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!

charles_boyle_4th_earl_of_orrery_by_charles_jervas

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.

jv49ciucts26tdpp3tfe_motion-of-molecules1971016-arrowjv49ciucts26tdpp3tfe_motion-of-molecules1

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.

jv49ciucts26tdpp3tfe_motion-of-molecules1971016-arrowjv49ciucts26tdpp3tfe_motion-of-molecules1

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!

8d4af9a2f6b8cbb5c6c0454eeb73a910

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.

Creative Corner: One Word

If there’s one thing I’ve learned from eighteen years of life, it’s that boredom can be to a fault. Here I am, slouched down on my parent’s leather-upholstered couch, staring at a blank computer screen that is adjusted for maximum brightness. There are a number of websites that I could easily search up and scroll through until a snazzy picture or article catches my eye and prompts me to click on the tempting link. I could just as easily remove myself from the couch and find something mildly productive to do, but I don’t.

Please don’t get me wrong. I don’t in any way attempt to suggest that sheer boredom, strong enough to slay Argus, has led me to this degenerative state of mere existence. It is, in fact, a series of vaguely annoying events that has thrown me into a lack of being which I am halfheartedly pulling myself out of.

You see, this year, which is coincidentally my senior year of high school, has allowed me to realize my supposedly deepest fears. I wouldn’t typically downplay my fears with the word “supposedly,” but I’ve entered into unemotional territory as of late and I feel that I can’t honestly state my fears without something of a qualifier to describe my intense lack of feeling. And really my only goal here is to be honest, if not with others then at least with myself.

I may be a little naive due to the fact that I pictured senior year as one long episode of “Hannah Montana” or another equally picturesque high school sitcom. I would be riding around with people piled in the backseat of my car, going out to basketball games with my friends, picking up takeout on random school nights. The issue with my high school fantasy is that I left out the most important, fate-determining factor–myself. When you’re the type of person who worries over safety and legal responsibility for minors, you might not be the best driver to tote around a horde of wild teenagers in your mom’s beat up minivan. If you’re taking six advanced placement courses, you are more likely to be buried under sheets of math homework than getting takeout at ten at night. But if I have to hear the words “you did this to yourself” one more time, I just might burst.

The issue with things is that I can’t say that I’m unhappy. I desperately seek an aching sadness that clings to my rib cage and pulls me inward, away from everyone and into a self-constructed cocoon. In a way, I feel that that type of emotional distress would be reasonable as everything I thought I was working towards has been swept cleanly away like it never existed in the first place. Picture a blackboard with differential equations and trigonometric identities haphazardly written across to suggest intense concentration and high levels of academics. I’m the clean slate next to the blackboard confused because my identity seems to have been misplaced without the possibility of blaming it on disorganization.

My life is organized. One look in the mirror and I see a young girl with neatly combed brown hair, lips parted in a wide grin. There’s a splash of tiny blemishes across the cheeks, but there’s nothing inherently messy about them, despite their undesired presence. In fact, their symmetry is almost unnaturally perfect. A pert nose rests under a forehead that has remained unlined from youthful energy, despite the amount of stress that has been placed on the delicate shoulders that curve down into slim arms. Everything is as it should be. There’s still the big, bright eyes, opened wide with optimistic faith, the curious mind questioning what it is that life is all about. This person hasn’t changed on the outside, so what’s the distinction?

I suppose that the distinction here isn’t even about myself. It’s about the unfavorable, though entirely irrelevant, events that have unfolded around me into an inescapable ring of fire. Maybe I’ve been singed. But I have this uncanny ability to consistently believe that even a third-degree burn can be healed.

At this point, I’m still sitting on the couch, but I no longer feel a weighted opposition to all movement. I guess I’m just not bored anymore. Even my computer screen no longer bears the sickening whiteness of a blank monitor. Now there’s one word typed in the top search bar.

And I only need one look to comprehend the dire importance of this word, “live.”

Don’t Count Your Acceptances Before They’ve Come

As a senior in high school on the threshold of college acceptances (or rejections?), the question of the moment is undoubtedly “where are you going to college?” It’s safe to say that this question is directed at me at least once per day, if not more, and that I have absolutely no idea how to answer it. Where am I going to college?

With university admissions becoming more and more competitive, it’s no surprise that students across the nation are placing less faith in their academic and extracurricular qualifications, no matter how impressive they may seem. The declining admissions rates for top-ranking universities ensure students that there is no absolute certainty about the likelihood of their being admitted to the schools of their choice. This uncertainty has led to the great increase in applications submitted by individual students. In my twenty-student high school English course alone, I know at least two peers who are applying to over twenty universities due to fear of not being admitted at any institution.

And it is with good reason that they fear rejection from their dream schools: Harvard College’s undergraduate admissions rate for the class of 2019 was a record-low with only 5.3% of applicants accepted. Yale University, with a slightly larger admissions rate than Harvard, welcomed a whopping 6.5% of applicants to its prestigious facility. Universities claim that dwindling acceptance rates are due to larger influxes of undergraduate applications, but the suggestion that a larger applicant pool precipitates more rejections for prospective students predicts a grave future for higher-level education in America.

The United States appears to be heading on a trajectory towards the competitive educational characteristics of European countries where only select middle school students are admitted to high school. Yes, in countries like Romania, some 14 or 15 year-olds are forced to accept trade school as an alternative to high school. While high school is mandatory for all teenagers in the U.S., the declining possibility for gifted students to enroll in Ivy League or other comparable institutions parallels the lack of opportunity in the Romanian education system. My own mother, now a successful Treasury Accountant at a notable law firm, was forced to opt out of university in Romania due to her lacking physics exam score and went to work immediately after graduating from high school. It was only when she came to America that she was able to enroll in college courses and pursue a career in accounting.

If the United States were to become a country where intelligent students are forced to develop their education at universities that are unable to challenge them intellectually, the very heart of progress would be diminished. Students are told to aim for universities where they will neither be too comfortable with the courses nor challenged too greatly for their academic capacity. Yet, when many qualified teenagers are being rejected from schools that suit their abilities, there seems to be some sort of hypocrisy.

I guess the only thing that is safe to say now is that America will once again get a glimpse of its educational future come March when admissions decisions roll out.