Charles’s Law

Charles’s Law

Charles’s Law says the gas volume is directly related to gas temperature. As the temperature of a gas increases, so does its volume. And as the volume of a gas increases, so does its temperature.

charles-law

 

V1 is the initial volume, T1 is the initial temperature and V2 is the new volume, and T2 is the new temperature.

Here are some examples of gas volume being directly related to gas temperature.

charles-law-balloon

The volume of the above balloon will expand as the flask is heated. The hot air balloon works by that same principle. Hot air balloons are inflated by firing up the air inside of them, thereby increasing their volume.

charles-law-hot-air-balloon

 

The following graph illustrates the direct relationship between volume and temperature as described by Charles’s Law.

charles-law-graph

 

As temperature increases, so does volume.

Let’s look at some sample problems.

Sample Problem

The volume of a gas at 25 ºC is 250 ml. Find its volume at standard temperature if pressure is held constant.

Since pressure is held constant, we’re not going to worry about it. Pressure will be the same before and after the temperature change. So what is the temperature change? The problem asks us to find its new volume at standard temperature. Standard temperature is actually a value. Standard temperature is equal to 0 ºC. And, since this is a gas law problem, and ALL gas law problems must be computed with the Kelvin temperature scale, we will use 273.15 K as standard temperature.

Charles’s Law is as follows:

charles-law

We are given a temperature of 25 ºC, which we’ll call T1, and a volume at that temperature of 250 mL, which we’ll call V1. We want to find out the new volume V2 when the temperature is changed to standard temperature, 273.15 K.

T1 = 25 ºC

T2 = 273.15 K

V1 = 250 mL

V2 = ?

Before we do anything, we need to convert all temperatures to the Kelvin scale. Therefore, we need to convert 20 ºC to K. We do this by adding to it 273.15.


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T1 = 25 ºC = 298.15 K

T2 = 273.15 K

V1 = 250 mL

V2 = ?

To solve for V2 we need to isolate the variable. We’ll do that by first multiplying each side by T2.

charles-law-t2

T2 cancels out on the right hand side and our equation becomes:

charles-law-v2

Plugging in our values for V1, T2 and T1, we get:

v2229mL

The new volume is 229 mL.

Here’s another sample problem.

Sample Problem

5.00 L of a gas is collected at 100. K and then allowed to expand to 20.0 L. What is the new temperature in order to maintain the same pressure?

We are given an initial volume of 5.00 L, so that will be V1. The temperature at that initial volume is T1, 100. K. The gas is then allowed to expand to 20.0 L, which is V2.

V1 = 5.00 L

T1 = 100. K

V2 = 20.0 L

T2 = ?

Charles’s Law is:

charles-law

To solve for T2, we first need to get T2 out of the denominator. We do that by cross-multiplying.

charles-law-cross-multiply

We get:

V1T2

Finally, to isolate T2, divide each side by V1:

charles-law-next

And we get:

charles-law-t2t1v1

Plugging in our values for T1, V2 and V1, we get:

charles-law-400k

The new temperature required to maintain the same temperature is 400. K.