Gas pressure is a key player in understanding how gases behave. It's all about the force gases exert on surfaces due to particle collisions. Knowing pressure 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 pascals to atmospheres, each unit tells us something about gas behavior. Devices like manometers and barometers help us quantify pressure, making it easier to predict and control gas-related phenomena.

Gas Pressure

Pressure in gas behavior

• 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 ($1 \text{ Pa} = 1 \frac{\text{N}}{\text{m}^2}$)
  • Atmospheres (atm): pressure exerted by Earth's atmosphere at sea level ($1 \text{ atm} = 101,325 \text{ Pa}$)
  • Torr (mmHg): pressure required to support a column of mercury 1 mm high ($1 \text{ torr} = 133.322 \text{ Pa}$)
  • Pounds per square inch (psi): pressure exerted by a force of one pound on an area of one square inch ($1 \text{ psi} = 6,894.76 \text{ Pa}$)
• 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: $2.5 \text{ atm} \times 101,325 \frac{\text{Pa}}{\text{atm}} = 253,312.5 \text{ Pa}$
• Standard temperature and pressure (STP) 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 manometer, the pressure difference ($\Delta P$) is related to the height difference ($h$) of the liquid by: $\Delta P = \rho gh$
  • $\rho$ is the density of the liquid
  • $g$ 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 $\Delta P = \rho gh$
  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 $\Delta P$ to the reference pressure
     • If the gas is connected to the high-pressure side, subtract $\Delta P$ 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: $h = 25 \text{ mm} = 0.025 \text{ m}$
  2. Pressure difference: $\Delta P = \rho gh = 13,600 \frac{\text{kg}}{\text{m}^3} \times 9.81 \frac{\text{m}}{\text{s}^2} \times 0.025 \text{ m} = 3,332.4 \text{ Pa}$
  3. Absolute pressure: $P_{\text{abs}} = P_{\text{atm}} + \Delta P = 101,325 \text{ Pa} + 3,332.4 \text{ Pa} = 104,657.4 \text{ Pa}$

Gas mixtures and partial pressures

• Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its components
• Partial pressure 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 absolute zero is the lowest possible temperature (-273.15°C or 0 K) where all molecular motion theoretically ceases