CHEM 1001 Section P: Chemical Dynamics – Chemical Kinetics and Mathematical Foundations

Course Introduction and Structure

Instructor and Course Logistics

• Instructor: René Fournier ([e-mail])

• Course Director: Kyle Belozerov ([e-mail])

• Class Times: MWF 11:30–12:30, R 10:30–11:30

• Office Hours: W 13:30–14:30, R 12:30–13:30

• First Tutorial: Thursday, Jan. 8

• First Labs: Week of Jan. 20

Course Communications

• Administrative questions: [e-mail]

• Chemistry questions: [e-mail]

• Use your YorkU email, include "CHEM 1001 P" in the subject, and sign with your name and student number.

• Check eClass regularly for announcements and updated lecture notes.

• Lectures will not be recorded.

Course Materials and Topics

• Textbook: Chemistry: A Molecular Approach by Tro, Fridgen, Shaw

• Assumed knowledge: Chapters 1–4 (unit conversions, significant figures, stoichiometry, oxidation numbers, etc.)

• Covered in this course:

  • Chapter 13: Chemical Kinetics

  • Chapter 14: Chemical Equilibrium

  • Chapter 15: Acids and Bases

  • Chapter 16: Aqueous Ionic Equilibrium

  • Chapter 17: Gibbs Energy and Thermodynamics

  • Chapter 18: Electrochemistry

Evaluation Scheme

• 10%: Weekly online eClass quizzes (starting Jan. 19)

• 20%: Test 1 (Feb. 22)

• 20%: Test 2 (Mar. 22)

• 20%: 5 Labs

• 30%: Final exam (cumulative, 3 hours)

Chapter 13: Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical reactions occur and the factors that affect these rates. Understanding kinetics allows chemists to control reaction speeds, optimize industrial processes, and elucidate reaction mechanisms.

• Applications:

  • Slowing down undesirable reactions (e.g., corrosion)

  • Speeding up beneficial reactions (e.g., plastic decomposition)

  • Controlling pharmacokinetics for better medical treatments

  • Understanding complex systems (oceans, atmosphere, biology)

Defining the Rate of Reaction

The rate of reaction is defined as the change in the amount of a product (or reactant) per unit time:

• General formula: $\text{Rate of reaction} \sim \frac{\text{change in amount of product}}{\text{time interval}}$ $\sim \frac{\Delta(\text{amount of product})}{\Delta t}$

• Time ($t$) is usually measured in seconds (s).

• The choice of which product/reactant and how to express its amount depends on the system and measurement capabilities.

Expressing Amounts in Kinetics

• Mass ($m$): Useful for solids.

• Volume ($V$): Useful for gases and liquids.

• Number of moles ($n$): Fundamental chemical quantity.

• Concentration ($[X]$): Preferred for solutions and gases; an intensive property (defined at every point in space).

• Pressure ($P_X$): Useful for gases.

Intensive properties (e.g., concentration, pressure) are preferred because they are independent of system size, unlike extensive properties (e.g., mass, volume, moles).

Calculating Average and Instantaneous Rates

• For a reaction: $\mathrm{H}_2(g) + \mathrm{Cl}_2(g) \rightarrow 2\mathrm{HCl}(g)$

• Average rate over a time interval $t_1$ to $t_2$: $R_{\text{avg}} = \frac{1}{2} \frac{[\mathrm{HCl}]_{t_2} - [\mathrm{HCl}]_{t_1}}{t_2 - t_1}$

• The factor $\frac{1}{2}$ is the inverse of the stoichiometric coefficient of HCl.

• General formula for a reaction $aA + bB \rightarrow pP + qQ$: $R_{\text{avg}} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{p} \frac{\Delta [P]}{\Delta t} = \frac{1}{q} \frac{\Delta [Q]}{\Delta t}$

• Instantaneous rate at time $t$ is the derivative: $R = \frac{1}{2} \left. \frac{d[\mathrm{HCl}]}{dt} \right|_{t}$

Units in Kinetics

• Concentration: $\mathrm{mol} \cdot \mathrm{L}^{-1}$ (M)

• Rate: $\mathrm{mol} \cdot \mathrm{L}^{-1} \cdot \mathrm{s}^{-1}$ (M/s)

