Acidity of Carboxylic Acids

Carboxylic Acids (or organic acids) are, as their name implies, acids! I never even gave them a second thought until I came across a section in the Chemistry textbook I’m reading that provided an analysis of why they were acidic. I found it quite fascinating and I hope you do as well.

If we look at the carboxylic group:

1. The additional doubly-bonded oxygen atom is very electronegative and will attract the electrons that are shared in the OH bond, which further polarizes the bond and thus makes the H easier to “pop off.”
2. After the H detaches from the carboxyl group, it becomes of carboxylate ion, which is negatively charged. The two oxygens then form resonance structures, which stabilizes the anion and “distributes” the negative charge to a greater volume, effectively decreasing the charge density. With the diminished charge density it it less likely to grab a hydrogen from water.

For those of you that may be wondering, the first reason I cited is due to a phenomenon called electron drift.

Why I Love Break

It’s Thursday already, and spring break is coming to a close. It’s been quite a relaxing and stress-reducing week so far! My reasons for saying so may be quite different than yours, but perhaps somewhere deep down we share some common ground, no matter how little you consider yourself a “nerd.” Here are a few of the reasons why I specifically love breaks:

Catching up on Homework

This is probably the most mundane reason for my loving break, and definitely a shared trait amongst all young students. It’s hard to maintain a spartan-like focus and drive in the days leading up to break. Even the teachers have a hard time assigning serious homework and projects (more work to grade)!

That being said, reading and learning still needs to carry on. Whether your motivation is your GPA, the fear of the looming AP tests, or a desire to challenge your mental faculties, break is one of the best times to learn for retention and not for regurgitation. I personally find it very frustrating to try to cram for tests and overload my brain with rote memorization—it just doesn’t feel genuine to me. Not only do I suck at memorizing things, but I have no understanding of the material, and I most likely forget everything the very next day. It’s just not worth the stress, the bad grade, and the frivolity of it all.

Exploration and Genuine Curiosity

Probably the primary reason I look forward to the many breaks we have every year is because I have time to explore all of the little questions and curiosities that build up over the hustle and bustle of everyday life. I keep a little “idea” bank in my room that consists really of a tattered paper folder with a bunch of sticky notes, ripped pieces of paper, and crumpled napkins. On each little piece of “garbage” is a small thought I had that I thought would be worth further exploration.

They include everything from writing prompts I found interest and math concepts that I need some more work on to business expansion ideas and interesting points that come up during conversations. Finally having the time to read and act on those glimpses of my prior thought processes makes me happy and quite satisfied.

Writing without Guilt

As with the commencement of this blog, which has been an idea of mine for quite a while now*, I realized how much I like reflecting on my thoughts and sharing it with the world. As is stated in the Purpose of This Blog page, my short pieces are not so much catered toward increased readership but more for the release of my own self-expression.

During the regular school weeks, writing just about anything takes up more time that its worth. During break, though, I can finally find the time to write without the guilt of feeling like I should be doing something else.

*I never acted on it because I thought blogging was reserved only for emasculated guys.

The last reason I’m going to list (but definitely not the only remaining reason) for my loving break is because I have time to “get down to business” with INNO, the non-profit that a few of my closest friends and peers have been working on. If you don’t know what I’m talking about and are interested in what it’s about, feel free to follow the link in the previous sentence.

I have to admit, being a full-time student, part-time musician, quarter-time homework machine, and entrepreneur at the same time is a hard thing to pull off. Spring break has given me the time to follow up with parents interested in our services, contact the local school board to approve our sending information to local schools, and update our registration/website with an early-bird discount. You gotta do whatchu gotta do!

Carbon Steel as an Interstitial Alloy and How its Chemical Structure Contributes to Elasticity of Collisions

Background

Back when our high school physics class was learning about elastic and inelastic collisions with the conservation of momentum, I noticed that a disproportionate number of the practice problems we were assigned that had to do with elastic collisions involved steel. Obviously, when we think of steel we think of its “hardness.” It is used in a lot of heavy-duty construction, after all.

