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  • For a gas, temperature and pressure are directly proportional. When you keep everything else

  • constant, as the temperature of a gas goes up, its pressure goes up. As the temperature

  • of a gas goes down, its pressure goes down.

  • If you heat up a gas, the gas particles move faster. If the gas is in a solid container,

  • with fixed volume, this means that the faster the gas particles move, the more times per

  • second they collide with the sides of the container. That registers as increased pressure.

  • The converse is also true - if you cool down this container of gas, that means the gas

  • particles are moving more slowly. So there will be fewer collisions with the sides of

  • the container per second, which means lower pressure.

  • Joseph Louis Gay-Lussac shares credit with Guillaume Amontons for establishing a Gas

  • Law describing the relationship between temperature and pressure. Gay-Lussac’s Law says that

  • when the volume and amount of gas is constant, pressure and temperature are directly proportional.

  • P ∝ T You can write this mathematically as P = kT

  • where P = pressure, T = temperature in Kelvin, and

  • k = is a proportionality constant. We can rearrange this equation so it reads

  • P/T = k, or the ratio of pressure to temperature is a constant, k.

  • Very often, Gay-Lussac’s law is used to compare two situations, a “beforeand

  • anafter.” In that case, you can say P1 / T1= k, and P2 / T2 = k, so you can write

  • Gay-Lussac’s law as P1 / T1= P2 / T2. Let’s see an example.

  • Example 1: A canister of nitrogen gas has a pressure of 2000 psi (pounds per square

  • inch) at 20 C°. What will the pressure be if you increase the temperature to 25 C° ?

  • Let’s write down Gay-Lussac’s Law:

  • P1/ T1= P2 / T2, because we have a “beforeandafter.”

  • Convert temperatures to Kelvin: Kelvin = C°+ 273.15.

  • T1 = 293.15 K, T2 = 298.15 K Substitute in what we know:

  • 2000 psi / 293.15K = P2/ 298.15 K

  • Solve for P2 (multiply both sides by 298.15 K)

  • P2 = (2000 psi )(298.15 K)/293.15 K

  • P2 = 2034 psi

  • Example 2. Here’s another example: At 10 C°, a gas exerts 0.95 atm of pressure. At

  • what temperature (in Celsius) will it exert a pressure of 0.75 atm?

  • P1 /T1= P2/T2. Convert temperatures to Kelvin:

  • Kelvin = C°+ 273.15. T1 = 283.15 K

  • 0.95 atm/ 283.15 K = 0.75 atm/T2 Solve for T2

  • T2 = (283.15 K)(0.75 atm)/0.95 atm T2 = 223.54 K

  • Convert to Celsius: 223.54K - 273.15 = - 49.6 C°

  • Gay-Lussac’s Law relates temperature and pressure for a gas, 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. Boyle’s Law is the relationship between

  • pressure and volume. 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, temperature and pressure are directly proportional. When you keep everything else

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A2 初級

化學--------Gay-Lussac定律 Gay-Lussac定律(氣體定律)與2個例子|家庭作業輔導員 (Chemistry: Gay-Lussac's Law (Gas Laws) with 2 examples | Homework Tutor)

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    林宜悉 發佈於 2021 年 01 月 14 日
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