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9.1 Gas Pressure

4 min read•june 25, 2024

is a key player in understanding how gases behave. It's all about the force gases exert on surfaces due to particle collisions. Knowing helps us grasp why balloons inflate, tires stay firm, and weather patterns change.

Measuring and converting pressure units is crucial for real-world applications. From to , each unit tells us something about gas behavior. Devices like and help us quantify pressure, making it easier to predict and control gas-related phenomena.

Gas Pressure

Pressure in gas behavior

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  • Pressure is the force exerted per unit area on a surface
    • Gases exert pressure on their container walls due to collisions of gas particles (molecules or atoms) with the walls
    • Higher pressure indicates more frequent and/or more forceful collisions (increased kinetic energy)
  • Pressure is a crucial factor in determining gas behavior and properties
    • Changes in pressure can affect gas volume (compression or expansion), temperature (heating or cooling), and solubility (increased or decreased)
    • Understanding pressure is essential for applications such as tire inflation, scuba diving, and weather forecasting

Pressure unit conversions

  • Common units of pressure include:
    • Pascals (Pa): SI unit of pressure, equal to one newton per square meter (1 Pa=1Nm21 \text{ Pa} = 1 \frac{\text{N}}{\text{m}^2})
    • Atmospheres (atm): pressure exerted by Earth's atmosphere at sea level (1 atm=101,325 Pa1 \text{ atm} = 101,325 \text{ Pa})
    • (mmHg): pressure required to support a column of mercury 1 mm high (1 [torr](https://www.fiveableKeyTerm:Torr)=133.322 Pa1 \text{ [torr](https://www.fiveableKeyTerm:Torr)} = 133.322 \text{ Pa})
    • Pounds per square inch (psi): pressure exerted by a force of one pound on an area of one square inch (1 psi=6,894.76 Pa1 \text{ psi} = 6,894.76 \text{ Pa})
  • To convert between units, use conversion factors based on the relationships between the units
    • Multiply the given pressure value by the appropriate conversion factor to obtain the desired unit
    • For example, to convert 2.5 atm to Pa: 2.5 atm×101,325Paatm=253,312.5 Pa2.5 \text{ atm} \times 101,325 \frac{\text{Pa}}{\text{atm}} = 253,312.5 \text{ Pa}
  • is a reference point used in chemistry, defined as 0°C (273.15 K) and 1 atm pressure

Pressure measurement devices

  • Manometers measure the difference in pressure between two points
    • Consist of a U-shaped tube filled with a liquid (usually mercury)
    • The difference in height of the liquid in the two arms indicates the pressure difference
    • Used in applications such as measuring gas pressure in a container or determining fluid flow rates
  • Barometers measure atmospheric pressure
    • Consist of a sealed vacuum tube partially filled with mercury
    • The height of the mercury column is proportional to the atmospheric pressure
    • Used in weather forecasting and altitude measurements
  • Digital pressure sensors convert pressure into an electrical signal
    • Utilize various technologies such as piezoelectric, capacitive, or piezoresistive elements
    • Provide accurate and continuous pressure readings for industrial and scientific applications

Calculations with manometer data

  • In a , the pressure difference (ΔP\Delta P) is related to the height difference (hh) of the liquid by: ΔP=ρgh\Delta P = \rho gh
    • ρ\rho is the density of the liquid
    • gg is the acceleration due to gravity (9.81 m/s²)
  • To calculate the absolute pressure of a gas using a manometer:
    1. Determine the height difference between the liquid levels in the manometer
    2. Calculate the pressure difference using the formula ΔP=ρgh\Delta P = \rho gh
    3. Add or subtract the pressure difference from the reference pressure (e.g., atmospheric pressure) depending on the setup
      • If the gas is connected to the low-pressure side, add ΔP\Delta P to the reference pressure
      • If the gas is connected to the high-pressure side, subtract ΔP\Delta P from the reference pressure
  • For example, if a manometer filled with mercury (density = 13,600 kg/m³) shows a height difference of 25 mm and the gas is connected to the low-pressure side, with atmospheric pressure at 1 atm:
    1. Height difference: h=25 mm=0.025 mh = 25 \text{ mm} = 0.025 \text{ m}
    2. Pressure difference: ΔP=ρgh=13,600kgm3×9.81ms2×0.025 m=3,332.4 Pa\Delta P = \rho gh = 13,600 \frac{\text{kg}}{\text{m}^3} \times 9.81 \frac{\text{m}}{\text{s}^2} \times 0.025 \text{ m} = 3,332.4 \text{ Pa}
    3. Absolute pressure: Pabs=Patm+ΔP=101,325 Pa+3,332.4 Pa=104,657.4 PaP_{\text{abs}} = P_{\text{atm}} + \Delta P = 101,325 \text{ Pa} + 3,332.4 \text{ Pa} = 104,657.4 \text{ Pa}

