The invisible push of the air
When you drink through a straw, the air outside actually pushes the drink up into your mouth. In 1654, the mayor of Magdeburg fit two copper hemispheres together and pumped the air out from inside; two teams of eight horses could not pull them apart. High in the mountains, water boils below 100 °C, and food takes longer to cook. All of these come from the pressure of a gas.
Gas pressure
Pressure压强 is force per unit area:
Here F is the force and A is the area it pushes on. A force is a push or a pull, measured in newtons (N); holding up a small apple takes a force of about 1 N.
The SI unit of pressure is the pascal帕斯卡 (Pa); 1 Pa = 1 N/m². A pascal is small, so kilopascals (kPa) are common.
Why does a gas push at all? As in 1.2.1, gas particles move constantly and randomly. Each time one hits the wall of its container, it pushes on the wall a tiny bit, and billions of collisions add up to a steady force. The more often the particles hit, and the harder they hit, the higher the pressure. Because the particles move in every direction, a gas pushes equally in every direction.
Atmospheric pressure and the barometer
Gravity pulls the air down onto Earth’s surface, producing atmospheric pressure大气压. In 1643, Evangelista Torricelli filled a glass tube with mercury and turned it upside down in a dish of mercury. The mercury fell until the column was about 760 mm tall, leaving a vacuum above it; the air pushing on the dish holds up that column. This was the first barometer气压计.
- At sea level and 0 °C, the air holds up about 760 mm of mercury. One standard atmosphere is defined as 1 atm = 760 mmHg = 101.325 kPa.
- Mercury is used because it is so dense (13.6 g/cm³). Air pressure could hold up a column of water about 10.3 m tall.
- The higher you go, the less air is above you, and the lower the pressure.
Pressure units
| Unit | Relation to 1 atm | Where you see it |
|---|---|---|
| pascal (Pa), kilopascal (kPa) | 1 atm = 101,325 Pa = 101.325 kPa | SI unit; Chinese textbooks mostly use kPa |
| millimeters of mercury (mmHg) | 1 atm = 760 mmHg | barometers, blood pressure |
| torr | 1 atm = 760 torr; 1 torr ≈ 1 mmHg | US chemistry, labs |
| bar | 1 bar = 100 kPa, slightly less than 1 atm | weather, industry |
| pounds per square inch (psi) | 1 atm = 14.7 psi | tire pressure in the US |
The AP Chemistry equation sheet gives 1 atm = 760 mm Hg = 760 torr. Chinese textbooks, in both chemistry and physics, work mostly in kPa and write standard conditions as 0 °C and 101 kPa. The hectopascals (hPa) on weather maps are 100 Pa each, so 1013 hPa is about 1 atm.
Manometers
A U-shaped tube used to measure the pressure of a gas in a container is a manometer压强计. In an open-end manometer, one arm connects to the gas and the other is open to the air:
- If the liquid is lower on the gas side, the gas pushes harder than the air: P(gas) = P(atm) + h.
- If the liquid is higher on the gas side, the gas pushes less than the air: P(gas) = P(atm) − h.
Here h is the difference in liquid heights. With mercury, h in millimeters is the pressure difference in mmHg.
P(gas) = P(atm) + h
The gas pushes the mercury down further than the air does, so the gas pressure is higher than air pressure.
P(gas) = P(atm) − h
The air pushes the mercury down further than the gas does, so the gas pressure is lower than air pressure.
h is the difference between the two mercury levels; measured in millimeters, it’s the pressure difference in mmHg. To decide whether to add or subtract, ask which side pushes the mercury lower: that side has the higher pressure.
Drag the altitude to see how air pressure changes, or type in a pressure to convert it into every unit:
🔧 Math tool card · Units & ConversionsSkip it if you already know this
Pressure conversions use conversion factors too. Write the relationship between the two units, such as 1 atm = 760 mmHg, as a fraction, with the unit you want to cancel on the opposite side:
Two steps at once. To go from mmHg to kPa, pass through atm: 745 mmHg × (1 atm / 760 mmHg) × (101.325 kPa / 1 atm) = 99.3 kPa. Both 1 atm = 760 mmHg and 1 atm = 101.325 kPa are exact definitions, so they don’t limit significant figures.
