Chemistry: Atoms First 2e · Gases

Gas Pressure

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On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

A gas exerts because its molecules are in constant, rapid motion, colliding with the walls of any container and bouncing off with a change in momentum. Each collision is tiny, but there are astronomically many of them — at room temperature and 1 atm, roughly 10²³ collisions per second per square centimeter of wall. The summed force of all those impacts, divided by the wall area, is what we call gas pressure:

$P = F A$

where P is pressure, F is the force exerted perpendicular to a surface, and A is the area of that surface. This topic develops the definition of pressure, the units used to report it (and how to convert among them), and the instruments — the and the — used to measure atmospheric and confined-gas pressures. These ideas are the foundation for every gas law that follows in this chapter.

Why this matters

Every gas law depends on pressure: Boyle's law, the ideal gas law, and gas stoichiometry all use P as a key variable, so unit conversions are unavoidable.
Weather and altitude: atmospheric pressure changes with weather systems and elevation; it is the reason your ears "pop" on a flight and why water boils at a lower temperature on a mountain.
Medical and breathing applications: ventilators, oxygen tanks, and blood pressure readings all report pressures in everyday units (, , atm) that must be converted correctly.
Industrial and lab safety: pressure vessels, gas cylinders, and vacuum systems are rated in specific pressure units; misreading a unit can be a safety hazard.
Exams: pressure conversions and manometer/barometer readings are classic calculation items, and the numbers carry units that must be tracked through every formula.

The college version

Core Concepts

Pressure is force spread over an area

Pressure is not the same as force. A heavy person standing on one heel exerts far more pressure on the floor than the same person standing flat-footed, because the force is concentrated on a smaller area. In SI units, force is measured in newtons (N) and area in square meters, so the SI unit of pressure is the pascal:

$1 Pa = 1 N m -2$

One pascal is a very small pressure — a sheet of paper resting on a table exerts roughly 1 Pa. Chemists therefore commonly use the , the , millimeters of mercury (mmHg), the , and pounds per square inch (psi).

Standard conversion relationships

By definition and measurement, one standard atmosphere equals:

$1 atm = 760 torr = 760 mmHg = 101.325 kPa = 1.01325 bar \approx 14.7 psi$

Note that torr and mmHg are numerically equal (both defined so that 1 atm = 760 of each), though they arose from different conventions: the torr is named after Torricelli, while mmHg literally describes the height of a mercury column. These equalities are exact conversion factors, so dimensional analysis converts any pressure into any other unit by multiplying by the appropriate ratio.

The barometer: measuring atmospheric pressure

A barometer measures the pressure of the atmosphere. A classic mercury barometer is a glass tube closed at one end, filled with mercury, and inverted into a dish of mercury. The mercury column falls until the weight of the column balances the atmospheric pressure pushing on the dish. At sea level on a standard day, the column stands about 760 mm tall — which is exactly why "760 mmHg" equals 1 atm.

The relationship is:

$P = ρ g h$

where ρ is the density of the liquid, g is gravitational acceleration, and h is the column height. For a given liquid, height alone reports pressure, which is why mmHg works as a pressure unit.

The manometer: measuring confined gas pressure

A manometer measures the pressure of a gas in a closed container. The simplest version is a U-shaped tube partially filled with mercury, connected to the gas on one side and open to the atmosphere on the other.

If the mercury level is equal on both sides, the gas pressure equals atmospheric pressure.
If the gas side is lower, the gas pressure is greater than atmospheric: P_gas = P_atm + h.
If the gas side is higher, the gas pressure is less than atmospheric: P_gas = P_atm - h.

Here h is the difference in mercury column heights, expressed in the same pressure units as P_atm.

Common Confusions

Do Not Confuse	With	Difference
Pressure	Force	Pressure is force divided by area; the same force on a smaller area gives higher pressure
Torr	mmHg	Numerically equal (1 torr = 1 mmHg), but defined differently — torr from Torricelli's name, mmHg from column height
atm	bar	1 atm = 1.01325 bar; they are close but not identical
Barometer	Manometer	Barometer measures the atmosphere itself; manometer compares a confined gas with the atmosphere
Gas pressure greater than atmospheric	Gas pressure less than atmospheric	Read the mercury heights: gas side lower = gas pressure higher; gas side higher = gas pressure lower
kPa	Pa	1 kPa = 1000 Pa; 1 atm = 101.325 kPa, not 101.325 Pa

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a crowd of people pushing against a fence from the inside. Each person is a gas molecule, and the fence is the container wall. The harder and more often they push, the more pressure they create. A barometer is like a mercury straw that the air holds up — the air can hold up a 760 mm column when the weather is normal. A manometer is a U-shaped tube that compares the push of your gas sample with the push of the air outside.

Worked example

Example 1: Converting torr to atm and kPa

A weather report states the atmospheric pressure is 742 torr. Express this pressure in atmospheres and in kilopascals.

