Gas pressure and its units

Pressure as force per area

Gas pressure is force divided by area: the total push of particle collisions spread over the surface they strike. Double the collisions per second and the pressure doubles; spread the same collisions over twice the wall area and the pressure halves.

The SI unit is the pascal (Pa), one newton per square meter. A pascal is tiny: atmospheric pressure is over a hundred thousand of them. That is why scientists usually work in kilopascals (kPa) and define the standard atmosphere as

$$1\ \text{atm} = 101{,}325\ \text{Pa} = 101.325\ \text{kPa}$$

A useful sense of scale: 1 atm presses about 10 newtons onto every square centimeter, roughly the weight of a liter of water balanced on a postage stamp. You are not crushed because air and fluid inside your body push back with equal pressure.

A worked example: a textbook problem gives a tire pressure of 35.0 psi. Convert to atmospheres using $14.7\ \text{psi} = 1\ \text{atm}$: $35.0 \div 14.7 \approx 2.38$ atm. That reading is gauge pressure, measured above the atmosphere, so the absolute pressure inside is about 3.38 atm, a reminder to check whether a problem wants gauge or absolute values.

The barometer and mercury units

In 1643 Torricelli filled a glass tube with mercury, inverted it into a dish, and watched the column fall to about 760 mm. Air pressure pushing on the dish's surface supported the column, and its height became the first quantitative measure of the atmosphere.

That experiment is the origin of millimeters of mercury (mmHg) and the torr, named for Torricelli. By definition:

$$1\ \text{atm} = 760\ \text{mmHg} = 760\ \text{torr}$$

Mercury was chosen because it is dense: water would need a column over 10 meters tall to balance the atmosphere. Modern barometers use electronic sensors, but weather maps in the United States still report inches of mercury, and blood pressure cuffs still read in mmHg.

A worked example: a storm report lists 29.2 inches of mercury. Convert: $29.2 \times 25.4 = 741.7$ mmHg, then $741.7 \div 760 \approx 0.976$ atm. Falling pressure below 1 atm signals an approaching storm, which is why sailors watched the barometer.

Converting between pressure units

Chemistry problems mix units freely, so one conversion chain handles them all:

$$1\ \text{atm} = 760\ \text{mmHg} = 760\ \text{torr} = 101.325\ \text{kPa} = 1.01325\ \text{bar} = 14.7\ \text{psi}$$

The strategy is always the same: multiply by a fraction equal to one, arranged so the unwanted unit cancels. Write the starting unit, then chain conversion factors until only the target unit survives.

A worked example with two hops: convert 2.50 atm to psi. First hop to kPa: $2.50 \times 101.325 = 253.3$ kPa. The psi equivalent of 1 atm is 14.7, so skip kPa entirely and go direct: $2.50 \times 14.7 = 36.8$ psi. Now reverse it to check: $36.8 \div 14.7 \approx 2.50$ atm. Round-trip checks catch upside-down conversion factors, the most common unit error in gas-law work.

Memorize the atm row and derive the rest. Every other conversion is just the atm chain with one end swapped.

Matching units to the gas constant

The unit you choose dictates the gas constant you must use in $PV = nRT$. The two pairings to memorize:

• Pressure in atm with volume in liters goes with $R = 0.08206\ \text{L·atm/(mol·K)}$.
• Pressure in kPa with volume in liters goes with $R = 8.314\ \text{L·kPa/(mol·K)}$, and pressure in Pa with volume in cubic meters goes with $R = 8.314\ \text{J/(mol·K)}$.

Mixing an atm pressure with the 8.314 constant is the single most common ideal-gas-law error, and it silently shifts answers by a factor of about 100.

A worked example: 0.500 mol of gas at 2.00 atm and 300 K occupies $V = nRT/P = (0.500 \times 0.08206 \times 300) \div 2.00 = 6.15$ L. Redo it in kilopascals: $2.00\ \text{atm} = 202.65$ kPa, so $V = (0.500 \times 8.314 \times 300) \div 202.65 = 6.15$ L. Same answer, as it must be; the unit system is a choice, not a property of the gas.

Common mistakes

Real-world applications

• Reading tire gauges, weather reports, and scuba tank dials

• Calibrating laboratory manometers and barometers

• Converting between engineering and scientific pressure specs

• Interpreting blood pressure readings in mmHg