in this video we're going to talk about the kinetic molecular theory of gases the kinetic molecular theory is a model it's a model that attempts to describe the behavior of an ideal gas now real gases they don't always live up to the standard of an idol gas and these assumptions that are listed here these five facts these are assumptions that describe the behavior of an idol gas which a real gas can deviate from such behavior so the first assumption the volume of the individual particles is assumed to be negligible and for an ideal gas that's it's not important so let's say if you have a very large container the gas particle is very very small that the volume of that particular gas particle is negligible compared to the distance between gas particles so the volume of the actual particles are so small that we don't have to worry about it's negligible now for a real gas that volume may be significant depending on the size of the gas some gas particles are bigger than others and so the identity of the gas the size that it has can play a role in the pressure volume relationship of a real gas so for instance according to boyle's law if you increase the volume the pressure will decrease for an ideal gas if you double the volume the pressure will decrease by a factor of two for a real gas if you double the volume the pressure will decrease but it may not exactly be by a factor of two it may decrease by 1.95 by 1.9 or 1.7 and each real gas will behave slightly differently but for an ideal gas if you double the volume the pressure will decrease by a factor of 2. but for real gas it will deviate from that value because the actual gas particles do take up space but for an ideal gas we assume that such volume is negligible now the second assumption is that particles are in constant random motion and for the most part this is pretty true as long as the temperature is above absolute zero the gas particles will be in motion they're not going to just be sitting there and not moving they're constantly moving and they move in straight lines however the motion is random let's say for example if you place a gas particle inside a test tube it's not going to cruise directly straight rather what's going to happen is because there's so many other molecules in its way it's going to collide with these molecules and so it's going to constantly bounce around with the walls of the container and with the molecules in what appears to be a random motion so it doesn't just go straight imagine if you're trying to hit a ball let's say you're playing pool and there's like a thousand other balls on the table and you're trying to hit a ball straight because there's so many balls in the table it's going to be very difficult for you to hit it straight it's going to knock another ball it's going to bounce around in different directions now in this test tube you have billions and billions of other gas particles and for this gas particle to go straight it's not going to happen so because of so many of the gas particles in its way the motion will appear to be random it's constantly going to be bouncing up and down as it makes its way through the test tube now the collisions between gas particles are elastic an elastic collision means that kinetic energy is conserved in an inelastic collision kinetic energy is not conserved you have loss of energy but what we have is an elastic collision where kinetic energy is conserved by the way momentum which is mass times velocity is conserved for any uh collision but for an elastic collision the kinetic energy is conserved and when i mean kinetic energy i mean the total kinetic energy of the system not necessarily the kinetic energy of one particle because one particle could transfer its energy to another particle when you have billions of particles the total sum remains constant so we can say the collisions are elastic there's no loss of kinetic energy now number four the particles do not attract or repel they exert no forces on each other and this is true for an ideal gas however for real gases they do exert attractive and repulsive forces so for example let's use a polar gas like ammonia nitrogen is more electronegative than hydrogen so therefore it bears a partial negative charge and hydrogen bears a partial positive charge so when you have two ammonia molecules next to each other the nitrogen of one molecule is going to be attracted to the hydrogen of another ammonia molecule because opposites attract the hydrogen has a partial positive charge the nitrogen has a partial negative charge and so it's going to have an attractive force between them now this nitrogen atom is repelled by the other nitrogen atom because they both have like charges they're both partially negative and so those two atoms will repel each other and so whenever you have a polar gas it tends to deviate from the behavior of an ideal gas because there's forces between these molecules they can attract or repel each other but an ideal gas is assumed to have no such forces so the lesson to be learned from it is this polar gases tend to behave less ideally than non-polar gases polar gases have intermolecular forces like dipole interactions and hydrogen bonds non-polar gases they only have weak london dispersion forces and so non-polar gases tend to behave more ideally than polar gases so make sure you keep that in mind now the last statement the average kinetic energy of a gas is assumed to be directly proportional to the kelvin temperature and this is true gases that exist at a higher temperature tend to be moving faster and as a result they have more kinetic energy the average kinetic energy of a gas is equal to three over two rt it's directly proportional to the temperature so if you increase the kelvin temperature the average kinetic energy of a gas increases now this is not the kinetic energy of a single gas particle rather it's the kinetic energy of a collection of gas particles billions of gas particles together and so when you