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Intro to Chemistry
Table of Contents
Unit 9 Overview: Gases
9.1 Gas Pressure
9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
9.4 Effusion and Diffusion of Gases
9.5 The Kinetic-Molecular Theory
9.6 Non-Ideal Gas Behavior

💏intro to chemistry review

9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions

Citation:

Gas laws are crucial for understanding how gases behave under different conditions. They explain relationships between pressure, volume, temperature, and amount of gas. These laws help predict gas behavior in various situations, from weather patterns to industrial processes.

Stoichiometry applies these laws to chemical reactions involving gases. It allows us to calculate quantities of gases produced or consumed in reactions. This is essential for many applications, from designing efficient engines to controlling air pollution.

Gas Laws and Stoichiometry

Ideal gas law calculations

  • Ideal gas law $PV = nRT$ relates pressure ($P$), volume ($V$), number of moles ($n$), ideal gas constant ($R$), and temperature ($T$) for ideal gases
  • Gas density ($d$) calculated by dividing mass ($m$) by volume ($V$) or using the combined ideal gas law and density equation $d = \frac{PM}{RT}$ (air, helium)
  • Molar mass ($M$) determined by rearranging the ideal gas law to $M = \frac{m}{n} = \frac{dRT}{P}$ (carbon dioxide, methane)
  • Molar volume is the volume occupied by one mole of an ideal gas at a given temperature and pressure

Gas stoichiometry in reactions

  • Balanced chemical equations provide mole ratios between reactants and products in gas-involving reactions (combustion, synthesis)
  • Mole ratios used to calculate the amount of gas consumed or produced in a reaction (hydrogen, oxygen)
  • Solving gas stoichiometry problems:
    1. Balance the chemical equation
    2. Convert given quantities to moles using $PV = nRT$
    3. Apply mole ratios from the balanced equation to find moles of the unknown substance
    4. Convert moles of the unknown substance to the desired unit using the ideal gas law or molar mass (liters, grams)
  • Standard temperature and pressure (STP) conditions are often used as a reference point in gas stoichiometry calculations

Gas Mixtures

Dalton's law for mixtures

  • Dalton's law states that the total pressure ($P_{total}$) in a mixture of non-reacting gases is the sum of the partial pressures ($P_n$) of each gas: $P_{total} = P_1 + P_2 + ... + P_n$ (air, natural gas)
  • Partial pressure ($P_n$) is the pressure each gas would exert if it occupied the container's volume alone, calculated using the mole fraction ($X_n$) and total pressure: $P_n = X_n \times P_{total}$ (nitrogen, oxygen in air)
  • Mole fraction ($X_n$) is the ratio of the number of moles of one component ($n_n$) to the total number of moles in the mixture ($n_{total}$): $X_n = \frac{n_n}{n_{total}}$ (carbon dioxide in exhaled breath)
  • Applying Dalton's law involves calculating partial pressures using mole fractions and total pressure or determining gas mixture composition using partial pressures and the ideal gas law (scuba tanks, greenhouse gases)

Gas Laws

  • Charles's law describes the relationship between volume and temperature of a gas at constant pressure
  • Boyle's law explains the inverse relationship between pressure and volume of a gas at constant temperature
  • Gay-Lussac's law relates the pressure and temperature of a gas at constant volume

Key Terms to Review (54)

