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The Laws of Gases Help (page 2)

By — McGraw-Hill Professional
Updated on Aug 29, 2011

Examples

If we have a balloon of 1.0 liter that is flexible and can expand with increased temperature (from 20°C to 45°C), find the volume of the balloon after it is heated. (Hint: add 273 to the Celsius temperatures to get everything into Kelvin.)

T 1 = 20 + 273 = 293 K

T 2 = 45 + 273 = 318 K

V 1 = 1.0 liter, V 2 = X

1.0 liters/293 K = x liters/318 K

x = 1.0 liter × 318 K/293 K

x = 1.09 liters = V 2

Gay-lussac’s Law

Around the same time that Charles was ballooning and experimenting in France, another French scientist, Joseph Gay-Lussac, was studying the connection between temperature and gas pressure. His research added the third of the ideal gas laws. Gay-Lussac discovered that as temperature increases and kinetic energy increases, pressure increases too.

In Gay-Lussac’s law , when volume is held constant, the pressure of a gas is directly proportional to the Kelvin temperature; P α T .

It’s a case of atoms dancing wildly in a constant volume again. As the temperature increases, the pressure increases and the atoms collide with the container’s walls faster and harder. This increases the kinetic energy. The following equation describes what happens:

P 1 / T 1 = P 2 / T 2

P 2 = P 1 × T 2 / T 1 or T 2 = T 1 × P 2 / P 1

When you read the label of a pressurized spray paint can, you will probably see a warning not to let the can come in contact with heat. You can thank Gay-Lussac for this warning. If the can is heated enough, the pressure will increase and the can will explode. Besides being very dangerous, you will paint everything in sight. The take home chemistry message is, never heat a spray can !

Examples

If you have a pressurized (875 torr), room temperature (25°C) hair spray can with a volume of 15 ounces (oz.) that is in a house fire and heated to 1500°C, find the pressure inside the can before it explodes.

V 1 = 15 oz., V 2 = 15 oz. (just before it explodes)

T 1 = 27°C, T 2 = 1500°C

Remember to add 273 to get the temperature in kelvin.

T 1 = 27 + 273 = 300 K

T 2 = 1500 + 273 = 1773 K

P 1 = 875 torr

P 2 = x torr

P 2 = 875 torr × 1773 K/300 K = x torr

P 2 = 5171 torr

The pressure at this high heat is nearly 6 times what the spray can is designed to hold!

Ideal Gas Law

These three gas laws are referred to as the ideal gas laws . They were discovered by different scientists at different times, but all add up to explain the strange and amazing things that gases do in different conditions. The formula that considers all three laws is written as:

PV = n RT

where P = pressure, V = volume, n = number of moles of gas at constant pressure and temperature, R = molar gas constant (0.821 liter × atm/(kelvin × mol)), T = temperature. An ideal gas is one that meets all the rules of the gas laws. Gases that are mixtures of different molecules have some quirks that don’t follow the gas laws exactly.

Dalton’s Law Of Partial Pressures

John Dalton that we learned about in Chapter 1 as the father of the atomic theory, came up with an idea about how gas pressure works. Like Gay-Lussac, Dalton had a hobby. He was interested in meteorology; the study of the weather. While studying changes in the weather, Dalton did some experiments with vapor pressure. What he found was that, like people, gases are unique and behave in their own way when in a mixture. Each gas, for example, compresses at its own pressure. When using three different gases at a constant temperature, Dalton found that the total pressure of the three gases was equal to the sum of each of the three individual gases. This general rule became known as Dalton’s law of partial pressures.

Dalton’s law of partial pressures says that when you have more than one gas mixed with one or more different gases, the pressures of each gas will add together to give the total pressure of the mixture.

Dalton’s law is probably the easiest of all the gas laws to remember. It is written like this:

P total = P 1 + P 2 + P 3 + P 4 + P 5 + · · ·

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