GS_Avogadro's Law Lesson

Avogadro's Law

Don't let the combined gas law lead you to believe that the number of moles of a gas is not important. It is equally as important to understand the relationship between number of moles of a gas and the other variables. During his work, Avogadro determined a very important relationship between the volume of a gas and the number of moles. When measured at the same temperature and pressure, equal volumes of gases contain equal numbers of moles. This is true regardless of the type of gas. This is known as  Avogadro's Law.

Avogadro's Law At the same temperature and pressure, equal volumes of gases contain equal numbers of moles. V₁/n₁ = V₂/n₂

image of person blowing up balloonBlowing up a balloon is a great example of this law. When you blow air into the balloon, you increase the number of molecules. This increases the number of collisions on the walls of the balloon. For an instant, this increase in number of collisions causes the pressure inside the balloon to also increase, becoming greater than the atmospheric pressure outside the balloon. Since the walls of the balloon are flexible, the increased pressure will cause the volume of the balloon to expand. Now there is more room inside the balloon, so the brief increase in pressure is eliminated. The pressure returns to its original amount. This tells us that volume is directly proportional to number of moles.

Example Problem: 10.0 moles of carbon dioxide gas has a volume of 245 L at 25° and 1 atm pressure. If 5.0 moles of the carbon dioxide is removed at the same temperature and pressure, what volume will the gas now occupy? Start by making a list of your data. V₁ = 245L n₁= 10.0 mol V₂ = ? n2= 5.0 mol Now, simply plug the values in to the equation. V ₁/n₁ = V₂/n₂ 245L /10.0mol = V₂/ 5.0mol (245L)(5.0mol) = (10.0mol)V₂ V₂ =122.5 rounded to 120L

Temperature and Pressure (STP) and Molar Volume

Avogadro's Law states that the volume occupied by a certain number of moles of any gas must be identical for all gases under the same conditions of pressure and temperature. Because constant conditions of pressure and temperature are used so frequently, scientists agreed to establish a standard set of conditions. The standard conditions of temperature and pressure, or STP, are 1 atm and 273.15 K (0°C). You need to memorize these conditions!

The volumes of numerous gases have been measured at STP. For 1 mole of any gas, the volume of that gas at STP is 22.4 L. This is known as molar volume. This is a very important number, one that you need to memorize! You will learn how in later lessons.

STP T = 273.15 K (0°C) P = 1 atm MOLAR VOLUME 1 mol gas = 22.4L

Law of Combining Volumes

The concept of Avogadro's Law was extended by Gay-Lussac and applies to chemical reactions of gases. We already understand that in a balanced equation, the coefficients of the reactants and products exist in a certain ratio. We call this molar ratio. According to Avogadro's Law, under constant temperature and pressure, the coefficients will also represent the ratio of the volumes. In reactions of gases, the numbers of moles and the volumes are in the same ratio (when all are at the same T and P).

Look at the following example to see this relationship:

Consider the equation for the reaction of hydrogen and chlorine. H2(g) + Cl2(g) 2HCl(g) The molar ratios are 1:1:2 According to Avogadro's Law (under constant T and P), the volume ratios will also be 1:1:2.

This is an important relationship to remember when solving many gas law problems as it is often overlooked!

 

Example Problem: If ozone, hydrogen, and oxygen were all measured at 35°C and at 753 mmHg, how many liters of ozone were consumed if 5 liters of oxygen gas was produced? O3(g) + H2O(l) → H2(g) + 202(g) Normally, we start by making a list of our data. But, it is especially important when dealing with gases that you pause and think about relationships such as the Law for Combining Volumes. Often, this can actually save you lots of time doing calculations that are not necessary. So, stop and think! We are asked to calculate volume of a gas. We are given a balanced equation that contains gases that were all measured at the same temperature and pressure. Any time this is true, the Law for Combining Volumes applies. This means that the ratio of coefficients not only represents moles, here it also represents volume! ?LO₂ =5LO₂(ILO,/ 2L0₂)= 2.5L Notice that the values given for temperature and pressure were not needed. We only needed to know that they remained constant for all of the gases in the reaction.

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

[CC BY-NC-SA 4.0 Links to an external site.] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION - INTENDED ONLY FOR USE WITHIN LESSON.