Reading Notes for Chapter 9

These are Dr. Bodwin's reading notes for Chapter 9 of "Chemistry 2e" from OpenStax. I am using a local .pdf copy that was downloaded in May 2020.

Chapter Summary:

Understanding states of matter and how matter interacts is a fundamental topic and worthy of a lifetime of study. We will look at a number of important points as dedicated topics as well as in the context of other topics. Gases offer a number of advantages when we want to study the interactions and behaviour of matter, so they are a nice place to start when looking at states of matter in a little more detail.

States of Matter:

Before getting too deep into gases, let's look at the bigger picture.
In Gen Chem I, we often engage in what I call "sorting exercises". We define a couple bins (usually no more than 3 or 4) and figure out how to sort the world into those bins. "States of Matter" is one of those sorting activities... look back at Chapter 1. We made our "bins" (solid, liquid, gas, plasma) and tried to classify the world around us into those bins.
"Sorting exercises" are designed to answer "what" questions. "What is this?" - "It's a solid."
Let's move on to "how" and "why" questions.
Matter at the microscopic scale experiences two competing forces - kinetic energy and intermolecular forces. Kinetic energy (E_kin) is the energy of motion, and all matter that "has temperature" is in motion. That motion may only be vibrations of the molecules, but it's still motion. Intermolecular forces (IMFs) are the forces that attract moleclues to each other.
States of matter are the balance between E_kin and IMFs - if a molecule is moving "slowly" (low E_kin) and has "strong" IMFs, then the particles are likely to stick together and be solid; if a molecule is moving extremely fast and has very weak IMFs, then the particles will fly past each other before they stick together and be a gas.
{This is actually Chapter 10.1 in your textbook, but it's important to touch on it here to discuss gases.}

Intermolecular Forces (IMFs):

There are a number of different intermolecular forces with varying strength. In general, their strength from strongest to weakest is in the following order.

Ion-Ion - These are sometimes called "Coulombic Forces", and are (usually) very strong compared to other IMFs. This is why most ionic compounds are solids; the IMF is strong enough to overcome a lot of kinetic energy.
Dipole-Dipole - Polar molecules have a region that is slightly more positive and a regiuon that is slightly more negative. These are also coulombic forces, but because we're dealing with partial positive and negative charges, dipole-dipole interactions are (usually) not as strong as ion-ion interactions.
Hydrogen bonds - Most books discuss hydrogen bonds as if they are a unique IMF, but a hydrogen bond is just a special case of a dipole-dipole interaction. When hydrogen is bound to a significantly more electronegative element (N, O, F especially), the bond is polar with a partial positive charge on H. Because hydrogen is so small, that "partial" positive charge is actually quite concentrated, so the dipole-dipole interaction can be very strong. Because this is a special case, it's been given its own name "hydrogen bonds", but don't forget that this is just a special case of dipole-dipole interactions.
Induced dipole-Induced dipole - These have a number of different names: London Forces, Dispersion Forces, London Dispersion Forces. These are all the same thing. An induced dipole is a dynamic condition in which a non-polar electron cloud distorts to appear polar for a moment. This is easier to do with a large and relatively "squishy" electron cloud, so larger atoms tend to have stronger London forces. For smaller atoms (like carbon), the individual London forces are relatively small, but if there are a lot of carbon atoms connected together in a large molecule, the accumulated London forces can be quite strong. You can lift up a car with thread as long as you have a lot of individual threads. Everything has London forces.

{This is actually Chapter 10.1 in your textbook, but it's important to touch on it here to discuss gases.}

Kinetic Molecular Theory of Gases (KMT):

Why do gases behave the way they do? I like to look at Kinetic Molecular Theory (KMT) at the beginning of a discussion of gas laws because it gives a common framework for our discussion. This is presented in your textbook, section 9.5.
Kinetic Molecular Theory of Gases:

Gases are mostly empty space - the distance between gas particles is MUCH larger than the size of the particles themselves.
Gas particles move randomly (speed and direction) in a straight line until they collide with other gas particles or the wall of the container.
Except during collisions, attractive and repulsive forces between particles is negligible. IMFs are MUCH smaller than kinetic energy.
Collisions are elastic - the total kinetic energy going into a collision is the same as the total kinetic energy coming out of a collision.
The average kinetic energy of particles in a sample of gas is proportional to the absolute temperature of the sample.

These are all true for a idealized gas sample, and they tend to be a pretty good guide for common gases at relatively "high" temperature and relatively "low" pressure... for our purposes, room temperature and atmospheric pressure are "high" and "low".

Volume and Pressure:

One definition of a gas is that it "assumes the volume and shape of its container". This is because gas particles have relatively high kinetic energy and relatively low IMFs, so the individual particles are flying around insode the container and only stop or change direction when they run into another gas particle or the wall of the container.
Because the volume of a gas can vary, it is a very convenient property for us to observe when trying to understand the behaviour of gases.
Pressure is another useful property that is somewhat unique to gases, and it is helpful for us to think about the microscopic reason for pressure. "Pressure" is caused by atoms or molecules colliding with the walls of a container (or colliding with a pressure sensor). The number and energy of those collisions defines the observed pressure.
REMINDER - When we talk about pressure, it is important to remember that we all live in a big gas sample: the atmosphere. Often when we are talking about pressure, we are talking about a pressure difference between the sample we are observing and the pressure of the air or atmosphere outside that sample.

