11: Gases
- Page ID
- 47425
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Of the three basic phases of matter—solids, liquids, and gases—only one of them has predictable physical properties: gases. In fact, the study of the properties of gases was the beginning of the development of modern chemistry from its alchemical roots. The interesting thing about some of these properties is that they are independent of the identity of the gas. That is, it doesn’t matter if the gas is helium gas, oxygen gas, or sulfur vapors; some of their behavior is predictable and very similar. In this chapter, we will review some of the common behaviors of gases. Gases have no definite shape or volume; they tend to fill whatever container they are in. They can compress and expand, sometimes to a great extent. Gases have extremely low densities, a one-thousandth or less of the density of a liquid or solid. Combinations of gases tend to mix together spontaneously—that is, they form solutions. Air, for example, is a solution of mostly nitrogen and oxygen. Any understanding of the properties of gases must be able to explain these characteristics.
- 11.1: Extra-Long Straws
- This page explains how a drinking straw operates by creating a vacuum that allows liquid to be drawn up through pressure difference. It highlights that atmospheric pressure pushes the liquid upward, and notes that the maximum height for water to be lifted by a straw is approximately 10.3 meters due to atmospheric limits, indicating that using a longer straw won’t result in a higher liquid level.
- 11.2: 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.
- 11.3: Pressure - The Result of Constant Molecular Collisions
- 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.
- 11.4: 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.
- 11.5: 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.
- 11.6: The Combined Gas Law- Pressure, Volume, and Temperature
- 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.
- 11.7: 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.
- 11.8: The Ideal Gas Law- Pressure, Volume, Temperature, and Moles
- 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.
- 11.9: Mixtures of Gases - Why Deep-Sea Divers Breathe a Mixture of Helium and Oxygen
- This page covers Dalton's Law of Partial Pressures, explaining that the total pressure of a gas mixture equals the sum of individual partial pressures. It compares the atmospheres of Venus and Earth, focusing on composition differences. The page also discusses gas collection via water displacement, stressing the importance of accounting for water vapor in pressure calculations. A practical example illustrates how to determine the volume of dry gas at STP after subtracting water vapor influences.
- 11.11: 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. It compares to Charles's Law but applies to rigid containers.