrations.

$$\text{Rate} = k[A]^m[B]^n$$

Where: \(k\) = rate constant, \(m,n\) = reaction orders

First-Order Integrated Rate Law: Relates concentration to time for a first-order reaction.

$$\ln[A]_t - \ln[A]_0 = -kt$$

Where: \([A]_t\) = conc. at time t, \([A]_0\) = initial conc.

Second-Order Integrated Rate Law: Relates concentration to time for a second-order reaction.

$$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$$

Half-Life (First-Order): Time required for concentration to decrease by half.

$$t_{1/2} = \frac{0.693}{k}$$

Where: \(t_{1/2}\) = half-life

Arrhenius Equation: Relates rate constant to activation energy and temperature.

$$k = Ae^{-E_a/RT}$$

Where: \(A\) = frequency factor, \(E_a\) = activation energy, \(R\) = gas constant, \(T\) = temperature

Linear Arrhenius Equation: Linear form used to determine activation energy graphically.

$$\ln k = -\frac{E_a}{RT} + \ln A$$

Practice quiz

  1. A first-order reaction has a half-life of $150 \text{ s}$. If the initial concentration of reactant $A$ is $0.80 \text{ M}$, what percentage of $A$ remains after $450 \text{ s}$?

    • $6.25\%$
    • $12.5\%$
    • $25.0\%$
    • $33.3\%$

    Answer: $12.5\%$

  2. For a reaction $2A \rightarrow B$, the initial rate is $0.020 \text{ M/s}$ when $[A]_0 = 0.10 \text{ M}$. If the reaction is second-order with respect to $A$, how long will it take for the concentration of $A$ to decrease to $0.025 \text{ M}$?

    • $5 \text{ s}$
    • $10 \text{ s}$
    • $15 \text{ s}$
    • $20 \text{ s}$

    Answer: $15 \text{ s}$

  3. A reaction $A + B \rightarrow C$ is first-order in $A$ and first-order in $B$. Its activation energy is $50 \text{ kJ/mol}$. If the temperature is increased from $298 \text{ K}$ to $308 \text{ K}$, by what factor does the initial rate of reaction increase, assuming $[A]$ and $[B]$ are constant? ($R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $1.5$ times
    • $1.9$ times
    • $2.5$ times
    • $3.0$ times

    Answer: $1.9$ times

  4. For the reaction $2NO_2(g) \rightarrow 2NO(g) + O_2(g)$, the rate constant $k$ is $0.54 \text{ M}^{-1}\text{s}^{-1}$ at $300 \text{ K}$. If the initial concentration of $NO_2$ is $0.20 \text{ M}$, what is the rate of formation of $O_2$ after $10 \text{ s}$?

    • $0.0012 \text{ M/s}$
    • $0.0025 \text{ M/s}$
    • $0.0050 \text{ M/s}$
    • $0.0100 \text{ M/s}$

    Answer: $0.0025 \text{ M/s}$

  5. The rate constant for a first-order reaction is $2.0 \times 10^{-4} \text{ s}^{-1}$ at $25^\circ\text{C}$ and $8.0 \times 10^{-4} \text{ s}^{-1}$ at $40^\circ\text{C}$. What is the half-life of this reaction at $50^\circ\text{C}$? ($R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $173 \text{ s}$
    • $245 \text{ s}$
    • $369 \text{ s}$
    • $481 \text{ s}$

    Answer: $369 \text{ s}$

  6. Consider two reactions, one first-order and one second-order, both with the same initial concentration $[A]_0$ and the same initial rate. If the concentration of $A$ is halved, how does the ratio of their new half-lives ($t_{1/2, \text{second-order}} / t_{1/2, \text{first-order}}$) change compared to their initial half-lives?

    • It remains the same.
    • It doubles.
    • It halves.
    • It quadruples.

    Answer: It doubles.

  7. For the reaction $2X + Y \rightarrow Z$, the following initial rate data were collected: \n\n| Experiment | $[X]_0$ (M) | $[Y]_0$ (M) | Initial Rate (M/s) |\n| :--------- | :---------- | :---------- | :----------------- |\n| 1 | $0.10$ | $0.10$ | $1.0 \times 10^{-3}$ |\n| 2 | $0.20$ | $0.10$ | $4.0 \times 10^{-3}$ |\n| 3 | $0.10$ | $0.20$ | $2.0 \times 10^{-3}$ |\n\nWhat is the rate of disappearance of $Y$ when $[X] = 0.05 \text{ M}$ and $[Y] = 0.05 \text{ M}$?

    • $6.25 \times 10^{-5} \text{ M/s}$
    • $1.25 \times 10^{-4} \text{ M/s}$
    • $2.50 \times 10^{-4} \text{ M/s}$
    • $5.00 \times 10^{-4} \text{ M/s}$

    Answer: $1.25 \times 10^{-4} \text{ M/s}$

  8. A reaction $A \rightarrow 2B$ is studied. The initial concentration of $A$ is $0.50 \text{ M}$. After $100 \text{ s}$, the concentration of $B$ is $0.60 \text{ M}$. If the reaction is known to be either first-order or second-order with respect to $A$, what is the rate constant $k$ for this reaction?

    • $0.00916 \text{ s}^{-1}$ (first-order)
    • $0.0300 \text{ M}^{-1}\text{s}^{-1}$ (second-order)
    • $0.00600 \text{ s}^{-1}$ (first-order)
    • $0.0150 \text{ M}^{-1}\text{s}^{-1}$ (second-order)

    Answer: $0.00916 \text{ s}^{-1}$ (first-order)

  9. A catalyst lowers the activation energy of a reaction from $75 \text{ kJ/mol}$ to $50 \text{ kJ/mol}$ at $300 \text{ K}$. By what factor does the rate constant increase due to the catalyst? ($R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $1.5 \times 10^2$
    • $2.3 \times 10^3$
    • $2.3 \times 10^4$
    • $1.5 \times 10^5$

    Answer: $2.3 \times 10^4$

  10. For a certain first-order reaction, a plot of $\ln k$ versus $1/T$ yields a straight line with a slope of $-8.5 \times 10^3 \text{ K}$. If the half-life of the reaction at $350 \text{ K}$ is $120 \text{ s}$, what is the value of the frequency factor $A$? ($R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $1.0 \times 10^6 \text{ s}^{-1}$
    • $5.0 \times 10^7 \text{ s}^{-1}$
    • $1.0 \times 10^8 \text{ s}^{-1}$
    • $5.0 \times 10^8 \text{ s}^{-1}$

    Answer: $1.0 \times 10^8 \text{ s}^{-1}$

Select a subject

Select a subject from the left panel to begin exploring formulas.