14.7aFree
Your guide: Miss SanaCounts atoms the way you count rupees: carefully.
Kinetic theory says a gas presses on its container because its molecules keep hitting the walls. More hits per second means more pressure.
Three laws follow. Each keeps two things fixed and links the other two.
Halve the volume and twice as many molecules hit each patch of wall per second, so the pressure doubles.
Law: the volume of a given mass of gas is inversely proportional to its pressure at constant temperature. V ∝ 1/P.
Activity 14.1: Boyle trapped air in a J-tube at 760 mm Hg. Adding about 760 mm more mercury raised it to about 2 atm, and the volume halved.
Heating speeds molecules up, so they hit the walls harder and more often. To keep the pressure fixed, the piston must rise and the volume grows.
Law: the volume of a given mass of gas varies directly with its kelvin temperature at constant pressure. V ∝ T.
Add more gas to a container and the pressure rises. To keep it the same, the volume must grow.
Law: equal volumes of different gases contain equal numbers of molecules at the same temperature and pressure. V ∝ n.
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Kinetic theory says a gas presses on its container because its molecules keep hitting the walls. More hits per second means more pressure.
Three laws follow. Each keeps two things fixed and links the other two.
Halve the volume and twice as many molecules hit each patch of wall per second, so the pressure doubles.
Law: the volume of a given mass of gas is inversely proportional to its pressure at constant temperature. V ∝ 1/P.
Activity 14.1: Boyle trapped air in a J-tube at 760 mm Hg. Adding about 760 mm more mercury raised it to about 2 atm, and the volume halved.
Heating speeds molecules up, so they hit the walls harder and more often. To keep the pressure fixed, the piston must rise and the volume grows.
Law: the volume of a given mass of gas varies directly with its kelvin temperature at constant pressure. V ∝ T.
Add more gas to a container and the pressure rises. To keep it the same, the volume must grow.
Law: equal volumes of different gases contain equal numbers of molecules at the same temperature and pressure. V ∝ n.
Boyle fixes temperature, Charles fixes pressure, Avogadro fixes both. In every case, the volume changes so that the hits on the walls match the conditions.
Q1. In Activity 14.1 the trapped air has volume V1 at 760 mm Hg. Mercury is added until the pressure is 2 × 760 mm Hg. What is the new volume V2?
V2 = V1 ÷ 2. Boyle found the volume was one half of the initial volume.
Q2. A gas is cooled while its pressure and mass stay constant. How does its volume change? (Quick Check 14.4)
The volume decreases, in proportion to the kelvin temperature (Charles' law).
✗ Squeezing a gas harder makes its volume bigger.
✓ Boyle: more pressure, less volume (inverse).
✗ In Charles' law you can use °C directly.
✓ Your book: the temperature must be on the absolute (kelvin) scale.
✗ Boyle's law works even if the temperature changes.
✓ Each law holds only with its two quantities fixed: Boyle needs constant temperature and mass.
1. According to kinetic theory, the pressure of a gas is caused by:
(c) p. 9: pressure is caused by the collisions of molecules with the walls of the container.
2. At constant temperature, the pressure on a fixed mass of gas is doubled. Its volume:
(a) Boyle's law and Activity 14.1 (pp. 9–10): doubling the pressure reduced the volume by one half.
3. In Charles' law, temperature must be measured in:
(d) p. 10: the temperature must be measured on the absolute or kelvin scale.
4. At the same temperature and pressure, equal volumes of different gases contain:
(b) Avogadro's law (p. 11).
5. Which law keeps both temperature and pressure constant?
(d) p. 11: V ∝ n at constant temperature and pressure.
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