Kinetic Molecular Theory of Gases - Practice Problems

of water increases and that is why it is more difficult to boil water at high pressure, but it is easier to boil water at low pressure, so if the pressure decreases it is much easier for a liquid to enter the gas phase because the boiling point has been lowered. reduced the energy needed to vaporize a liquid is not as high as before you just have to reach a temperature of 86 to boil water on, say, the top of a mountain instead of 100 at sea level, when you lower the atmospheric pressure, you make it easier The liquid enters the gas phase, so you will travel down the phase diagram, therefore, if you decrease the pressure, a substance will behave more like a gas.

If you increase the pressure, it can behave more like a solid or more like a liquid depending on where you are on the temperature axis, so a real gas will behave more like an ideal gas at low pressure, so if you think about the location of the gas phase on this phase diagram it exists towards the right , that is, towards high temperature and it does not exist at the top of the graph, it exists at the bottom of the graph, so at low pressure

gases

tend to form under low pressure and high temperature conditions. solids tend to form under low temperature conditions and high pressure liquids tend to form under conditions of relatively higher temperatures than solids but higher pressures than

gases

, but the answer for this problem is c, so if any time you see a question like this, a real gas behaves like an ideal gas under conditions of low pressure and high temperature number five, which of the following real gases will best approximate the behavior of an ideal gas.

Now keep in mind what we said above. Polar molecules will not behave like an ideal gas, but nonpolar molecules will. behave more like an ideal gas, polar molecules tend to deviate from the behavior of an ideal gas, so which molecules are polar and which are not, if you want to know if you need to review polar and non-polar molecules, you can search the video that i've created on youtube that can help you distinguish it, but normally if a molecule has hydrogen bonds it will be polar for the most part, so whenever you see h hydrogen bonded directly to one of these elements, nitrogen, oxygen or fluorine , those bonds are polar, so hf is a polar molecule, fluorine is very electronegative and therefore tends to attract electrons to itself, so fluorine takes on a partial negative charge and hydrogen takes on a partial positive charge so as long as you have a molecule where one side is partially positive and the other side is partially negative and if there is a net dipole moment then the molecule will be polar so hf will not behave like an ideal gas because to the forces it will exert on other hf molecules.

The current nh is another polar molecule. As you can see, we have hydrogen bonds between the ammonia molecules, so we can remove this one as well. It will not behave like an ideal gas. What happens to carbon dioxide? Is it polar or non-polar? Carbon dioxide has polar bonds. To determine if a bond is polar, you must look at the difference in electronegativity values. Carbon has an electronegativity value of 2.5 and oxygen is 3.5. If you type the electronegativity table into Google Images, you can find these values ​​if the electronegativity difference is equal to or greater than 0.5. then the bond is polar, so oxygen carries a partial negative charge and carbon carries a partial positive charge;

However, dipole moments, which are arrows drawn from a positive atom to a negative atom, note that the arrows point in opposite directions, so the lattice dipole moment of co2 is zero, so co2 is a nonpolar molecule hf and ammonia are polar molecules. Now, if you have an element or substance that is made up of a single element, it will always be non-polar, so the two oxygen atoms in an oxygen molecule will share. electrons equally because they are chemically the same and therefore you are not going to have a positive atom and a negative atom, it is just not going to happen in this case, so the O2 molecule is non-polar and helium is just one atom , is electrically neutral. the electrons are distributed evenly around that atom, so it will not be polar when the electrons are not distributed evenly in the case of hf because fluorine attracts the electrons to the right, that's why you have a negative side and the other positive side, for which the unequal distribution of electrons creates a polar molecule, but in o2 the two atoms are equal, so the distribution of electrons is equal, which makes the molecule non-polar, so these three gases, helium, oxygen and co2, will behave more ideally than hf or any current, but among these three gas molecules which one will behave more ideally compared to b c and d now the only type of inter

molecular

force that acts on a non-polar molecule are the London dispersion forces and those forces depend on the molar mass of the molecule as well as the molar mass of the molecule. increases, the London dispersion forces will increase and an ideal gas is one that has no force exerted between the particles of the gas, so we want to reduce this as much as possible.

The only way to do this is to decrease the molar mass and therefore we can decrease the London dispersion forces, so we need to identify which non-polar gas molecule has the lowest molar mass. Co2 has a molar mass of 44. O2 has a molar mass of 16 times two, it is 32 according to the periodic table and helium. is four, so helium has the lowest molar mass, so it has the least amount of inter

molecular

forces between the helium atoms, therefore it will behave ideally. Now you can see this problem from another perspective. Remember that one of the assumptions of the

kinetic

molecular

theory

of gases is that the volume of the gas particles has to be negligible, so a gas that has the smallest amount of volume will also behave more ideally now, if we look In the case of oxygen, oxygen is made up of two oxygen atoms, carbon dioxide is made up of three atoms and helium is made up of a single atom and helium is much smaller than oxygen or carbon, so Helium has the smallest volume, which is another reason why it behaves more ideally than O2 and CO2, so the substance with the lowest molar mass tends to exert fewer forces while also taking up space. less space or less volume, which makes it behave more ideally, so there are two reasons why substances with a small molar mass will behave ideally with fewer forces and less volume number six, which of the following graphs? shows the relationship between pressure and volume, so think about Boyle's law, the graph of which is associated with Boyle's law.

