Lately I’ve been thinking about Avogadro’s Law (SPOILER ALERT: I am probably/definitely a nerd). When I was taking chemistry honors and AP Chem in high school I accepted Avogadro’s Law as a universal fact, the very definition of a law. There was so much more information in my textbooks that I needed to learn and I took the easy way out, not caring about understanding why any of the gas laws had to be fundamentally correct. In short, I left the proofs to geometry.
Of course now that I’m a recently graduated high school senior with absolutely no summer homework and way too much time on my hands, I’ve been going back to things that I wish I had time to do when I was in high school: cooking, hanging out with friends, reading, LEARNING THE EXPLANATIONS BEHIND DIFFICULT CHEMISTRY CONCEPTS.
And so, here we return to Avogadro’s Law. The definition of Avogadro’s Law is that equal volumes of gas, held at constant temperature and pressure, contain equal numbers of molecules.
A superficial glance at this statement and I wholeheartedly agree! Equal volumes of gas must have equal numbers of molecules because…well…duh. A few minutes later and suddenly I’m thinking about molar mass and stoichiometry and the relationship between moles and volume and now I’ve opened up a massive black hole and I have no idea where I am or why there are 22.4 Liters of gas per one mole at standard pressure and temperature. Basically, I need help.
Thank goodness for the internet because otherwise I would be sitting in my room for a week with marker stains on my face and crumpled up papers surrounding me, just trying to find an explanation for Avogadro’s Law.
Without further ado, here is a concise look at Avogadro’s Law:
Let’s assume that we have 1.00 Liter each of nitrogen gas and hydrogen gas in separate containers. We have also held both temperature and pressure constant in each of the containers.
Hydrogen and nitrogen particles have different masses (1.01 g/mol H and 14.00 g/mol N) which means that they have different sizes, nitrogen being the larger atom. However, we will soon learn that size is independent of this particular concept.
Pressure of a gas is determined by the average kinetic energy of gas particles and the number of particles present. The average kinetic energy in each container must be the same because the temperatures of the containers are the same.
*Average kinetic energy = (1/2)(m)(u²rms)
*urms= root mean square speed
The size of the particles doesn’t change the average kinetic energy of each container because smaller particles will move faster and larger particles will move more slowly, averaging out the kinetic energy.
So, if kinetic energy is the same for each of the containers, the only difference that would change pressure is the number of particles. BUT we already established that the pressure is equal in both containers. Therefore, the number of molecules in each container must be equal as well!
There we have it! The explanation is so much simpler than all the nonsensical thoughts and frustration that were building up in my head.
Volume and the number of particles in a gas are directly proportional; that’s the main point of Avogadro’s Law. The trouble for me was understanding that the average kinetic energy wouldn’t change according to different-sized particles, unless temperature changed.
Hopefully in two hours I’ll still feel that this explanation is simple.