SI Units and Prefixes

• 1 femtosecond (fs) = $10^{-15}$ s

• 1 picosecond (ps) = $10^{-12}$ s

• 1 nanometer (nm) = $10^{-9}$ m

• 1 microgram ($\mu$g) = $10^{-6}$ g = $10^{-9}$ kg

• 1 milliliter (mL) = $10^{-3}$ L = $10^{-6}$ m$^3$

• 1 kilogram (kg) = $10^3$ g

• 1 megahertz (MHz) = $10^6$ s$^{-1}$

• 1 gigahertz (GHz) = $10^9$ s$^{-1}$

• 1 terabyte (TB) = $10^{12}$ bytes

• 1 Å = $10^{-10}$ m; 1 L = $10^{-3}$ m$^3$; 1 bar = $10^5$ Pa

Gas Laws and Concentration

• The rare gas constant $R$ is the product of the Boltzmann constant $k_B$ and Avogadro's number $N_A$:

$R = k_B \times N_A$

$8.3145\ \mathrm{J}\,\mathrm{K}^{-1}\,\mathrm{mol}^{-1} = 1.38065 \times 10^{-23}\ \mathrm{J}\,\mathrm{K}^{-1} \times 6.02214 \times 10^{23}\ \mathrm{mol}^{-1}$

• For an ideal gas "X" with partial pressure $P_X$:

$nRT = PV \implies (n/V) = P/RT$

$[X] = n_X/V = P_X/RT$

$P_X = RT[X]$

When to Use [X], $P_X$, $n_X$, or $m_X$ in Kinetics

• For solutions and gases, use concentration $[X]$.

• For gases, pressure $P_X$ can also be used: $P_X = RT[X]$.

• For solids, use changes in moles or mass ($\Delta n_X$, $\Delta N$, $\Delta m_X$).

• Radioactive decay and solid decomposition are typically first-order reactions.

Mathematical Operations and Rearrangement Rules

• Valid operations on equations:

  • Do the same operation on both sides

  • Substitute equal quantities

  • Multiply by 1

  • Add 0 (rarely needed)

• Be careful with algebraic manipulations (e.g., distributing multiplication/division, roots, logarithms).

Gas Density and Molar Mass

• From the ideal gas law: $PV = nRT$

• Let $M$ be the molar mass, $d$ the density: $PM/RT = d$

• To fly a balloon, the gas inside must have a density much less than air, achievable with a lighter gas (e.g., H$_2$, He) or hot air (large $T$).

Arrhenius Equation and Rate Constants

• The temperature dependence of the rate constant $k$ is given by the Arrhenius equation: $k = A e^{-E_a/RT}$

• Taking the natural logarithm: $\ln k = \ln A - \frac{E_a}{RT}$

• Plotting $\ln k$ vs $1/T$ yields a straight line with slope $-E_a/R$ and intercept $\ln A$.

Unit Conversions

• Most unit conversions (except Celsius to Kelvin) can be done by multiplying by 1 in the appropriate form.

• Examples:

  • $m$ grams $= m$ grams $\times (1\ \mathrm{kg}/1000\ \mathrm{g})$

  • $V$ cubic meter $= V$ cubic meter $\times (1000\ \mathrm{L}/1\ \mathrm{m}^3)$

  • $8.3145\ \mathrm{J}\,\mathrm{K}^{-1}\,\mathrm{mol}^{-1} = 0.08206\ \mathrm{L}\,\mathrm{atm}\,\mathrm{K}^{-1}\,\mathrm{mol}^{-1}$

Summary Table: Key Kinetic Quantities

Quantity	Symbol/Formula	Units	Description
Concentration	$[X]$	mol/L (M)	Amount of substance per unit volume
Rate of Reaction	$R$	M/s	Change in concentration per unit time
Rate Constant	$k$	Varies (see rate law)	Proportionality constant in rate law
Gas Constant	$R$	J K$^{-1}$ mol$^{-1}$	Universal constant in gas laws
Activation Energy	$E_a$	J/mol	Minimum energy required for reaction

Best Practices for Success in CHEM 1001

• Attend every class, lab, and test (80% of success is showing up).

• Dedicate at least 4 hours per week to study and practice.

• Reflect on your learning strategies and adapt as needed.

• Remember: Excellence is a habit, not an act.