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Background:

Charles' Law:

Assuming that pressure remains constant, the volume and absolute temperature of a certain quantity of a gas are directly proportional.

Mathematically, this can be represented as:

Temperature = Constant x Volume
or
Volume = Constant x Temperature
or
Volume/Temperature = Constant

Substituting in variables, the formula is:

V/T=K

Because the formula is equal to a constant, it is possible to solve for a change in volume or temperature using a proportion:

V/T = V1/T1

Explanation and Discussion:

Charles' Law describes the direct relationship of temperature and volume of a gas. Assuming that pressure does not change, a doubling in absolute temperature of a gas causes a doubling of the volume of that gas. A drop of absolute temperature sees a proportional drop in volume. The volume of a gas increases by 1/273 of its volume at 0°C for every degree Celsius that the temperature rises.

To explain why this happens, let's explore temperature and volume in terms of gases. Temperature is an average of molecular motion. This means that, while all of the gas molecules are moving around their container in different directions at different speeds, they will have an average amount of energy that is the temperature of the gas. The volume of the gas is the size of its container because the molecules will move in a straight line until they impact something (another molecule or the container). However, to move as they do, the molecules require kinetic energy, which is measured by temperature.

So, the volume and temperature are very closely related. If the temperature was not sufficient, the molecules would not be able to overcome the weak forces of attraction among them and would not be able to fill the container.

Charles' Law must be used with the Kelvin temperature scale. This scale is an absolute temperature scale. At 0 K, there is no kinetic energy (Absolute Zero). According to Charles' Law, there would also be no volume at that temperature. This condition cannot be fulfilled because all known gases will liquify or solidify before reaching 0 K. The Kelvin temperature scale is Celcius minus 273.15 °. Therefore, zero Kelvin would be -273.15 ° and any Celcius temperature can be converted by to Kelvin by adding 273.15 (273 is often used).

Any unit of volume will work with Charles' Law, but the most common are liters (dm3) and milliliters (cm3).

Calculations with Charles' Law

Let's try a problem with Charles' Law. For example, let's try to solve for an unknown volume of a gas. The unknown volume is at 32°C. At 18°C the gas occupied a volume of 152 mL.

Set-up
First, we must convert degrees Celcius to Kelvins. To do this, we add 273 to the Celcius measure. So:

32°C + 273 = 305 K
18°C + 273 = 291 K

We know that the temperature and volume are directly related. The temperature only went up a little bit (slightly more than 5%). So, we can expect the volume to increase by about 5%, which would be about 7.5 mL. Now, we can use the formula. (Really, we should use fraction ratios.)

Plug values into formula
Our formula is: V/T = V1/T1

In this problem, V = 152 mL, T = 291 K, and T1 = 305 K. V1 is unknown. Therefore, we can arrange the formula as:

152 mL/291 K = ? /305 L

Because this is a direct proportion, we can multiple the means and extremes to create an ease to solve equation:

152 mL x 305 K = 291 K x ?

Which can be divided by 291 K to yield:
152 mL x 305 K / 291 K = Volume1 = 159.3127 mL

However, we only have three degrees of precision in this problem, so our answer is: Volume1 = 159 mL.

Check
To check our answer, we need to compare it to our earlier estimate. We expected the volume to increase by about 7.5 mL, and it increased by 7 mL (7.3 before round). This answer is acceptable.

Continued Study
For continued study, you can visit our Charles' Law bonus page. You can also test yourself. You can also learn about Jacques Charles.

Sources:
Brown, Theodore L., H. Eugene LeMay, Jr. and Bruce E. Burston, Chemistry: The Central Science, Englewood Cliffs, NJ: Prentice Hall, Inc., 1994

Dorin, Henry, Peter E. Demmin, and Dorothy L. Gabel. Prentice Hall Chemistry: The Study of Matter, Needham, Massachusetts and Englewood Cliffs, New Jersey: Prentice Hall, Inc., 1989.

Roper, Gerald C., "gas laws" Groliers New Multimedia Encyclopedia, Release 6, 1993

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