Kinetics — Practice Quiz

A Chemistry cheat sheet for Kinetics — every key formula with its symbols defined — plus a medium-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. For the reaction $2NO_2(g) \rightarrow 2NO(g) + O_2(g)$, if the rate of disappearance of $NO_2$ is $4.0 \times 10^{-3} \text{ M/s}$, what is the rate of appearance of $O_2$?

    • $2.0 \times 10^{-3} \text{ M/s}$
    • $4.0 \times 10^{-3} \text{ M/s}$
    • $8.0 \times 10^{-3} \text{ M/s}$
    • $1.0 \times 10^{-3} \text{ M/s}$

    Answer: $2.0 \times 10^{-3} \text{ M/s}$

  2. Consider the reaction $A + B \rightarrow C$. The following initial rate data were collected:\n\n| Experiment | $[A]_0$ (M) | $[B]_0$ (M) | Initial Rate (M/s) |\n|---|---|---|---|\n| 1 | $0.10$ | $0.10$ | $2.0 \times 10^{-3}$ |\n| 2 | $0.20$ | $0.10$ | $4.0 \times 10^{-3}$ |\n| 3 | $0.10$ | $0.20$ | $8.0 \times 10^{-3}$ |\n\nWhat is the overall order of the reaction?

    • $1$
    • $2$
    • $3$
    • $4$

    Answer: $3$

  3. A first-order reaction has a rate constant $k = 5.0 \times 10^{-2} \text{ s}^{-1}$. If the initial concentration of the reactant is $0.50 \text{ M}$, what will be its concentration after $20 \text{ s}$?

    • $0.18 \text{ M}$
    • $0.25 \text{ M}$
    • $0.37 \text{ M}$
    • $0.05 \text{ M}$

    Answer: $0.18 \text{ M}$

  4. The half-life of a first-order reaction is $150 \text{ s}$. What is the rate constant $k$ for this reaction?

    • $0.00462 \text{ s}^{-1}$
    • $0.00693 \text{ s}^{-1}$
    • $104 \text{ s}^{-1}$
    • $150 \text{ s}^{-1}$

    Answer: $0.00462 \text{ s}^{-1}$

  5. A second-order reaction has a rate constant $k = 0.025 \text{ M}^{-1}\text{s}^{-1}$. If the initial concentration of the reactant is $0.40 \text{ M}$, how long will it take for the concentration to decrease to $0.10 \text{ M}$?

    • $100 \text{ s}$
    • $200 \text{ s}$
    • $300 \text{ s}$
    • $400 \text{ s}$

    Answer: $300 \text{ s}$

  6. According to the Arrhenius equation, $k = Ae^{-E_a/RT}$, what happens to the rate constant $k$ of a reaction if the temperature $T$ is increased, assuming $E_a$ is positive?

    • $k$ decreases exponentially.
    • $k$ increases exponentially.
    • $k$ remains unchanged.
    • $k$ decreases linearly.

    Answer: $k$ increases exponentially.

  7. The rate constant $k$ for a reaction is $1.5 \times 10^{-3} \text{ s}^{-1}$ at $27^\circ C$ and $6.0 \times 10^{-2} \text{ s}^{-1}$ at $77^\circ C$. Calculate the activation energy $E_a$ for this reaction. (Use $R = 8.314 \text{ J} \cdot \text{mol}^{-1}\text{K}^{-1}$)

    • $32.3 \text{ kJ/mol}$
    • $64.5 \text{ kJ/mol}$
    • $96.8 \text{ kJ/mol}$
    • $129.0 \text{ kJ/mol}$

    Answer: $64.5 \text{ kJ/mol}$

  8. A certain radioactive isotope decays by a first-order process with a half-life of $10.0 \text{ days}$. If you start with $100.0 \text{ g}$ of the isotope, how much will remain after $30.0 \text{ days}$?

    • $50.0 \text{ g}$
    • $25.0 \text{ g}$
    • $12.5 \text{ g}$
    • $6.25 \text{ g}$

    Answer: $12.5 \text{ g}$

  9. For the reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, which of the following relationships between the rates of reaction is correct?

    • $\frac{\Delta[H_2]}{\Delta t} = \frac{3}{2}\frac{\Delta[NH_3]}{\Delta t}$
    • $-\frac{\Delta[H_2]}{\Delta t} = \frac{3}{2}\frac{\Delta[NH_3]}{\Delta t}$
    • $-\frac{1}{3}\frac{\Delta[H_2]}{\Delta t} = \frac{1}{2}\frac{\Delta[NH_3]}{\Delta t}$
    • $\frac{\Delta[H_2]}{\Delta t} = -\frac{2}{3}\frac{\Delta[NH_3]}{\Delta t}$

    Answer: $-\frac{1}{3}\frac{\Delta[H_2]}{\Delta t} = \frac{1}{2}\frac{\Delta[NH_3]}{\Delta t}$

  10. What are the units of the rate constant $k$ for a reaction that is third-order overall?

    • $\text{M}^{-1}\text{s}^{-1}$
    • $\text{s}^{-1}$
    • $\text{M}^{-2}\text{s}^{-1}$
    • $\text{M}\text{s}^{-1}$

    Answer: $\text{M}^{-2}\text{s}^{-1}$

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