9.1 Gas Pressure

Gas pressure is the force that gas particles exert on surfaces through constant collisions. Understanding pressure is essential for explaining everyday phenomena like tire inflation and weather changes, and it's the foundation for the gas laws you'll encounter throughout this unit.

Gas Pressure

Pressure in gas behavior

Pressure is the force exerted per unit area on a surface. Gas particles (molecules or atoms) are in constant random motion, and when they slam into the walls of their container, those collisions create pressure.

• More frequent collisions or more forceful collisions (from faster-moving particles with greater kinetic energy) produce higher pressure.
• Changes in pressure directly affect other gas properties: volume (compression or expansion), temperature, and even how well gases dissolve in liquids.
• Real-world examples include tire inflation, scuba diving (where water pressure increases with depth), and weather forecasting (where pressure differences drive wind patterns).

Pressure unit conversions

Several units are used to measure pressure, and you need to be comfortable converting between them:

• Pascals (Pa): The SI unit. One pascal equals one newton per square meter: $1 \text{ Pa} = 1 \frac{\text{N}}{\text{m}^2}$
• Atmospheres (atm): The average pressure exerted by Earth's atmosphere at sea level. $1 \text{ atm} = 101{,}325 \text{ Pa}$
• Torr (mmHg): The pressure needed to support a 1 mm column of mercury. $1 \text{ atm} = 760 \text{ torr}$, and $1 \text{ torr} = 133.322 \text{ Pa}$
• Pounds per square inch (psi): Common in engineering contexts. $1 \text{ atm} = 14.696 \text{ psi}$

To convert between units, multiply by the appropriate conversion factor. For example, converting 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 defined as 0°C (273.15 K) and 1 atm. You'll use STP frequently when comparing gas behavior under consistent conditions.

Pressure measurement devices

Barometers measure atmospheric pressure. A traditional mercury barometer is a sealed glass tube, closed at the top (creating a vacuum), inverted in a dish of mercury. The atmosphere pushes down on the mercury in the dish, supporting a column in the tube. At sea level, that column stands about 760 mm high, which is why 1 atm = 760 mmHg.

Manometers measure the pressure of a gas sample, often by comparing it to atmospheric pressure. They use a U-shaped tube filled with liquid (usually mercury). The difference in mercury height between the two arms tells you how the gas pressure compares to the reference pressure.

Digital pressure sensors convert pressure into an electrical signal using technologies like piezoelectric or capacitive elements. These provide continuous, precise readings for industrial and laboratory use.

Calculations with manometer data

The pressure difference in a manometer relates to the height difference of the liquid through:

$\Delta P = \rho g h$

• $\rho$ = density of the manometer liquid
• $g$ = acceleration due to gravity ($9.81 \text{ m/s}^2$)
• $h$ = height difference between the two liquid levels

To find the absolute pressure of a gas using a manometer:

1. Measure the height difference ($h$) between the liquid levels in the two arms.
2. Calculate the pressure difference: $\Delta P = \rho g h$
3. Determine whether to add or subtract:
   • If the gas pushes the mercury down on its side (gas pressure > atmospheric), then $P_{\text{gas}} = P_{\text{atm}} + \Delta P$
   • If the gas lets the mercury rise on its side (gas pressure < atmospheric), then $P_{\text{gas}} = P_{\text{atm}} - \Delta P$

Worked example: A mercury manometer ($\rho = 13{,}600 \text{ kg/m}^3$) shows a 25 mm height difference, and the gas pressure is greater than atmospheric pressure (1 atm).

1. Convert height: $h = 25 \text{ mm} = 0.025 \text{ m}$
2. Pressure difference: $\Delta P = 13{,}600 \times 9.81 \times 0.025 = 3{,}332.4 \text{ Pa}$
3. Absolute pressure: $P_{\text{gas}} = 101{,}325 + 3{,}332.4 = 104{,}657.4 \text{ Pa}$

Gas mixtures and partial pressures

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture equals the sum of the partial pressures of each individual gas:

$P_{\text{total}} = P_1 + P_2 + P_3 + \dots$

A partial pressure is the pressure a single gas in a mixture would exert if it occupied the container alone. For example, in a container holding oxygen and nitrogen, each gas contributes its own partial pressure, and together they add up to the total pressure you'd measure.

Vapor pressure is the pressure exerted by a vapor when it's in equilibrium with its liquid (or solid) phase at a given temperature. This matters when you collect a gas over water, because the water vapor contributes its own partial pressure to the total. To find just the gas pressure, you subtract the water's vapor pressure from the total:

$P_{\text{gas}} = P_{\text{total}} - P_{\text{water vapor}}$