How many kPa is 1.50 atm?
1.50 atm × (101.325 kPa / 1 atm) = 152 kPa. 1140 is the value in mmHg.
Example 1: the pressure in a weather report
A weather report gives today’s air pressure as 1015 hPa. What is that in kPa, in atm, and in mmHg?
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The plan. The conversions are 1 hPa = 100 Pa and 1 atm = 101.325 kPa = 760 mmHg. Multiply by a conversion factor whose top and bottom are equal, so the unit you don’t want cancels.
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To kPa.
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To atm. kPa is on the bottom, so it cancels and atm is left:
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To mmHg. Convert straight from kPa instead of from the rounded 1.002:
Using 1.002 × 760 gives 761.5, which is off in the last digit.
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Check. Slightly above 1 atm (760 mmHg), so today’s pressure is a little higher than standard. Reasonable. 1015 has four significant figures, so all three answers keep four.
Example 2: reading an open-end manometer
An open-end mercury manometer is connected to a flask of gas. The mercury on the gas side is 25 mm lower than on the open side, and the air pressure is 755 mmHg. What is the gas pressure in mmHg and in kPa?
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Which is bigger? The gas has pushed its side of the mercury down, so the gas pressure is greater than the air pressure: add.
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Find the pressure. The 25-mm difference in mercury levels is a pressure difference of 25 mmHg:
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To kPa. 760 mmHg = 101.325 kPa:
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A common mistake. Subtracting without checking which side is higher, to get 755 − 25 = 730 mmHg. Subtract only when the mercury on the open side is lower, meaning the gas pressure is less than the air pressure.
- 101 kPa
1 atm = 101.325 kPa, so 101 kPa ≈ 1.0 atm.
- 380 mmHg
380 ÷ 760 = 0.50 atm.
- 152 kPa
152 ÷ 101.325 ≈ 1.5 atm.
- 1520 torr
1520 ÷ 760 = 2.0 atm.
- 25.3 kPa
25.3 ÷ 101.325 ≈ 0.25 atm.
- 14.7 psi
1 atm = 14.7 psi.
- 1.01 bar
1.01 bar = 101 kPa ≈ 1.0 atm. A bar is slightly smaller than an atmosphere.
- 190 mmHg
190 ÷ 760 = 0.25 atm.
- 50.7 kPa
50.7 ÷ 101.325 ≈ 0.50 atm.
Common mistakes
Mistake 1: “Air pressure only pushes down.” Gas particles move in every direction, so air pressure acts in every direction. The Magdeburg hemispheres were squeezed together from the sides, and a full glass of water covered with a card can be turned upside down: the air pushing up holds the card in place.
Mistake 2: “1 atm is 100 kPa.” 1 atm = 101.325 kPa; it is 1 bar that equals 100 kPa. They differ by only about 1%, but don’t mix them up in careful work.
Mistake 3: “A wider barometer tube gives a shorter mercury column.” The height depends only on the air pressure, not on how wide or tilted the tube is. A wider column holds more mercury, but it also has more area to push on, so the pressure is the same.
Quick check
Which statement about pressure units is correct?
1 atm = 760 mmHg = 760 torr = 101.325 kPa; 1 bar = 100 kPa, about 750 torr.
If you built Torricelli’s barometer with water instead of mercury, about how tall would the tube need to be?
Water is about 1/13.6 as dense as mercury, so the air can hold up about 0.76 m × 13.6 ≈ 10.3 m of water.
Summary
- Pressure is force per area, P = F/A, measured in pascals. Gas pressure comes from countless particles hitting the walls, and it acts in every direction.
- Torricelli measured air pressure with a column of mercury: 1 atm = 760 mmHg = 760 torr = 101.325 kPa, and 1 bar = 100 kPa. Air pressure falls as altitude rises.
- In an open-end manometer, P(gas) = P(atm) + h when the gas side is lower, and P(atm) − h when it is higher.
On to AP (for later)
AP Chemistry Unit 3 gas problems use atm, torr, mmHg, and kPa, and the equation sheet gives 1 atm = 760 mm Hg = 760 torr. AP free-response questions often ask you to explain pressure at the particle level: how often and how hard the particles hit the walls. Lesson 2.8.7 builds that picture fully with kinetic molecular theory.