Worked example: Using the ideal gas law to calculate a change in volume. Gas mixtures and partial pressures. Worked example: Calculating partial pressures. Practice: Ideal gas law. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter.
Video transcript - [Instructor] In this video we're gonna talk about ideal gasses and how we can describe what's going on with them. So the first question you might be wondering is, what is an ideal gas?
And it really is a bit of a theoretical construct that helps us describe a lot of what's going on in the gas world, or at least close to what's going on in the gas world. So in an ideal gas, we imagined that the individual particles of the gas don't interact. So particles, particles don't interact. And obviously we know that's not generally true.
There's generally some light intermolecular forces as they get close to each other or as they pass by each other or if they collide into each other. But for the sake of what we're going to study in this video, we'll assume that they don't interact. And we'll also assume that the particles don't take up any volume. Don't take up volume. Now, we know that that isn't exactly true, that individual molecules of course do take up volume. But this is a reasonable assumption, because generally speaking, it might be a very, very infinitesimally small fraction of the total volume of the space that they are bouncing around in.
And so these are the two assumptions we make when we talk about ideal gasses. That's why we're using the word ideal. In future videos we'll talk about non-ideal behavior. But it allows us to make some simplifications that approximate a lot of the world.
So let's think about how we can describe ideal gasses. We can think about the volume of the container that they are in. We could imagine the pressure that they would exert on say the inside of the container.
That's how I visualize it. Although, that pressure would be the same at any point inside of the container. We can think about the temperature.
And we wanna do it in absolute scale, so we generally measure temperature in kelvin. And then we could also think about just how much of that gas we have.
And we can measure that in terms of number of moles. And so that's what this lowercase n is. So let's think about how these four things can relate to each other. So let's just always put volume on the left-hand side. How does volume relate to pressure? Well, what I imagine is, if I have a balloon like this and I have some gas in the balloon, if I try to decrease the volume by making it a smaller balloon without letting out any other air or without changing the temperature, so I'm not changing T and n, what's going to happen to the pressure?
Well, that gas is going to, per square inch or per square area, exert more and more force. It gets harder and harder for me to squeeze that balloon. How big is a mole? On a macroscopic level, one mole of table tennis balls would cover the Earth to a depth of about 40 km.
Find the number of active molecules of acetaminophen in a single pill. We first need to calculate the molar mass the mass of one mole of acetaminophen. This value is very close to the accepted value of The slight difference is due to rounding errors caused by using three-digit input.
Again this number is the same for all gases. In other words, it is independent of the gas. Thus the mass of one cubic meter of air is 1. At what pressure is the density 0. The best way to approach this question is to think about what is happening. If the density drops to half its original value and no molecules are lost, then the volume must double. A very common expression of the ideal gas law uses the number of moles, n , rather than the number of atoms and molecules, N. How many moles of gas are in a bike tire with a volume of 2.
Identify the knowns and unknowns, and choose an equation to solve for the unknown. The most convenient choice for R in this case is 8. The pressure and temperature are obtained from the initial conditions in Example 1, but we would get the same answer if we used the final values. The ideal gas law can be considered to be another manifestation of the law of conservation of energy see Conservation of Energy. Let us now examine the role of energy in the behavior of gases.
When you inflate a bike tire by hand, you do work by repeatedly exerting a force through a distance. This energy goes into increasing the pressure of air inside the tire and increasing the temperature of the pump and the air. The ideal gas law is closely related to energy: the units on both sides are joules.
This term is roughly the amount of translational kinetic energy of N atoms or molecules at an absolute temperature T , as we shall see formally in Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature. The left-hand side of the ideal gas law is PV , which also has the units of joules. We know from our study of fluids that pressure is one type of potential energy per unit volume, so pressure multiplied by volume is energy.
The important point is that there is energy in a gas related to both its pressure and its volume. The energy can be changed when the gas is doing work as it expands—something we explore in Heat and Heat Transfer Methods—similar to what occurs in gasoline or steam engines and turbines.
Step 1. Examine the situation to determine that an ideal gas is involved. Most gases are nearly ideal. Step 2. Make a list of what quantities are given, or can be inferred from the problem as stated identify the known quantities.
Convert known values into proper SI units K for temperature, Pa for pressure, m 3 for volume, molecules for N , and moles for n. Step 3. Identify exactly what needs to be determined in the problem identify the unknown quantities. A written list is useful. Step 4. Determine whether the number of molecules or the number of moles is known, in order to decide which form of the ideal gas law to use. Step 5. Solve the ideal gas law for the quantity to be determined the unknown quantity.
You may need to take a ratio of final states to initial states to eliminate the unknown quantities that are kept fixed. Step 6. Substitute the known quantities, along with their units, into the appropriate equation, and obtain numerical solutions complete with units.
Be certain to use absolute temperature and absolute pressure. Liquids and solids have densities about times greater than gases. Explain how this implies that the distances between atoms and molecules in gases are about 10 times greater than the size of their atoms and molecules.
Atoms and molecules are close together in solids and liquids. In gases they are separated by empty space. Thus gases have lower densities than liquids and solids. Density is mass per unit volume, and volume is related to the size of a body such as a sphere cubed. So if the distance between atoms and molecules increases by a factor of 10, then the volume occupied increases by a factor of , and the density decreases by a factor of Find out the human population of Earth.
Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth? Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law? A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature? The difference between this value and the value from part a is negligible.
The final temperature needed is much too low to be easily achieved for a large object. Skip to main content. Temperature, Kinetic Theory, and the Gas Laws. Search for:. The Ideal Gas Law Learning Objectives By the end of this section, you will be able to: State the ideal gas law in terms of molecules and in terms of moles. Use the ideal gas law to calculate pressure change, temperature change, volume change, or the number of molecules or moles in a given volume.
Example 1. Strategy The pressure in the tire is changing only because of changes in temperature. Example 2. Calculating the Number of Molecules in a Cubic Meter of Gas How many molecules are in a typical object, such as gas in a tire or water in a drink? Solution We first need to calculate the molar mass the mass of one mole of acetaminophen.
Example 3. Strategy and Solution We are asked to find the number of moles per cubic meter, and we know from Example 2 that the number of molecules per cubic meter at STP is 2. Solution The best way to approach this question is to think about what is happening.
Example 4. Strategy Identify the knowns and unknowns, and choose an equation to solve for the unknown. Step 7. Check the answer to see if it is reasonable: Does it make sense? Check Your Understanding Liquids and solids have densities about times greater than gases. Solution Atoms and molecules are close together in solids and liquids. Conceptual Questions Find out the human population of Earth.
What is their gauge pressure later, when their temperature has dropped to — Convert an absolute pressure of 7. This value was stated to be just less than Is it?
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