Step 1 — Write the conversion factor from the bridge:

$1 atm = 760 torr$

Step 2 — Multiply so that torr cancels:

$P = 742 torr \times 1 atm 760 torr = 0.976 atm$

Step 3 — Convert to kPa using 1 atm = 101.325 kPa:

$P = 0.976 atm \times 101.325 kPa 1 atm = 98.9 kPa$

Dimensional check: torr cancels in step 2 and atm cancels in step 3, leaving atm then kPa. The answer makes sense: 742 torr is slightly less than 760 torr, so slightly less than 1 atm — and 98.9 kPa is indeed just under 101.325 kPa.

Example 2: Reading an open-end manometer

An open-end mercury manometer is attached to a flask of nitrogen. The mercury is 38 mmHg higher on the side open to the atmosphere than on the gas side, and the barometric pressure is 745 torr. What is the pressure of the nitrogen in the flask, in torr and in atm?

Step 1 — Decide which case applies. The gas-side mercury is lower than the open-side mercury, so the gas is pressing harder than the atmosphere:

$P gas = P atm + h$

Step 2 — Substitute and add (torr and mmHg are numerically equal):

$P gas = 745 torr + 38 mmHg = 783 torr$

Step 3 — Convert to atm:

$P gas = 783 torr \times 1 atm 760 torr = 1.03 atm$

Sanity check: 783 torr > 760 torr, so the answer must be greater than 1 atm — consistent with 1.03 atm.

Example 3: Converting psi to atm and kPa

A scuba tank gauge reads 3000 psi when full. Express this in atm and kPa.

Step 1 — Use the approximate bridge 1 atm ≈ 14.7 psi:

$P = 3000 psi \times 1 atm 14.7 psi = 204 atm$

Step 2 — Convert to kPa:

$P = 204 atm \times 101.325 kPa 1 atm = 2.07 \times 104 kPa (20,700 kPa)$

Note: the 14.7 psi value is approximate, so the final answers carry that limitation; report to the precision the conversion factor justifies.

Key takeaways

Gas pressure comes from molecular collisions with container walls; P = F/A.
SI unit: pascal (1 Pa = 1 N m^-2); common chemistry units: atm, torr, mmHg, bar, psi.
Memorize the bridge: 1 atm = 760 torr = 760 mmHg = 101.325 kPa = 1.01325 bar ≈ 14.7 psi.
Torr and mmHg are numerically identical, but they are defined differently.
A barometer measures atmospheric pressure; a manometer measures a confined gas against the atmosphere.
Manometer rule of thumb: gas side lower ⇒ P_gas = P_atm + h; gas side higher ⇒ P_gas = P_atm - h.
Always convert pressure to the units required by the gas-law constant you plan to use (e.g., atm for R = 0.08206 L atm mol^-1K^-1).

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

In words and in an equation, what causes gas pressure on the walls of a container?
Show answer
Gas molecules collide with the walls, transferring momentum; the summed force per unit area is P = F/A.
Write the full bridge of equalities for 1 atm (torr, mmHg, kPa, bar, psi).
Show answer
1 atm = 760 torr = 760 mmHg = 101.325 kPa = 1.01325 bar ≈ 14.7 psi.
A barometer reads 735 mmHg. What is this pressure in atm and in kPa?
Show answer
735 mmHg × (1 atm/760 mmHg) = 0.967 atm; 0.967 × 101.325 = 98.0 kPa.
An open-end manometer shows the mercury 25 mmHg higher on the gas side than the open side, with atmospheric pressure 760 torr. Is the gas pressure greater or less than atmospheric, and what is it in torr?
Show answer
The gas side is higher, so the gas pressure is less than atmospheric: P_gas = 760 - 25 = 735 torr.
Why is the pascal inconvenient for reporting everyday gas pressures, and which units do chemists actually use?
Show answer
One pascal is tiny (about the pressure of a sheet of paper); atmospheric pressure is ~101,325 Pa, an awkward number, so chemists use atm, torr, mmHg, bar, and psi.
A tire gauge reads 32 psi. Convert this to atm and to kPa, showing your conversion factors.
Show answer
32 psi × (1 atm/14.7 psi) = 2.2 atm; 2.2 × 101.325 ≈ 220 kPa.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Pressure: Force exerted per unit area, P = F/A
Pascal (Pa): The SI unit of pressure: 1 N of force per 1 m² of area
Atmosphere (atm): The average pressure of Earth's atmosphere at sea level
Torr: A pressure unit equal to 1/760 of an atmosphere
mmHg: Pressure equal to the force of a 1 mm column of mercury
Bar: A pressure unit equal to 100,000 Pa
psi: Pounds of force per square inch
Barometer: Instrument that measures atmospheric pressure using a liquid column
Manometer: U-shaped tube comparing a gas's pressure with atmospheric pressure

Sources & references

openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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