π* antibonding molecular orbital: A π* antibonding molecular orbital is a type of molecular orbital formed when atomic orbitals combine in such a way that their electron density resides outside the internuclear axis, leading to decreased stability of the molecule. It is characterized by having a higher energy level than the original atomic orbitals.
Combustion analysis: Combustion analysis is a method used to determine the elemental composition, especially carbon and hydrogen, of an organic compound by burning the sample and analyzing the resulting products. This technique is essential for quantitative chemical analysis.
Ideal gas law: The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of an ideal gas. It is represented by the formula $PV = nRT$ where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature.
Hydrogen bonding: Hydrogen bonding is a strong type of dipole-dipole interaction that occurs between molecules when hydrogen is covalently bonded to electronegative atoms like oxygen, nitrogen, or fluorine. This bond results in higher boiling and melting points for substances.
Lavoisier: Antoine Lavoisier was a French chemist known as the 'Father of Modern Chemistry'. He formulated the Law of Conservation of Mass and helped systematize chemical nomenclature.
Mole fraction (X): Mole fraction (X) is a dimensionless quantity that represents the ratio of moles of a component to the total moles in a mixture. It is used to express the concentration of each component in gaseous mixtures.
Nitrogen fixation: Nitrogen fixation is the process by which molecular nitrogen ($N_2$) in the atmosphere is converted into ammonia ($NH_3$) or related nitrogenous compounds in soil. This process is essential for making nitrogen available to living organisms.
Partial pressure: Partial pressure is the pressure that a single gas in a mixture of gases would exert if it occupied the entire volume by itself. It is an essential concept for understanding gas mixtures and reactions in chemistry.
Orbital diagrams: Orbital diagrams are graphical representations of the electron configurations in atoms. They use boxes or lines to represent orbitals and arrows to represent electrons with their spins.
Standard molar volume: Standard molar volume is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), which is 0°C (273.15 K) and 1 atm pressure. It is approximately 22.414 liters.
Vapor pressure of water: Vapor pressure of water is the pressure exerted by water vapor in equilibrium with its liquid or solid phase at a given temperature. It increases with temperature as more molecules escape the liquid phase into the vapor phase.
Carbon Dioxide: Carbon dioxide (CO2) is a colorless, odorless gas that is present in the atmosphere and is a product of various chemical and biological processes, including respiration and combustion. It is a vital component in the carbon cycle and plays a crucial role in the functioning of the Earth's ecosystems.
Hydrogen: Hydrogen is the simplest and lightest element in the periodic table, with a single proton and electron in its neutral state. It is a highly reactive nonmetal that plays a crucial role in various chemical processes and is a fundamental component of many compounds, making it a key topic across several areas of chemistry.
Nitrogen: Nitrogen is a chemical element with the atomic number 7 and the symbol N. It is a colorless, odorless, and tasteless gas that makes up approximately 78% of the Earth's atmosphere. Nitrogen is an essential element for life, playing crucial roles in various chemical and biological processes.
Oxygen: Oxygen is a highly reactive nonmetallic element that is essential for most forms of life. It is the third most abundant element in the universe and the most abundant element on Earth's crust. Oxygen plays a crucial role in various chemical and biological processes, including respiration, combustion, and oxidation-reduction reactions.
Grams: Grams are a unit of measurement in the metric system that is used to quantify the mass or weight of an object or substance. It is a fundamental unit in chemistry and plays a crucial role in various chemical concepts and calculations.
M: M is a widely used term in chemistry that represents various important concepts, including molarity, stoichiometry, effusion and diffusion, rate laws, and precipitation and dissolution. This versatile term is crucial for understanding and applying fundamental chemical principles across multiple topics in the field of chemistry.
Mole Fraction: The mole fraction is a dimensionless quantity that represents the ratio of the amount of a particular substance to the total amount of all substances present in a mixture. It is a useful concept in understanding the composition of solutions, gaseous mixtures, and the behavior of colligative properties.
Liters: Liters (L) is a unit of measurement used to quantify the volume of a substance, particularly in the context of chemistry. It is a metric unit that is commonly used to measure the volume of liquids and gases.
Molar Volume: Molar volume is the volume occupied by one mole of a substance at a given temperature and pressure. It is a fundamental concept in chemistry that relates the amount of a substance to its physical volume and is essential for understanding the behavior of gases, reaction stoichiometry, and the ideal gas law.
