10: Gases
- Page ID
- 568677
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 10.1: Kinetic Molecular Theory- A Model for Gases
- This page discusses the kinetic theory of gases, which describes gases as tiny, constantly moving particles. Key principles include elastic collisions, significant distances between particles, and negligible attractive forces, explaining properties like low density and expansibility. While ideal gases perfectly fit this model, real gases show minor deviations. Overall, the kinetic theory effectively accounts for the behaviors of gases, making it a widely accepted framework in science.
- 10.2: What is Gas Pressure?
- This page explores the concept of pressure, describing it as the force exerted by gas particles colliding with container walls, and outlines its measurement in various units, including pascals (Pa) and atmospheres (atm). It provides conversion factors and examples for converting between these units, highlighting the relationship between atmospheric pressure and other measurements. The key takeaway is the fundamental understanding of pressure and how it is measured in different contexts.
- 10.3: Boyle’s Law - Pressure and Volume
- This page discusses gas laws, particularly Boyle's Law, highlighting the inverse relationship between pressure and volume of a gas at constant temperature and quantity. It emphasizes the equation P1V1 = P2V2 for predicting gas behavior, along with a problem-solving approach that includes identifying variables, rearranging equations, and maintaining consistent units.
- 10.4: Charles’s Law- Volume and Temperature
- This page explains Charles's Law, highlighting the direct relationship between a gas's volume and its absolute temperature at constant pressure, supported by examples and data. It emphasizes the importance of using the Kelvin scale and explores implications for gas behavior near absolute zero. The mathematical relationship enables calculations regarding volume and temperature changes, with exercises provided to enhance comprehension.
- 10.5: Gay-Lussac's Law- Temperature and Pressure
- This page explains Gay-Lussac's Law, which states that in a rigid container, the pressure of a gas increases directly with its absolute temperature when the volume is constant. The increase in pressure is due to higher kinetic energy of gas molecules resulting in forceful collisions with the container walls.
- 10.6: Avogadro’s Law- Volume and Moles
- This page highlights the significance of tire pressure for safety and comfort, while introducing Avogadro's Law, which relates gas volume to the number of moles at constant temperature and pressure. It includes examples such as balloon inflation and offers a step-by-step approach for problem-solving. Additionally, there's an exercise aimed at reinforcing comprehension of the volume-mole relationship in gases through practical calculations using the law.
- 10.7: The Combined Gas Law
- This page introduces the Combined Gas Law, illustrating the relationship between pressure, volume, and temperature of gases through the equation \(\dfrac{P_{1}V_{1}}{T_{1}}=\dfrac{P_{2}V_{2}}{T_{2}}\). It emphasizes the necessity of using consistent units, especially Kelvin for temperature, and provides an example of calculating final gas pressure when variables change.
- 10.8: The Ideal Gas Law
- This page covers the Ideal Gas Law, described by the equation \(PV = nRT\), connecting pressure, volume, temperature, and moles of gas. It explores how other gas laws contribute to this formulation and emphasizes that more moles of gas result in larger volumes.
- 10.9: Molar Volume of a Gas at STP
- This page explains Avogadro's Hypothesis, which asserts that equal volumes of gas at the same temperature and pressure contain the same number of particles, regardless of mass. The effects of pressure and temperature on gas volume are highlighted, with standard temperature and pressure (STP) defined at 0°C and 1 atm, where one mole of gas occupies 22.4 liters.
- 10.10: Converting Between Moles and Gas Volume - STP is a Conversion Factor!
- This page discusses the measurement of gas volume in chemistry, focusing on the calculation of moles for optimal reactions. It highlights the concept of molar volume at standard temperature and pressure (STP), where \(1 \, \text{mol} = 22.4 \, \text{L}\), and provides examples for converting gas volumes to moles and vice versa. The importance of maintaining STP conditions during these calculations is emphasized, along with practice questions for further comprehension.
- 10.11: Gas Stoichiometry
- This page introduces the idea of gas phase stoichiometry calculations. Students can use ideal gas law (PV = nRT) or the STP molar volume of a gas as a method to "get to moles" when solving gas stoichiometry problems.
- 10.12: Dalton's Law of Partial Pressures
- This page discusses Venus' inhospitable atmosphere, dominated by carbon dioxide, high pressure, and extreme temperatures. It also explains Dalton’s Law of Partial Pressures, which states that in a gas mixture, each gas independently contributes to the total pressure. This principle is illustrated with Earth's atmosphere, where gases like nitrogen and oxygen combine to create the overall pressure.