14: The Behavior of Gases
- Page ID
- 53819
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 14.1: Compressibility
- This page discusses the compressibility of gases, likening it to packing for a vacation. It explains how scuba diving involves using compressed air in tanks, highlighting the ability of gases to occupy smaller spaces compared to solids or liquids due to the space between particles. This property enables gases to be applied in diverse fields, including medical oxygen supply, anesthesia, welding, and fueling barbeque grills.
- 14.2: Factors Affecting Gas Pressure
- This page discusses how basketball pressure influences bounce height and is adjusted with a hand pump. It outlines the four factors affecting gas pressure: amount of gas, volume, temperature, and gas particle behavior. Increasing gas in a rigid container raises pressure, as does reducing volume or increasing temperature. Conversely, reducing gas, increasing volume, or lowering temperature decreases pressure. The summary emphasizes that these factors directly impact gas behavior and pressure.
- 14.3: Boyle's Law
- This page discusses the daily launch of weather balloons made from synthetic rubber to gather atmospheric data. It explains Boyle's Law, which describes the inverse relationship between gas volume and pressure at constant temperature, illustrating how this principle applies to gas behavior. The summary emphasizes the importance of Boyle's Law in understanding gas dynamics in different conditions.
- 14.4: Charles's Law
- This page explains how freshly-baked bread becomes fluffy through yeast fermentation, producing carbon dioxide that expands the dough. It introduces Charles's Law, which describes the direct relationship between gas volume and absolute temperature at constant pressure. The law is mathematically represented and supported by temperature-volume data, depicted graphically as a straight line approaching the origin.
- 14.5: Gay-Lussac's Law
- This page discusses how temperature changes can mislead users about the remaining gas in propane tanks for barbeque grills, referencing Gay-Lussac's Law. This law explains that gas pressure increases with temperature in a rigid container. An example involving an aerosol can illustrates potential safety concerns. Understanding this relationship is vital for safely managing gas levels in propane tanks and similar containers.
- 14.6: Combined Gas Law
- This page explains how modern refrigerators function using gas laws to transfer heat. Compressed gas in coils expands to cool the interior by absorbing heat, then is compressed to release heat externally. It discusses the combined gas law, which connects pressure, volume, and temperature changes of gas at constant quantity and can derive individual gas laws like Boyle's, Charles's, and Gay-Lussac's when varying one variable at a time.
- 14.7: Avogadro's Law
- This page explains Avogadro's Law, which states that the volume of a gas is directly proportional to the number of moles at constant temperature and pressure. It includes examples, such as inflating a balloon, to illustrate the principle. A specific calculation shows how the volume changes when additional helium is added to a balloon from 1.90 L to 2.33 L using Avogadro's formula.
- 14.8: Ideal Gas Law
- This page emphasizes the significance of ammonia in chemical reactions and outlines the method for calculating its required amount using gas laws, particularly the ideal gas law.
- 14.9: Calculating the Molar Mass of a Gas
- This page discusses the use of helium in balloons and explains how to calculate the molar mass and density of gases through the ideal gas law. An example is provided for calculating the molar mass of nitrogen oxide, identified as \(\ce{N_2O}\), and the density of ammonia gas is also analyzed, highlighting its variation with temperature and pressure changes, which affect molecular spacing.
- 14.10: Gas Stoichiometry
- This page discusses the Haber cycle's importance in ammonia production, emphasizing the need for excess nitrogen and hydrogen. It highlights the use of stoichiometry, molar volume, and the ideal gas law for calculating gas reactions under various conditions. An example showcases the combustion of ethanol, demonstrating how 25.21 g produces 1.094 moles of CO2, with the ideal gas law determining the produced volume of 30.6 L.
- 14.11: Real and Ideal Gases
- This page discusses how molecular structure affects behavior, exemplified by ethanol and dimethylether's differing boiling points due to intermolecular interactions. It also covers the ideal gas law, noting that real gases deviate from ideal behavior at high pressures and low temperatures, with lighter gases like helium being more ideal than those with stronger intermolecular forces.
- 14.12: Mole Fraction
- This page discusses sulfur dioxide (SO₂) production from volcanic eruptions and coal combustion, highlighting its dual role in cooling and contributing to pollution. Efforts to lower SO₂ to mitigate acid rain could worsen global warming by decreasing cooling effects. The concept of mole fraction, important for gas mixture analysis, is introduced along with Dalton's law, which connects partial pressures to mole fractions using hydrogen and oxygen mixtures as examples.
- 14.13: Gas Collection by Water Displacement
- This page discusses the collection of gases in lab experiments through water displacement, which involves inverting a bottle in water to capture gas while pushing out water. It highlights the need to correct for water vapor using Dalton's law to find the gas's true pressure, combining atmospheric pressure and water vapor pressure at the reaction temperature. An example is provided to demonstrate the calculation of dry hydrogen gas volume at STP using these concepts.
- 14.14: 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.
- 14.15: Diffusion and Effusion and Graham's Law
- This page explains that gases are often invisible, with detection methods illustrated through an ammonia and hydrogen chloride experiment. It distinguishes between diffusion (moving from high to low concentration) and effusion (escaping through a hole), emphasizing that both are influenced by molar mass—lighter gases move more quickly. Thomas Graham's law is introduced, highlighting that the rate of these processes inversely correlates with the square root of the gas's molar mass.