GS_Ideal Gas Law Lesson

Ideal Gas Law

Did you notice that in the combined gas law examples that the amount of gas was not included? This is because it was held constant. So, how would we determine that amount of gas? Or, what would happen if the amount of gas were not held constant? We need another equation that puts all of this together, the ideal gas law. Before we get into the math of this equation, let's discuss the term "ideal gas".  

An ideal gas  is actually a hypothetical gas that follows a certain set of assumptions. These assumptions are really an oversimplification of some of the natural behaviors of gases.  

Here are the qualifications for ideal gases: 

• There are no intermolecular attractive forces (IMA).
• All the collisions between atoms or molecules are perfectly elastic, meaning that no kinetic energy is lost.
• The gas particles do not take up any space, meaning their actual volume is completely ignored. This is why we only consider the volume of the container.
• The gas particles are in constant, random, straight-line motion.

Think of these gas particles as perfect spheres which collide but do not interact with each other in any other way. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

You might wonder why chemists would have a concept or an equation for something that does not actually exist. It is because the assumptions make it easier to study the behavior of a gas. If you have taken physics, you know that we often ignore friction when first studying motion and the associated motion equations. This simplification makes the process easier to understand. Then, later, you learn about friction and adjust your conceptual understanding and math accordingly. We will do this with ideal gases as well. Once you understand the "ideal" behavior of gases, we will later learn how to correct this concept to apply to "real" gases.

Watch this video from Khan Academy for a deeper understanding of the ideal gas law.

Ideal Gas Law Calculations

The equation for the ideal gas law is similar to the combined gas law. Recall that:$\frac {P_1V_1}{T_1}=\frac{P_2V_2}{T_2} or \frac{P_1V_1}{T_1}=k$

The constant, k, above actually includes the number of moles of gas. So, k can be replaced with number of moles, n, and a different constant. This constant is known as the universal gas constant, R. And, the equation is rewritten to be

$\frac{PV}{T}=nR$

This equation is commonly rearranged and written as shown below:

Let's look at this equation to see the relationships between the variables. Can you tell the relationships just by looking at the equation? Yes!

Here is an easy way to tell if you have a direct or inverse proportion. Look at just two variables in your equation. (All other are assumed to be held constant.) The two variables are directly proportional if they are on opposite sides of the equal sign.  

The two variables are inversely proportional if they are on same sides of the equal sign.

You already knew these particular relationships (Boyle's Law and Gay-Lussac's Law). Now you should be able to tell the relationships between number of moles and each of the other variables.

Note - In order for this shortcut to work, you have to make sure that your equation does not have any denominators. For example, if you wanted to see the relationships between the mass and volume in the equation for density, $d=\frac{m}{v}$ , you must rearrange the equation to be  $dV=m$. Now, you can see that mass and volume are on opposite sides of the equal sign and are directly proportional. So, if density remains constant, mass must increase as volume increases.

Now, let's do the math! You will need to know the value for R, the universal gas constant. You will see R written as several different numbers, depending up the units used to measure volume and pressure. Using the most commonly used units, L and atm, gives R the value of 0.0821 (L)(atm)(mol^-1)(K^-1). You do not need to memorize this constant, but do write it down to use in your calculations. And, always pay attention to the units given for R. You may need to use your pressure unit conversions to change your quantities to match the units given for R (or vice versa). Also, remember that temperature must be expressed in Kelvin when doing any math problems involving gases.

Here are some ideal gas law example problems. Follow along with these videos from Khan Academy.

Ideal Gas Law Equation Examples

Watch the example 1 and 2 video. Notice in example 1 that different values for R are used, depending upon the units of the other variables. Example 2 shows how to use the ideal gas law and the combined gas law together.

As we proceed in this module, you will be learning many more equations. Often, the trickiest part of solving these is knowing which equation to use. As you learn a new equation, make sure to make note of when it is appropriate to use that equation. For example, the combined gas law is used when you are comparing one set of circumstances to another. When you have a "before and after" situation or are asked about changes in conditions, this is the equation to use. The ideal gas law, however, must be used any time you need information about the number of moles of a gas. You can also use the ideal gas law if you are given number of moles (and some of the other variables) to calculate a quantity that might be used in another equation. 

Remember to work on the module practice problems as you complete each section of content.

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