Charles's Law: Charles's Law is a fundamental principle in the study of gases that describes the relationship between the volume and absolute temperature of a gas, stating that the volume of a gas is directly proportional to its absolute temperature, provided the pressure and amount of gas remain constant.
V: V is a fundamental quantity in the study of stoichiometry of gaseous substances, mixtures, and reactions. It represents the volume of a gas, which is a crucial factor in determining the relationships between the amounts of reactants and products in chemical processes involving gases.
P_n = X_n × P_total: The partial pressure of a gas, P_n, is equal to the mole fraction of that gas, X_n, multiplied by the total pressure of the gas mixture, P_total. This relationship is a fundamental concept in the study of the stoichiometry of gaseous substances, mixtures, and reactions.
X_n: X_n is a general term used to represent the amount or quantity of a specific substance, often in the context of stoichiometry, gaseous substances, mixtures, and chemical reactions. It is a variable that can be used to represent the moles, mass, or volume of a particular component in a system.
Stoichiometry: Stoichiometry is the quantitative study of the reactants and products involved in a chemical reaction. It focuses on the relationships between the amounts, masses, and concentrations of the substances participating in a reaction, allowing for the prediction and analysis of reaction outcomes.
Mole Ratios: Mole ratios are the relative amounts of reactants and products in a chemical reaction, expressed in terms of moles. They are used to determine the stoichiometric relationships between the substances involved in the reaction.
N_n: n_n is a symbolic representation used to denote the amount of a substance in a chemical reaction or mixture, specifically in the context of stoichiometry. It refers to the number of moles of a particular substance, which is a fundamental unit in the study of chemical reactions and the quantitative relationships between reactants and products.
Molar Mass (M): Molar mass, denoted as M, is the mass per mole of a substance. It is a fundamental quantity in the study of stoichiometry, which describes the quantitative relationships between reactants and products in chemical reactions, particularly in the context of gaseous substances and mixtures.
P_total: P_total, or total pressure, is the sum of the partial pressures of all the gases present in a mixture. It represents the overall pressure exerted by a gaseous mixture and is a fundamental concept in the stoichiometry of gaseous substances, mixtures, and reactions.
Air: Air is the invisible gaseous mixture that surrounds the Earth and is essential for life. It is the medium in which many chemical reactions and physical processes occur, making it a crucial component in the study of stoichiometry, gas mixtures, and chemical reactions.
Partial Pressure: Partial pressure is the pressure exerted by a specific gas in a mixture of gases. It is the contribution of an individual gas to the total pressure of the system, and it is directly proportional to the mole fraction of that gas in the mixture.
P: P is a variable that represents pressure in the context of stoichiometry of gaseous substances, mixtures, and reactions. Pressure is a fundamental concept in these topics as it directly influences the behavior and interactions of gases.
D = PM/RT: The equation d = PM/RT, known as the ideal gas law, is a fundamental relationship that describes the behavior of gases. It connects the density (d) of a gas to its pressure (P), molar mass (M), and the temperature (T) of the system, using the universal gas constant (R).
Ideal Gas Law: The Ideal Gas Law is a fundamental equation that describes the relationship between the pressure, volume, amount, and absolute temperature of a gas. It is a crucial concept in understanding the behavior of gases and their applications in various fields of chemistry.
Balanced Chemical Equations: A balanced chemical equation is a representation of a chemical reaction where the number of atoms of each element is the same on both the reactant and product sides, ensuring the conservation of mass and charge. This concept is crucial in understanding the stoichiometry of gaseous substances, mixtures, and reactions.
Gas Density: Gas density refers to the mass per unit volume of a gaseous substance. It is a crucial property that governs the behavior of gases in various chemical and physical processes, particularly in the context of stoichiometry, effusion, and diffusion.
Scuba Tanks: Scuba tanks, also known as SCUBA (Self-Contained Underwater Breathing Apparatus) tanks, are specialized containers used by divers to store and deliver compressed air or other breathing gases during underwater activities. These tanks play a crucial role in the context of 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions by providing the necessary gas supply for divers to breathe and operate safely underwater.
Boyle's Law: Boyle's Law is a fundamental principle in the study of gas behavior that describes the inverse relationship between the pressure and volume of a gas at constant temperature. It states that the pressure of a gas is inversely proportional to its volume, meaning that as the volume of a gas increases, its pressure decreases, and vice versa.
