Chemistry Thoughts: The Relationship Between Volume and Pressure

The countdown has begun. It’s currently T minus 7 days till I head off to Berkeley, but today is exactly the day that my chemistry panic has set in! UC Berkeley has notoriously difficult classes but the course I’ve heard about the most by far has been Chemistry 1A/1AL. Of course this means that’s the exact course I have to take my first semester in order to satisfy some requirements for medical school and my actual major.

On the bright side, I can get in a little review before I go to my first chemistry class so I don’t have a panic attack in the lecture hall, so here we go…

Boyle Oh Boyle, This Is Going To Be Good!

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The most fundamental relationship between volume and pressure is illustrated through Boyle’s Law. The law is written down in several convertible forms, but we will consider it in the elementary format:

pv = C 

*p = pressure, v= volume, C= constant

The reason I chose the format pv = C is that it clearly displays the inverse relationship that pressure and volume have with one another. In mathematics, an inverse equation is shown as y = k/x, where k is a constant. Similarly, if we take the formula for Boyle’s Law and manipulate it by dividing the constant C by volume v, we will get the equation p = C/v. It’s an inverse function!

The inverse relationship means that if volume were to increase, pressure would decrease, and vice versa. Or, if pressure were to increase, volume would decrease, and once again vice versa!

If you think about it, this makes a lot of sense. Imagine a box that houses some gas, let’s say hydrogen.

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If we were to decrease the size of the box, meaning that we are decreasing the volume without changing the number of particles, then there is less space for the particles to move around without colliding. Pressure is determined by the number and force of collisions so more collisions from having less volume means greater pressure!

Changing volume in the opposite direction would work as well.

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If we were to increase the size of the box, meaning that we are increasing the volume without changing the number of particles, then there is more space for the particles to move around without colliding. Less collisions therefore equates to less pressure overall!

 

This is the basic point that Boyle’s Law makes but the applications, in my opinion, go so much farther than this. Hopefully if I understand this fundamental point, I’ll understand the math involved in Berkeley’s chemistry program! Thanks Charles Boyle!

 

 

 

 

 

Chemistry Thoughts: Avogadro’s Law

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!

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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.