"Simple" Gas Laws:

The term "simple" I use here means that these are gas laws that only involve 2 quantities; all the other properties are held constant. For example, Amonton's Law describes the relationship between pressure and temperature when volume and amount are held constant.
Most people have enough casual experience with gases that simple gas laws are somewhat intuitive. Think about balloons, or beverage containers, or cooking methods... you can probably think of an example of each of the simple gas laws.
If you want to keep the names of the simple gas laws straight... Amonton's Law is the only one that doesn't include volume. For the 3 volume-based laws, if the non-volume properties are put in alphabetical order, the names are also in alphabetical order: amount-Avogadro, pressure-Boyle, temperature-Charles.
Understanding the way simple gas laws work is more important than know which law goes with which name, BUT the names provide a useful shorthand to describe the law.
When working with gas laws, always use Kelvin temperatures. Kelvin is an absolute scale so "zero" really means zero. If I go from 5K to 10K, I have doubled the energy in the system; if I go from 5ºC to 10ºC, I have NOT doubled the energy in the system. In gas laws, temperature is a measure of the energy of the particles, so it is essential to use Kelvin.
Often when we're looking at gases, we are looking at changes in conditions. That means that the comparative forms of gas laws are important tools for us. For example, the comparative form of Boyle's Law is P₁V₁=P₂V₂; if all we're interested in is finding the "new" pressure of a sample when we change the volume, the comparative form is the easiest way to do it.

The Ideal Gas Law:

This is a combination of all the simple gas laws, and you can derive any of the simple gas laws from the Ideal Gas Law.
The Ideal Gas Law is often used in its single-point form, PV=nRT, but it is also extremely useful in its comparative form.
The "combined gas law" is really just the comparative form of the Ideal Gas Law with "n" held constant.
Gases are most "ideal" when they are not near a phase change. "Hot" and "low" pressure are most ideal
When you are looking up values of "R" for use in the Ideal Gas Law, make sure you use the value that has the units you need. For gas law problems, that is almost always 0.08206 L*atm/mol*K.

Gas Stoichiometry:

The Ideal Gas Law is another way to get into or out of moles in a stoichiometry problem.

Dalton's Law of Partial Pressures:

The sum of partial pressures for a mixture of gases is equal to the total pressure.
This one should be pretty obvious, but why is it true? Think on the molecular level. If I have 100 gas particles and 15 of them are Substance A (and conditions are such that the gas id behaving in an ideal fashion...), then 15% of the times that a gas particle collides with the pressure sensor, it will be an "A" particle.
Mole Fraction - this is actually a concentration unit! But don't make it something harder than it is. It's just a percentage that hasn't been multiplied by 100. If you have a 200 question survey and the answer to 46 of those questions is "C", then the "C fraction" is 46/200 = 0.23

Diffusion:

Diffusion is a measure of the mixing of gases. It's similar to the idea of a gas filling its container... when we change the size of the container that is holding a gas, the gas will (eventually) fill the new container. Depedning upon a number of factors, "eventually" could mean a few milliseconds.

Effusion:

Effusion is the escape of a gas through a small opening into a vacuum. It's really just diffusion with some specific conditions.

Non-Ideal Behaviour:

We've talked about ideal gases, and we're lucky that "normal" gases under "standard" conditions behave very ideally, BUT when does that ideal behaviour start to break down. A gas is "ideal" when it follows KMT. So, under what conditions does KMT fail? Let's look at a few important cases:

Gases are mostly empty space - the distance between gas particles is MUCH larger than the size of the particles themselves.

This one runs into the most trouble at high pressure. Gases are compressible because there's a lot of empty space between particles. As we increase the pressure, the space between molecules decreases. Eventually the space between particles is not large compared to the size of the particles which means that the particles experience IMFs even if they're still moving pretty quickly. It's like running through air in a parking lot compared to running through air in a field of tall grass. The air hasn't changed, but you're interacting with the "ground" a lot more.

Gas particles move randomly (speed and direction) in a straight line until they collide with other gas particles or the wall of the container.

This one is pretty safe, BUT as the temperature of a gas get lower, the particles move slower. The slower the particles are moving, the easier it is for other forces (IMFs, gravity, etc) to act upon them.

Except during collisions, attractive and repulsive forces between particles is negligible. IMFs are MUCH smaller than kinetic energy.

Again, we have to look at the comparison part of this point. When a gas sample cools, kinetic energy decreases, and at some point the IMFs are of a similar energy to the kinetic energy, so those attractive and repulsive forces become important. Low kinetic energy = lower temperature.

Collisions are elastic - the total kinetic energy going into a collision is the same as the total kinetic energy coming out of a collision.

Again, if the kinetic energy is HUGE compared to IMFs, any interaction during a collision can be ignored, BUT if the kinetic energy goes down... same thing again, it's a balance between IMFs and kinetic energy.

The average kinetic energy of particles in a sample of gas is proportional to the absolute temperature of the sample.

This one's OK because it's not really an observation, it's the definition of temperature. If you look up KMT, this point is not even included in many sources because of that. I include it here just because it's a handy reminder.

So the bottom line is that gases behave ideally as long as the kinetic energy of the particles is WAY higher than the energy of the IMFs and the particles are well-separated.

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