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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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# Chemistry: Gay-Lussac's Law (Gas Laws) with 2 examples | Homework Tutor

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林宜悉 posted on 2020/03/06
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