The APsolute RecAP: Chemistry Edition

The APsolute RecAP: Chemistry Edition - Introduction to Gas Laws

Episode Summary

Why do you have to measure the cold tire pressure? It all comes down to gases.

Episode Notes

Why do you have to measure the cold tire pressure? It all comes down to gases. Episode 7 recaps the Kinetic Molecular Theory (1:22), defines gas variables (2:15), and looks at the relationship between those. Therefore, it recaps Boyle’s Law (3:37), Charles Law (4:36) and Gay-Lussacs Law (5:50).

Question: How would an increase in particle number change the pressure within a rigid container? (7:33)

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Episode Transcription

Hi and welcome to the APsolute Recap: Chemistry Edition. Today’s episode will recap gas laws.

Lets Zoom Out 

Are you the proud owner of a car (or maybe borrowing the family van)? Part of car maintenance is to check your tire pressure regularly. Triple A recommends at least once a month. Following the guidelines of your car manual, you should measure the cold tire pressure. Ideally, that means your car has not been driven for a few hours or only a few miles before you measure it. But why measure the cold tire pressure? How does driving change the tire pressure? To answer this question, this episode will focus on gases and recap gas properties and gas laws. 

Let’s zoom in:

In our first episode, we look at the different states of matter: solid, liquid and gas. So far we’ve discussed that particles in a gas move at a comparable high speed, they fill up the entire space available and they are compressible. But let’s dive a bit deeper! 

Experimental observations of gases have been summarized in the Kinetic Molecular Theory, which connects the macroscopic observations to the particulate level. This theory is based on the following six assumptions or postulates: 1) Gases consists of a large number of particles that are in constant random motion 2) Gas particles move in straight lines unless they collide with another particle or the wall of a container 3) Most of the volume of a gas is empty space 4) The attractive and repulsive forces between gas particles as well as gas particles and the container wall are negligible 5) Collisions between particles as well as particles and the wall are elastic and no energy is lost and lastly, 6) The average kinetic energy of the gas particles solely depends on the temperature of the gas. 

When looking at, or in our case listening to, the Kinetic Molecular Theory, we can already identify four variables that are being taken into account when working with gases: temperature, volume, pressure and particle number. Temperature is equal to the average kinetic energy of a gas and is measured in Kelvin. Sorry, not sorry, no Fahrenheit! Volume is the amount of space the gas particles occupy, usually measured in liters. Again, sorry, not sorry, we are not using gallons. This is science!! Pressure in chemistry is the force the gas particles are exerting everytime they collide with the wall. It is a bit like hitting your head against the wall - but NO, don’t do it, your collisions are not elastic! We here at the APsolute Recap work hard so you don’t get to THAT to that point when studying. Pressure can be measured in different units, depending on application: atmosphere, mmHg or Pascal. And the number of particles is measured in mole - nope, not the fluffy little creature digging up your yard - the chemical mole, which is equivalent to 6.022 x 1023 particles. We will talk more about the mole in a later episode!

So let’s look at the relationship between those variables. We are starting with three laws that vary pressure, temperature and volume - keeping one of the three - and the particle number - constant and describing the relationship of the other two variables. 

 

The first one is Boyle’s Law named after the physicist Robert Boyle of the 17th century and states that pressure and volume are inversely proportional under constant temperature. What does that mean? If you are decreasing the volume of a container, the pressure increases, because there will be more collisions of particles with the container wall. If you are increasing the volume, the particles will collide less often and therefore the pressure will drop. An example is bubble wrap - who doesn’t love popping the bubbles? By decreasing the volume with your finger, you are increasing the pressure - until it pops! When looking at Boyle’s Law from a math perspective, we can for example calculate what a new pressure is when cutting the volume in half. To do that we use P1 x V1 = P2 x V2, where P1 and V1 are the initial values before the change and P2 and V2 are the values after the change. By rearranging the equation we can solve for the new volume. 

The second law is Charle’s law. Jacque Charles kept pressure constant and investigated the relationship between temperature and volume. His law states that temperature and volume are directly proportional. What does that mean? If you are increasing the temperature, the volume will also increase and vice versa. But why is that? Temperature is average kinetic energy, which is, according to your physics teacher, ½ mass times velocity squared. Increasing the temperature increases the average kinetic energy. Since you are not increasing the mass of the particles, the increase in temperature has to increase the velocity of the particles - they are moving at a higher speed. Moving at a higher speed means they are hitting the wall more often and with greater force. This would normally increase the pressure - more about this in a second -, but we want the pressure to stay constant! Therefore, if the container is elastic, the volume will increase. This will increase the distance the particles have to travel to hit the wall, therefore decrease the number that hit the wall and keep the pressure constant. An example are hot air balloons - the balloon fills up with the hot air, increasing the volume. Mathematically, similar to Boyle’s Law, we can again compare a gas before and after a change using V1 over T1 = V2 over T2. 

The third law, of course, looks at the relationship between Pressure and Temperature and is named after the scientist Joseph Gay-Lussac. And we have actually already covered it: It states that temperature and pressure are directly proportional. It is very similar to Charles Law, the difference is that its using a rigid container that cannot expand. Therefore the volume is kept constant. With increasing temperature and therefore increasing particle speed, the pressure in the container increases. And this brings us back to our car tires! Full circle. They are, granted, somewhat flexible, but driving for a longer time will increase the tire temperature and therefore the tire pressure. To have a “baseline”, car manufacturers recommend measuring the cold tire pressure. Since these two variables are directly proportional we can calculate a change using P1 over T1 equals P2 over T2. 

COMBINING these three laws, we are getting the combined gas law, which we can again use to calculate a change: P1 x V1 over T1 equals P2 x V2 over T2. You actually only have to remember the combined gas law and then take into account which variable is held constant and therefore equals 1. That way you don’t need to memorize three equations, but only one! 

To recap……

Kinetic Molecular Theory helps us to connect observations about gas variables like pressure, temperature and volume to a particulate level. According to Boyle’s Law, pressure and volume are inversely proportional. Charles’s Law states that temperature and volume are directly proportional. And Gay-Lussac’s Law describes that temperature and pressure are directly proportional, too. 

Coming up next on the Apsolute RecAP Chemistry Edition: Introduction to Solution Chemistry

Today’s Question of the day is about gas laws. 

Question: How would an increase in particle number change the pressure within a rigid container?