2: Gas Laws and STP Concepts

Lecture 2 Announcements

• Today's Topics: Brown 10.1 Characteristics of Gases, 10.2 Pressure, 10.3 The Gas Laws, 10.4 The Ideal Gas Equation, 10.5 Gas Mixtures and Partial Pressures, 10.6 The Kinetic-Molecular Theory of Gases, 10.7 Molecular Effusion and Diffusion, 10.8 Real Gases: Deviations from Ideal Behavior
• Problem Set 1: Due tomorrow, upload as a PDF on Moodle
• Tutorials: Completed after Exercise 2
• Useful Info Sheets: Found on Moodle, exam-related information sheets

Lecture 3

• Next Week's Topics: Brown 4.1 General Properties of Aqueous Solutions, 4.2 Precipitation Reactions, 4.3 Acids, Bases, and Neutralization Reactions, 4.4 Oxidation-Reduction Reactions, 4.5 Concentrations of Solutions

Review

• Lecture 1 topics: Definitions, nomenclature, elements, compounds, mixtures, atoms, atomic structure, atomic number, mass number, isotopes, periodic table, molecules, formulas, structural formulas, representations, ions, and ionic compounds
• Lecture 1 transition to Lecture 2: Discussion of chemical reactions, change one substance into another, chemical equations, stoichiometry, balancing equations, formula weights, mole, Avogadro's number, molar mass
• Atomic structure: Nucleus (protons and neutrons), electron cloud ( ~1Å to ~5Å)

Example Chemical Reaction

• Chemical equation: 2 H₂(g) + O₂(g) → 2 H₂O(l)
• Molecular interpretation: 2 molecules H₂, 1 molecule O₂, 2 molecules H₂O
• Mole-level interpretation: 2 mol H₂, 1 mol O₂, 2 mol H₂O
• Molar masses: 4.0 g H₂, 32.0 g O₂, 36.0 g H₂O

Types of Chemical Reactions

• Combustion: Reacting with O₂, example CH₄ + 2O₂ → CO₂ + 2H₂O (combustion of methane)
• Combination: A + B → C, example C(s) + O₂(g) →CO₂(g), N₂(g) + 3H₂(g) → 2NH₃(g) (burning coal, fixation of nitrogen)
• Decomposition: C → A + B, example 2 H₂O(l) → 2H₂(g) + O₂(g), CaCO₃(s) → CaO(s) + CO₂(g) (electrolysis of water, cement/concrete)

Today's Topic: Gases

• Three states: Solid, liquid, vapor
• Example: H₂O
• Gas properties: Similar physical properties, even with different chemical properties, expand to fill the container, compressible, and form homogeneous mixtures. Molecules occupy a small portion of the total volume.

Common Gases at Room Temperature

• Provides a table of common gases at room temperature with formulas, names, and characteristics (toxic, odor, color).

Parameters to Describe Gases

• Parameters: Volume (V), Amount (n, moles), Temperature (T), Pressure (P)
• Type: Extensive properties (depend on sample size) and intensive properties (do not depend on sample size or volume)

Origin of Pressure

• Pressure is caused by molecules moving and hitting surfaces.
• Atmospheric pressure is due to Earth's gravity acting on a column of air.
• Standard atmospheric pressure is approximately 100 kPa or 1 bar.

Measuring Atmospheric Pressure

• Barometer: measures atmospheric pressure using mercury.
• 760 mm Hg = 1 atmosphere (atm) = 101.325 kPa = 1.01325 bar

Measuring Relative Pressure

• Manometer: measures the pressure difference between a gas and the atmosphere.

P-V Relationship (Boyle's Law)

• Keep n and T constant: Pressure and volume are inversely proportional
• PV = constant, or P = constant * 1/V

V-T Relationship (Charles's Law)

• Keep n and P constant: Volume and temperature are directly proportional
• V = constant * T, or V/T = constant

V-n Relationship (Avogadro's Law)

• Keep P and T constant: Volume and number of moles is directly proportional
• V = constant * n, or V/n = constant

Standard Temperature and Pressure (STP)

• Defined as T=0°C (273.15K), and P=1 atm (101.325 kPa)
• Molar volume at STP is 22.41 L

Ideal Gas Law (IGL)

• PV = nRT
• where R is the gas constant with different values in different units.

Assumptions in IGL

• Molecules in gases do not interact, negligible volume compared to the total volume, and the amount of gas depends on the number of gaseous species present

Using Ideal Gas Law

• Type 1: Find a missing variable if three of the four (P, V, n, T) are known. Rearrange the IGL to isolate the unknown variable.
• Type 2: Two variables remain constant (n, T, etc.) while two other variables change. Rearrange IGL for desired relations like PV/T

Type 3

• One variable is constant and three other variables are changing. Using the IGL by isolating the variable and plugging in values to find the unknown

Other Uses of IGL

• Density: Rearranging IGL, the density of a gas can be determined if molar mass (Mw), pressure (p), and temperature (T) are known

Partial Pressures/Gaseous Mixtures

• Total pressure (Ptot): Depends on total number of moles, where the Ptot = P₁ + P₂ + ... + Pi.
• Partial Pressure: Individual pressure contributions from each component

Mixtures and Mole Fraction

• Mole fraction means, X₁ = nᵢ / nₜₒₜ where i is a component, meaning in a mixture

Kinetic-Molecular Theory of Gases

• Molecules are randomly moving with constant kinetic energy.
• Gas molecules occupy negligible volume
• Gas molecules collide but do not interact.
• Average Ek depends on temperature (T)

Velocity Distributions

• Molecules move with a range of velocities, depending on temperature and molecular mass.
• Distribution shifts to higher velocities with higher temperatures, and lower velocities for heavier molecules.
• The area under the speed distribution should always add up to 1.0

Special Velocities

• Vmp: Most probable speed
• Vav: Average speed
• Vrms: Root mean square speed (speed of a molecule with kinetic energy equal to the average kinetic energy of all molecules)

Diffusion

• Gases diffuse at much slower speeds than their RMS speed.
• Mean free path is dependent on different factors, such as pressure.

Nonidealities in Gases

• High Pressure: Volume occupied by molecules is no longer negligible
• Low Temperature: Molecules interact strongly with each other.
• Van der Waals Equation: Modifies IGL to account for molecular interactions and volume.

Next time: Reactions in Water

This quiz covers fundamental concepts related to Standard Temperature and Pressure (STP) and gas laws such as Boyle's and Charles's laws. Test your knowledge on the relationships between temperature, volume, and pressure of gases, as well as the properties of gases at STP. Ideal for students studying chemistry or physics.