Gas mixtures and partial pressures

  • states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its components
  • is the pressure exerted by a single gas component in a mixture
  • Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature
  • The concept of is the lowest possible temperature (-273.15°C or 0 K) where all molecular motion theoretically ceases

Key Terms to Review (29)

Absolute Zero: Absolute zero is the lowest possible temperature, representing the complete absence of thermal energy. It is the point at which the motion of atoms and molecules reaches its minimum, and no further heat can be extracted from a system.
Atmospheres: An atmosphere is the layer of gases surrounding a planet or other celestial body that is retained by the body's gravity. It plays a crucial role in the gas pressure and temperature of a planet, which are key factors in the Ideal Gas Law.
Bar: A bar is a unit of pressure defined as 100,000 Pascals. It is commonly used in scientific contexts to measure atmospheric and gas pressures.
Barometer: A barometer is an instrument used to measure atmospheric pressure. It helps determine weather changes and is crucial in studying gas behavior.
Barometers: Barometers are instruments used to measure atmospheric pressure, which is the force exerted by the weight of the air above a given surface area. They are essential tools for monitoring and predicting weather patterns, as changes in atmospheric pressure are closely linked to weather conditions.
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.
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.
Combined Gas Law: The Combined Gas Law is a fundamental relationship that describes the behavior of gases by relating their pressure, volume, and absolute temperature. It is a combination of Boyle's law, Charles' law, and Gay-Lussac's law, and is used to predict the changes in a gas's properties under different conditions.
Compressibility: Compressibility is a measure of how much a substance can be reduced in volume by the application of pressure. It is a fundamental property of gases, liquids, and solids that describes their ability to be compressed or squeezed into a smaller space without changing their chemical composition.
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.
Diffusion: Diffusion is the process by which gas molecules spread from an area of higher concentration to an area of lower concentration. It occurs due to the random motion of gas particles.
Diffusion: Diffusion is the spontaneous movement of particles from an area of higher concentration to an area of lower concentration, driven by the random thermal motion of the particles. This process occurs in gases, liquids, and solids and is a fundamental concept in understanding the behavior of matter and energy.
Gas Pressure: Gas pressure is the force exerted by the weight or bombardment of gas molecules per unit area on the walls of a container or surface. It is a measure of the average kinetic energy of the gas molecules and is an important concept in understanding the behavior and properties of gases.
Hydrostatic pressure: Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases proportionally with depth in a fluid.
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.
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.
Jacques Charles: Jacques Charles was a French physicist and mathematician who made significant contributions to the study of gas behavior and the relationship between temperature and volume. His work laid the foundation for the understanding of gas laws, which are crucial in the field of chemistry, particularly in the context of gas pressure.
Kinetic molecular theory: The kinetic molecular theory explains the behavior of gases in terms of motion and energy of their molecules. It states that gas particles are in constant, random motion and that the temperature of a gas is proportional to the average kinetic energy of its molecules.
Kinetic Molecular Theory: The kinetic molecular theory is a model that explains the behavior of gases by describing the motion and interactions of gas particles. It provides a framework for understanding the fundamental properties of gases, such as pressure, volume, and temperature, in the context of the microscopic behavior of gas molecules.
Manometer: A manometer is an instrument used to measure the pressure of gases. It typically consists of a U-shaped tube filled with a liquid, such as mercury or water, where the difference in liquid levels indicates the pressure.
Manometers: Manometers are instruments used to measure the pressure of gases or liquids by balancing the fluid column against an unknown pressure. They are essential for understanding gas behavior and pressure relationships, as they provide a visual representation of pressure changes, allowing for accurate readings in various scientific and industrial applications.
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.
Pascal (Pa): The pascal (Pa) is the SI unit of pressure, defined as one newton per square meter. It quantifies the force applied perpendicular to the surface area of an object.
Pascals: Pascals (Pa) is the unit of measurement for pressure in the International System of Units (SI). Pressure is a fundamental concept in the study of gas behavior and is directly related to the force exerted by a gas on its surroundings.
Pressure: Pressure is the force exerted per unit area on the surface of an object. It is commonly measured in units like Pascals (Pa) or atmospheres (atm).
Robert Boyle: Robert Boyle was a 17th century natural philosopher who made significant contributions to the development of modern chemistry and atomic theory. He is best known for his groundbreaking work on the properties of gases, which laid the foundation for our understanding of gas behavior and pressure.
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.
Torr: A torr is a unit of pressure defined as 1/760 of an atmosphere. It is named after Evangelista Torricelli, an Italian physicist who invented the barometer.
Torr: The torr is a unit of pressure, named after the Italian scientist Evangelista Torricelli, who invented the barometer. It is commonly used to measure low pressures, such as those found in vacuum systems and atmospheric conditions.
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9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law