General Chemistry 102 - Gases

General Chemistry 102 Course Notes

Instructor Information

• Professor: Pinchas Farkas

• Email: pinchas.farkas@touro.edu

• © 2018 Pearson Education, Inc.

Course Material

Textbook

• Primary Textbook:
  Brown, LeMay, and Bursten, "Chemistry, the Central Science", 14th edition, ISBN10: 0-13-441423-3

• Alternative Editions:
  12th and 13th editions can also be used.

Course Content Overview

Course Assignments

• Exam One: 15%

• Exam Two: 15%

• Final Exam: 30%

• Quizzes: 30%

• Labs: 10%

Test Requirements

• To access exams on Canvas:

  • Ensure access to the Internet and a supported web browser (Internet Explorer, Chrome, Firefox, Safari).

  • Update your browser before exams.

  • Download the Lockdown Browser; a practice quiz will be sent to familiarize you with its use.

  • Use your cellular phone to connect to Zoom and set up your desk as per provided instructions.

  • Your hands must be visible throughout the exam. No Exceptions!

  • You are expected to maintain focus in front of your screen; violations will result in a zero on your test.

Grading Guidelines

How to Succeed in this Course

1. Attend lectures.

2. Complete homework problems.

3. Work on extra problems if necessary.

4. Ensure a solid understanding of concepts covered in lectures.

Lecture Content Structure

• Lectures will closely follow the textbook.

• Example problems will be a key part of the lecture material.

Chapter 10: Gases

Chapter Overview

Key Topics Covered

• Characteristics of Gases

• Pressure

• The Gas Laws

• The Ideal-Gas Equation

• Applications of the Ideal-Gas Equation

• Gas Mixtures and Partial Pressure

• Real Gases: Deviations from Ideal Behavior

Characteristics of Gases

• Physical Properties:

  • All gases share similar physical properties.

  • Composed mainly of nonmetallic elements with simple formulas and low molar masses.

  • Gases can include substances that are liquids or solids under ordinary conditions, referred to as vapors (e.g., water).

• Unique Properties of Gases:

  • Expand to fill their containers.

  • Highly compressible.

  • Extremely low densities compared to solids and liquids.

• Two or more gases form a
  homogeneous mixture.

Behavior of Gas Molecules

• Gas molecules are relatively far apart in a given volume of air, occupying approximately 0.1% of the total volume ($V_{t}$) with the remaining space being empty.

• Only a few elements exist as gases at ordinary conditions:

  • Helium (He)

  • Neon (Ne)

  • Argon (Ar)

  • Krypton (Kr)

  • Xenon (Xe)

  • Hydrogen (H2)

  • Nitrogen (N2)

  • Oxygen (O2)

  • Fluorine (F2)

  • Chlorine (Cl2)

Common Gases

Table 10.1: Common Compounds That Are Gases at Room Temperature

Properties That Define the State of a Gas Sample

1. Temperature

2. Pressure

3. Volume

4. Amount of gas, usually expressed in moles

Pressure

• Definition of Pressure:

  • Pressure is defined as the amount of force applied to an area.

  P = \frac{F}{A}
  where:

  • P = Pressure

  • F = Force

  • A = Area

• Atmospheric Pressure:

  • Refers to the weight of air per unit area.

  • Gas molecules move chaotically, colliding with each other and with the walls of their container.

Impact of Pressure

Example: Pressure Comparison for Different Footwear

• Scenario:
  A 50 kg (110 lb) woman wears different types of footwear.

• Calculation:

  • Pressure on Stiletto Heel:
    P = \frac{(25\text{ kg})(10\text{ m/s}^2)}{(1.0 \times 10^{-2} \text{ m})^2} = 2.50 \times 10^6 ext{ Pa} = 24.7 ext{ atm}

  • Pressure on Sneaker Sole:
    P = \frac{(50\text{ kg})(10\text{ m/s}^2)}{(1.75 \times 10^{-2} \text{ m})^2} = 2.86 \times 10^3 ext{ Pa} = 0.28 ext{ atm}

Consequently, the pressure applied by the stiletto heel is 88 times greater than that of the sneaker.

Units of Pressure

• Pressure can be expressed in various units:

  • 1 ext{ atm} = 760 ext{ mmHg} = 760 ext{ Torr} = 14.7 ext{ psi} = 1.01325 \times 10^5 ext{ Pa} = 101.325 ext{ kPa}

Example Problem

• Convert: 745 torr into Pa:
  745 \text{ torr} \times \left( \frac{101325 \text{ Pa}}{760 \text{ torr}} \right) = 97900 \text{ Pa}

Standard Pressure

• Standard Atmospheric Pressure (STP):

  • Refers to normal atmospheric pressure at sea level, defined as:

  • Standard Temperature (ST) = 273 K (0 °C)

  • Pressure = 1 atm (101.3 kPa)

The Gas Laws

Fundamental Relationships

• The physical state of a gas is determined by four variables:

  • Temperature

  • Amount of gas (in moles)

  • Pressure

  • Volume

Key Laws

1. Boyle’s Law

   • At constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure:
     P1V1 = P2V2

2. Charles’ Law

   • At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature:
     \frac{V1}{T1} = \frac{V2}{T2}

3. Avogadro’s Law

   • At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas:
     \frac{V1}{n1} = \frac{V2}{n2}

Combined Gas Law

• This law combines Boyle’s Law, Charles’ Law, and Avogadro’s Law:
  P1V1 = P2V2 \quad \Rightarrow \quad \frac{P1V1}{T1} = \frac{P2V2}{T2}

Ideal Gas Equation

• Formulation: The ideal gas equation combines the relationships from the laws above: PV = nRT where:

  • P = Pressure (atm)

  • V = Volume (L)

  • n = moles of Gas (mol)

  • R = gas constant = 0.0821 (L·atm/mol·K)

  • T = Temperature (K)

Strategies for Using the Ideal Gas Law

• Organize information systematically.

• Convert all units as needed to maintain consistency.

• Use dimensional analysis to ensure correctness.

Example Problem Using Ideal Gas Equation

• A sample carbon dioxide gas in a 250-mL flask has a pressure of 1.3 atm at 31 °C. Calculate the moles:

  • Convert V to liters: V = 0.250 L

  • Convert T to Kelvin: T = 31 + 273 = 304 K

  • Using PV = nRT , rearranging gives: n = \frac{PV}{RT}

Density of Gases

• The density of a gas can be connected with the ideal gas law:
  d = \frac{MP}{RT}
  where M is the molar mass.

• To find molar mass:
  M = \frac{dRT}{P}

Practical Analyses

Problems Relating to Stoichiometry

• Gases can be related to chemical reactions through balanced equations:

  • Example: Inflated automotive airbags fill with nitrogen generated from sodium azide decomposition.

  • Calculate gas density and molar mass articulation through ideal gas law manipulation, ensuring proper unit conversions throughout.

Dalton’s Law of Partial Pressures

• States that if two non-reactive gases are mixed, the total pressure is the sum of the pressures each would exert if alone: Pt = P1 + P2 + P3 + …

  • The formula can also be adapted to express partial pressures with mole fractions.

Conclusion

The study of gases encompasses understanding their physical properties, behaviors, and the laws that govern them. This includes the mathematical relationships described above, providing a foundation for further study within the realm of chemistry.

Ensure to refer back to provided examples as practice problems for deeper comprehension and to streamline your understanding of complex concepts throughout this chapter.