T: T, in the context of 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions, refers to the absolute temperature of a gas. Temperature is a fundamental property that describes the average kinetic energy of the particles in a substance and plays a crucial role in the behavior and interactions of gases.
P_n: P_n, or partial pressure, is a term that describes the contribution of a specific gas component to the total pressure of a gaseous mixture. It is a fundamental concept in the study of stoichiometry of gaseous substances, mixtures, and reactions.
Dalton's Law: Dalton's Law is a fundamental principle in chemistry that describes the behavior of gas mixtures. It states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases that make up the mixture.
Standard Temperature and Pressure (STP): Standard temperature and pressure (STP) is a set of conditions used as a reference point to measure and compare the properties of gases. It defines a specific temperature and pressure at which the physical and chemical properties of gases are standardized, allowing for consistent and meaningful comparisons across different situations.
PV = nRT: PV = nRT is the ideal gas law, which describes the relationship between the pressure (P), volume (V), amount of substance (n), and absolute temperature (T) of an ideal gas. This fundamental equation is used to predict the behavior of gases and understand various gas-related phenomena.
Gay-Lussac's Law: Gay-Lussac's Law is a fundamental principle in chemistry that describes the relationship between the pressure and temperature of a gas. It states that the pressure of a gas is directly proportional to its absolute temperature, as long as the volume and amount of the gas remain constant.
R: R is a variable that represents the universal gas constant, a fundamental physical constant that relates the pressure, volume, amount, and temperature of an ideal gas. It is a crucial parameter in the Ideal Gas Law and is used in various calculations involving the behavior of gases.
N: The variable 'n' is a fundamental unit used in various contexts in chemistry, representing the amount or quantity of a substance. It is a key parameter in understanding stoichiometric relationships, gas laws, and reaction kinetics.
Combustion: Combustion is a chemical reaction that occurs when a fuel, such as a hydrocarbon, reacts with an oxidizing agent, typically oxygen, to release energy in the form of heat and light. This exothermic reaction is a fundamental process in the understanding of chemistry, particularly in the context of stoichiometry, the occurrence and preparation of oxygen, and the properties of hydrocarbons.
Synthesis: Synthesis is the process of combining multiple reactants or components to form a new, more complex product. It is a fundamental concept in chemistry that describes the creation of new substances through chemical reactions.
Greenhouse Gases: Greenhouse gases are atmospheric gases that absorb and trap heat from the sun, preventing it from escaping back into space. This process, known as the greenhouse effect, is essential for maintaining the Earth's temperature at a level that can support life. However, an excess of these gases can lead to global warming and climate change.
Methane: Methane is a colorless, odorless gas with the chemical formula CH₄, primarily composed of carbon and hydrogen. It is the simplest alkane and serves as a primary component of natural gas, making it an important fuel source and a significant greenhouse gas contributing to climate change.
N_total: n_total represents the total number of moles of gas present in a mixture or involved in a chemical reaction. This term is crucial for understanding how gases behave under various conditions, especially when using the ideal gas law and stoichiometric calculations, which require precise mole ratios to determine the amounts of reactants and products in reactions involving gaseous substances.
X_n = n_n/n_total: X_n, known as the mole fraction, is a way to express the concentration of a component in a mixture. It is calculated by dividing the number of moles of the component (n_n) by the total number of moles in the mixture (n_total). This ratio provides insights into how components behave in reactions and mixtures, particularly in terms of gas behavior and the stoichiometric relationships that govern reactions involving gaseous substances.
Natural gas: Natural gas is a fossil fuel primarily composed of methane (CH₄), a colorless and odorless gas that forms from the decomposition of organic matter over millions of years. It is a significant energy source, often used for heating, electricity generation, and as a raw material in chemical processes. Understanding its behavior in various conditions is crucial for stoichiometric calculations involving gaseous substances and reactions.
P_total = P_1 + P_2 + ... + P_n: The equation $P_{total} = P_1 + P_2 + ... + P_n$ represents the total pressure of a gas mixture as the sum of the partial pressures of its individual components. This principle, known as Dalton's Law of Partial Pressures, is crucial for understanding how gases behave in mixtures and reactions, particularly when analyzing stoichiometric relationships and the behavior of gases under different conditions. It highlights that in a mixture of non-reacting gases, each gas contributes to the total pressure independently of the others.