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  • For a gas, pressure and volume are inversely proportional.

  • If you keep everything else constant, then as the pressure on a gas goes up, its volume

  • goes down.

  • As the volume a gas occupies goes up, its pressure goes down.

  • If you exert pressure on a gas, you can compress it - make it take up less space.

  • Imagine a hard container that measures how many times gas particles bang against the

  • sides.

  • The more the gas particles bang against the sides, the higher the gas pressure on the

  • container.

  • If you make the container smaller, you compress the gas.

  • The particles of gas will run into the sides more often per second, so that means higher

  • pressure.

  • If you keep the amount of gas particles constant, but you make the size of the container bigger,

  • there will be fewer collisions per second with the sides.

  • That registers as lower pressure.

  • Robert Boyle stated the inverse relationship between pressure and volume as a Gas Law.

  • Boyle’s Law says that for a given amount of gas, at fixed temperature, pressure and

  • volume are inversely proportional.

  • P ∝ 1/V. You can write this mathematically as P = k/V

  • where P = pressure

  • V = volume, and k = is a proportionality constant.

  • We can rearrange this equation so it reads PV = k, or the product of pressure and volume

  • is a constant, k.

  • [4] Very often Boyle’s law is used to compare two situations, a “beforeand anafter.”

  • In that case, you can say P1V1 = k, and P2V2 = k, so you can write Boyle’s law as

  • P1V1 = P2V2.

  • Let’s see an example.

  • Example 1: A tire with a volume of 11.41 L reads 44 psi (pounds per square inch) on the

  • tire gauge.

  • What is the new tire pressure if you compress the tire and its new volume is 10.6 L?

  • Write out Boyle’s Law, and substitute in what we know.

  • This is one of thosebefore and aftersituations, so we write P1V1 = P2V2

  • (44 psi)(11.41L) = (P2)(10.6L) solve for P2 (divide both sides by 10.6L)

  • (44 psi)(11.41L)/10.6L = P2 P2 = 47.36 psi (There are 2 significant figures

  • in the measurement 44 psi, so we round our answer to 2 sig figs) = 47 psi

  • Example 2: Here’s another example: A syringe has a volume of 10.0 ccs (or 10 cubic centimeters).

  • The pressure is 1.0 atm.

  • If you plug the end so no gas can escape, and push the plunger down, what must the final

  • volume be to change the pressure to 3.5 atm?

  • P1V1 = P2V2 (1.0 atm)(10.0 cm3) = 3.5 atm (V2)

  • solve for V2 (divide both sides by 3.5 atm) (1.0 atm)(10.0 cm3) / 3.5 atm = V2

  • V2 = 2.9 cm3 (2.9 ccs)

  • Boyle’s law relates pressure and volume, but there are other gas laws which relate

  • the other essential variables associated with a gas.

  • Charles’s Law is the relationship between temperature and volume.

  • Gay-Lussac’s Law is the relationship between pressure and temperature.

  • And the combined gas law puts all 3 together: Temperature, Pressure, and Volume.

  • Notice that to use any of these laws, the amount of gas must be constant.

  • Avogadro’s Law describes the relationship between volume and the amount of a gas (usually

  • in terms of n, the number of moles).

  • When we combine all 4 laws, we get the Ideal Gas Law.

  • To decide which of these gas laws to use when solving a problem, make a list of what information

  • you have, and what information you need.

  • If a variable doesn’t come up, or is held constant in the problem, you don’t need

  • it in your equation.

For a gas, pressure and volume are inversely proportional.

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B1 中級

化学.ボイルの法則(気体の法則)2例付き|宿題の家庭教師 (Chemistry: Boyle's Law (Gas Laws) with 2 examples | Homework Tutor)

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    林宜悉 に公開 2021 年 01 月 14 日
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