It just so happened that at precisely this time, we were learning about alloys in chemistry, and I remembered specifically my teacher talking about steel being an alloy of iron and carbon. Thus, I had a little flicker of inspiration and decided to connect the two and make a little presentation for my physics class. An added bonus? A little bit of extra credit. Continue reading Carbon Steel as an Interstitial Alloy and How its Chemical Structure Contributes to Elasticity of Collisions

Rules Regarding Electron Configurations

I don’t know if it was just me, but when I was learning about the quantum orbitals and electron configurations, I never could find a complete list of the different rules to keep in mind. Additionally, they were worded in the most indirect language imaginable. Were they trying to confuse people? Here, I’ll try to clear up some of that confusion.

Aufbau Principle

When filling electrons in orbitals, always fill from the lowest energy level to the higher energy levels. This means to fill $1s$ then $2s$ then $2p$ then $3s$ and so on. Because of the Aufbau Principle, Chlorine’s electron configuration is $1s^22s^22p^63s^23p5$ and not something like $1s^23s^24p^65s^23p5$.

If you ask why this is true? Well it seems that all things in nature like to be in its least energy state, so why hold an electron way out where it’s highly energetic when you have space in the “ground level” so to speak?

A notable exception is when you have excited electrons. These electrons will seemingly “jump” into a higher energy level and violate the Aufbau Principle, but all you have to keep in mind is that the atom is not in its ground state and you’ll be okay.

Hund’s Rule

Electrons want to be as spread out as possible to minimize electron-election repulsion. Thus, fill one electron in each orbital first and then come back to fill the second orbital. Again, this should be rather intuitive after introduced. This of electrons as living, breathing creatures! I don’t know anybody who would rather be cramped in a small space when there are clearly other open spaces available!

Pauli Exclusion Principle

No two electrons can have the exact same four quantum numbers and live in the same “address” or place in the atom. The closest you can get is having the first 3 quantum numbers the same, but then the last number, the spin, must be different.

Architecture in Regency England

Phew! Finally finished a project for my British Literature class on Regency England architecture! It took a many hours (mainly playing around with pictures, design, and the like) but it was definitely worth it.

If it sounds weird that I’d randomly decide to tackle historic British housing accommodations, it wasn’t without due cause. We were reading Pride and Prejudice, and had to do a research project on something relating to the era.

Adobe Spark, the program we had to use to create our projects, was overall pretty simple and fun to use, but I don’t like how the end result has Adobe advertisements galore. I guess that’s capitalism in the technology age for ya.

Enjoy.

Period of Simple Harmonic Oscillators

Introduction

As you may already know the two types of simple harmonic oscillators are springs and pendulums. They have many characteristics such as amplitude, frequency, and period (to name a few). This short piece is about the periods of springs and pendulums.

Investigation

For springs, the equation for the period is $T=2\pi \sqrt{\frac{m}{k}}$. This makes intuitive sense because $T$ increases as $m$ increases because objects with more mass have more inertia and thus the spring will “have a harder time” whipping the mass back and forth and the period increases. The fact that $T$ decreases as $k$ increases also makes some natural sense because as $k$ increases, the stiffness and magnitude of force the spring can put out for the same displacement is much greater as well. With a greater amount of force, the speed at which the block travels back and forth (or up and down) increases and the period decreases.

Now what about the equation for the period of a pendulum $T=2\pi \sqrt{\frac{L}{g}}$? If we were to just look at them side by side it is difficult not to notice their many similarities.

$T=2\pi \sqrt{\frac{m}{k}}$ for Springs

$T=2\pi \sqrt{\frac{L}{g}}$ for Pendulums

The second equation seems awkward and unnatural at first glance. However, if we really think about it and infer what we already know from the first equation the second one makes just as much intuitive sense.

For those of you that are wondering why $m$ is not included, think about what would happen if you increased the mass. Sure, you would increase the difficulty of moving the mass at the length of the string, but you also increase the restoring force of the pendulum (as it depends on the gravitational force).