So if the volume of a container increases, what happens to the pressure according to Boyle's law? The pressure would be reduced. We have an inverse relationship, so it doesn't work. It's going to be b and it's not going to be a because as we increase the volume as we move to the right, the pressure increases and those two can be eliminated, so is it going to be c or is it going to be d? to be d the answer is c there are only two graphs you need to be familiar with this is the graph of boyle's law it is a curved graph it does not decrease that thinner rate the other laws look like this it is a straight line so for charles law if you increase the temperature the volume will increase so it has this form and then you have Galu Stack's law where if you increase the temperature the pressure will increase it also has the same form and finally Avogadro's law where if you increase the moles the volume will increase , so here is n and here is v number seven, which are the next gases contained and the two liter container will exert the most pressure with the walls of the container.

Will the sample now be xenon gas, fluorine gas or sulfur dioxide gas? going back to this equation pv is equal to nrt the pressure depends on the moles the temperature and the volume now the volume is the same so we don't have to worry about the temperature being the same because each container is at 300 kelvin the only thing that The difference is the moles and the pressure is proportional to the number of moles. If you increase the moles of gas inside the container, the pressure will increase and the reason the pressure increases is because if you have more molecules inside a container.

There will be more collisions with the walls of the container and each collision exerts a force on that container and the pressure is force per unit area so if the number of molecular collisions increases the pressure will increase therefore the correct answer is like this2 because we have the greatest number of molecules in that container then c is the correct answer because it has the greatest number of moles number eight which of the following statements is true so let's look at each of them the heavy gas molecules exert more pressure with the walls of the container since they exert more force, is it true or false?

Now you would think that a heavy object when it collides with something would exert more force and for the most part if the speed is the same that would be true, however when you compare heavy gas molecules to light gas molecules . molecules, heavy gas molecules, although they have more mass, move more slowly and then gas molecules, although they have less mass, tend to move faster, so these two balance each other and they happen to exert the same pressure . Pressure does not depend on the molar mass of a gas, so it doesn't really matter whether the gas is heavy or light.

The heavy gas particles move slowly and the light gas particles move fast, so it turns out that their average is the same, the average

kinetic

energy between the heavy gas molecules and the light gas molecules is the same, it only depends on temperature, so a and b are false statements, although lighter gas molecules will have a higher average velocity, which would normally produce a higher pressure. the mass is less and therefore if you have less mass, you have less force, although it moves at a higher speed and here there is more mass, which means that there is more force, but the speed is less, so it turns out that The pressure will be the same, so the pressure does not depend on the molar mass of a gas.

Now what about the density? Density is directly proportional to Kelvin temperature. Density is equal to pressure multiplied by molar mass divided by rt. Now notice that the temperature is at the bottom. of the equation every time you increase the denominator of a fraction the value of the whole fraction decreases so if you increase the temperature the density of the gas will decrease and it makes sense because if you increase the temperature the volume decreases and the density is mass. divided by the volume, so the mass of the gas will be the same, but every time the volume of an object increases, the density decreases and therefore the temperature leads to an increase in volume according to the law of Charles and that leads to a decrease in the density of the gas, so the density is inversely proportional to the kelvin temperature, which means that c is a false statement now the density is directly related to the pressure and the molar mass If the pressure of a gas increases, the density of that gas will increase and if the molar mass of the gas increases, the density will increase, so if you compare two substances like co2 with neon, where everything else is equal, co2 it will have a higher gas density because it has a higher molar mass.

Now, what about the average speed of the gas molecules? increases with temperatures, that's true or false, so remember this equation, the root mean square velocity is equal to the square root of 3rt divided by the molar mass, so if you increase the temperature, the average velocity will increase, so that d is a true statement if the molar mass increases the speed will decrease as we said before the heavy gas molecules move slower the lighter gas molecules move faster now what happens to e? The pressure is independent of the frequency of collision of a gas and the walls of the container.

That is a false statement. The pressure depends on the number of collisions between the gas particles and the walls of the container as the frequency of collision increases, the pressure increases. Now let's go over some free response questions, not only do you need to know the gas laws, but you also need to understand why they work the way they do. Do it, let's start with Boyle's law. If we decrease the volume, we know that the pressure will increase. The question is why that happens. Go ahead and explain it. Feel free to pause the video and write an explanation if you wish.