In a more analytical way, the best, easy explanation I could cook up is by recalling some basics of rotation and torque $\tau = I\omega$. If we have a mass $m$ on the end of a string, the rotational inertia would be $I=mL^2$. The torque would be supplied by $mg\sin(\theta)$ which, multiplied by the lever arm, would result in $\tau=L*mg\sin(\theta)$. Thus our original equation $\tau = I\omega$ can be rewritten as $L*mg\sin(\theta)=mL^2\omega$. It then becomes transparent that $m$ can be cancelled on both sides and thus $\omega$ (a measure of the period, of sorts) is independent of mass.

The above explanation for why mass is not included in the equation for period also tells us why $L$ is. In the case of a pendulum the inertia we are interested in is the rotational inertia and not simply the “regular” inertia. If we look at the equation we derived above $L*mg\sin(\theta)=mL^2\omega$ only one $L$ cancels on both sides because $\tau$ increases with $L$ in a linear fashion but $I$ increases with $L$ exponentially. Thus, as increasing $L$ increases rotational inertia and “difficulty” of moving the mass on our pendulum it makes sense that it is on the numerator in $T=2\pi \sqrt{\frac{L}{g}}$.

As for the $g$ at the denominator, we can really think about it as a more general $a$, the acceleration of masses on any planet, not just on Earth. As we increase the acceleration $a$, the force of the restoring force increases because the restoring force is given by $F_{restoring} = ma\sin\theta$. Thus, the period decreases. This is similar to increasing the $k$ in the formula for period in springs.

Recap

The equations for period for springs and pendulums are $T=2\pi \sqrt{\frac{m}{k}}$ and $T=2\pi \sqrt{\frac{L}{g}}$, respectively. They may seem different but are really telling us the same thing. The variables $m$ and $L$ describe the inertia of the body in linear and rotational terms. The denominators $k$ and $g$ model the strength of the restoring forces.

Salt Bridges in Galvanic Cells

As we may already know, galvanic cells are simply experimental setups that take advantage of the electron transfer during a redox reaction to do electrical work. It may be quite easy to grasp that idea that electrons flow from the anode to the cathode, but the salt bridge is a little less easy to understand.

For any of you out there that are just looking for an easy way to remember that you need a salt bridge for any galvanic cell to function properly, something you can remember is that the salt bridge simply completes the circuit. It provides that “return route” for electrical charge to travel back into the anode.

Chemistry textbooks often say that a salt bridge is necessary to “balance out the charges in the two half-cells” but what does this really mean? Let us look at the basic set-up of a galvanic cell again.

As the redox reaction occurs, electrons migrate from the anode to the cathode. In our specific case with $Zn_{(s)}$ as our anode, as the reaction carries on, more and more $Zn^{2+}_{(aq)}$ is formed. The net result is that the left half-cell becomes more and more positive. You can think of this in two ways:

1. Electrons are being taken out of the left side, and so the left side becomes more positive by virtue of subtracting negative entities.
2. $Zn^{2+}_{(aq)}$ is being formed on the left side and because they are cations, it becomes more positive.

Similarly, but in the exact opposite way, on the right half-cell $Cu^{2+}_{(aq)}$ is reduced to $Cu_{(s)}$. The net result is that the right side becomes more and more negative. Again, you can think of this in two ways:

1. Electrons are being added to the right side, and because we are adding negative-charged particles the right half-cell must become more negative.
2. $Cu^{2+}_{(aq)}$ (positive) is becoming $Cu_{(s)}$ (neutral) and so we are losing positive charge on the right, and thus becoming more negative.

By virtue of the left half-cell becoming positive and the right half-cell becoming negative, the electrons would be less inclined to move from the anode to the cathode. After all, why would a negative particle spontaneously move from something that is positive to something that is negative?

This is precisely where the salt bridge kicks in. The salt bridge contains both cations and anions (in our case $KCl$) that can enter either side as the reaction progress continues. Because the left half-cell becomes more positive, anions (negative) from the salt bridge will migrate there. The opposite occurs in the right half-cell. Given $KCl$, the $Cl^{-}$ will be attracted to the positive left half-cell and the $K^{+}$ will be attracted to the negative right half-cell.

Understanding this fact will help you grasp the textbook wording of “balancing out the charges in the two half-cells.” It helps keep the left side negative and the right side positive… for the happiest of balances!