So let's say yes. We have a container this big and it contains some gas particles. Now, if we reduce the volume, why does the pressure increase? When it comes to pressure, it is necessary to describe it in terms of collisions. As the volume is reduced, you notice that there is less space. the particles will collide more frequently with the walls of the container and that is why the pressure increases in the case of Boyle's law, so make sure you understand that when you reduce the volume, theCollision frequency increases as the particles collide more often with the walls of the container.

In the container, the pressure is rising now, the next thing we have to talk about is the Galoo Sachs law. Actually, let's review Avogadro's law first. If we increase the moles, the volume increases, so let's say if we have a balloon and there is only one mole of gas particles. inside the balloon, if we add more gas, we know that the balloon will expand. The question is why the balloon expands well. To begin with, as the number of moles of gas particles increases, initially the pressure will increase, so I'm going to have to draw this visually, so before the volume increases, the instant you add more gas particles , you will have more collisions between the gas particles and the inner wall of the balloon, so the pressure will increase, say now, before that happens on the outside.

The pressure is one atm, the pressure inside is also one atm, so the volume does not change, but as soon as you add more gas particles in the balloon, the pressure will increase. The inside pressure could be two, the outside pressure could be one. and then the forces on the inside exceed the forces on the outside and as a result, due to this lack of balance, the balloon will expand and expand until it reaches equilibrium, so it will still have more gas molecules. inside this balloon, but the volume will double to reduce the pressure to one atm, so the volume will no longer increase when the pressure inside is equal to the pressure outside and that is why the volume increases, so let's review what I just said that as the number of moles increases in a container like a balloon like a flexible container, initially the pressure increases, it went up from one to two and as the pressure increases, the internal pressure exceeds the external pressure, so that the volume will increase and According to Boyle's law, as the volume increases, the pressure will decrease, so the net result is that there is no change in pressure, the pressure rises and then falls again, so that change in pressure is zero, so as the moles increase, the end result is that the volume rises due to a change in pressure, but in the end the pressure returns to its normal level when the pressure inside is equal to the outside pressure the volume will not increase or decrease it will stay the same when you increase the moles the pressure increases which causes the volume to increase until equilibrium is reached it is restored and then the pressure drops again so the net result is that a As you increase the moles, the volume will increase, so that's Avogadro's law.

Now what about Gay Lew Sachs' law, where if we increase the temperature, the pressure will increase, so let's say if you have gas? particles in the container where the volume is fixed and the temperature is 300 kelvin, what will happen if you increase the temperature to, say, 500 kelvin? Now the number of particles will not change, however we know that the speed depends on the root mean square of the speed. in temperature, so as the temperature increases the average velocity will increase and therefore the particles will move much faster, so if they move faster they will collide more frequently with the walls of the container and, if you can increase the frequency of collision then the pressure will increase and this is how an increase in temperature will lead to an increase in pressure the speed of the molecules will increase, they will collide more frequently with the walls of the container, which leads to an increase in pressure now the last one is Charles's law, which is a combination of the other laws, as the temperature increases, the volume increases.

Now let's talk about why and use a balloon for this example. If the temperature increases we know that the average speed of the molecules will increase and this will lead to a higher frequency of collision and as a result the pressure will increase, so let's say if we have a balloon and the pressure inside is one atm and the Outside pressure is one atm to 300 kelvin, now as we increase let's say the temperature to 600 kelvin, the molecules inside the balloon will move faster and therefore instantly the pressure will increase from 1 atm to 2 atm. Now, because the internal pressure exceeds the external pressure, the gases inside will exert more force compared to the gases. on the outside and then the balloon will expand as it expands the internal pressure will decrease and it will stop expanding until the pressure is equal to the outside pressure so it will continue to expand until the internal pressure is once again one atm , so once the inside and outside pressure is the same, it will stop expanding, the volume will no longer change, so that increase in pressure will lead to an increase in volume, which will bring the pressure back to one atm or the atmospheric pressure, so this increase in pressure and then a decrease in pressure cancel each other out, so the net effect is that the pressure remains the same, as we can see, but the volume increases, so a Increase in temperature leads to an increase in volume if you have a container that is flexible and allowed. to expand if the container is rigid then we have Galux Sachs law where it stops right here when the temperature increases the pressure increases if the container does not expand but if the container is allowed to expand the pressure will reduce allowing the volume expands and Then we have Charles's law, so that's the difference between Saxon Galux's law and Charles's law.

It all depends on the container. If the container is rigid, the pressure will increase due to an increase in temperature. If the container is flexible, the pressure will increase at first, but then. the pressure will decrease causing the volume to increase and that is why we have charles law you