average out the energies of billions of gas particles you'll find that the kinetic energy is based on the temperature of the whole sample if you're just looking at one individual particle then the kinetic energy of that individual particle is dependent on the mass of the particle and the speed but that's just for one particle when you have billions of particles colliding with each other it's only dependent on a temperature so make sure you keep that in mind so keyword average so you're dealing with a large number of gas particles now let's work on some multiple choice practice problems which gas has the highest average kinetic energy is it going to be methane argon or helium we're given the temperature and pressure of each gas and the size of the container is the same so they all have the same volume the pressures they vary so is it going to be the one with the lowest pressure methane or the one with the highest pressure helium now as was mentioned before the average kinetic energy is proportional to the kelvin temperature and since the kelvin temperature for each sample of gas is the same then that means that they all have the same average kinetic energy so d is the right answer now what about this one which of the following gases will have the highest average velocity at stp standard temperature and pressure so keep in mind that stp the temperature is 0 celsius or 273 kelvin and the pressure is 1 atm so these conditions apply to each gas so do you think the answer is going to be a b c or d well we know that the average velocity represented by the root mean square velocity formula is equal to the square root of 3 rt divided by the molar mass of the gas so the velocity doesn't depend on the number of moles or the volume of the container and it doesn't depend on the pressure within the container it depends on two things the temperature and the molar mass now the temperature is the same every gas listed here is that stp so the only thing that's different is the molar mass what you need to understand is that heavy gases move slower and lighter gases move faster so we got to find out which of these gases has the lowest molecular weight or molar mass according to the periodic table neon has an atomic mass of 20. oxygen is going to be 16 times 2 so that's 32 and co2 that's 12 plus 16 times 2 which is about 44. so neon is the lightest gas molecule which means it's going to have the highest average velocity so a is the right answer so for average velocity here's what we need to take or here's what we need to keep in mind as the molar mass of the gas increases the average velocity will decrease and as the temperature increases the average velocity will increase as well let's move on to number three which of the following is not consistent with the kinetic molecular theory of ideal gases so let's go through each one the volume of gas particles is negligible compared to the distance between individual gas particles is that true or false is that a statement that's found in the kinetic molecular theory of gases a is the true statement b the average kinetic energy of a gas is directly proportional to temperature that's true as well it's directly proportional to the kelvin temperature not the celsius or fahrenheit temperature c gas particles are in constant random motion and collisions between particles are elastic c is true the gas particles are always moving as long as the temperature is above absolute zero and the collisions are elastic where the total kinetic energy is conserved d the pressure of a gas depends on the number of molecules and the molar mass of a gas now d is not part of the kinetic molecular theory of gases the first part of d is true the pressure does depend on the number of molecules however it does not depend on the molar mass of a gas so d is a false statement which means this is the answer based on this equation if you solve for p the pressure of a gas depends on n which is the moles of the gas particles and moles is proportional to the number of molecules so that's why that part is true the pressure depends on the temperature and also on the volume of the container as you can see molar mass is not part of this equation so the pressure does not depend on the molar mass of gas an e is a true statement gas particles exert no forces on each other now this is true for ideal gases a real gas may exert a force on another gas particle they can attract other gas particles they can repel them it depends on the structure of the molecule and what it's made of number four under which conditions will a real gas behave like an ideal gas is it at high pressure or at low pressure and at high temperature or at low temperature what would you say now imagine if you have a liquid if you decrease the temperature will the liquid become a solid or will it turn into a gas something i like to use to explain this is a phase diagram and if you haven't seen a phase diagram it basically tells you where a solid a liquid and a gas coexist under conditions of temperature and pressure so on the y-axis you have pressure on the x-axis you have temperature so let's start somewhere in the liquid phase if we decrease the temperature that means we have to travel towards the left on the x-axis if you decrease the temperature of a liquid it's going to turn into a solid so low temperatures do not favor the formation of a gas if you put liquid water in the freezer the temperature will decrease it's going to turn into it's going to turn to ice so you don't want that rather if you increase the temperature if you travel towards the right on the x-axis the liquid will become a gas if you take the liquid water and put it on a stove it's going to vaporize into steam thus a real gas will behave more like an ideal gas under conditions of high temperature and not low temperature if you decrease the temperature it will no longer be a gas it's going to eventually turn into a solid so high temperatures favor the formation of gases so we could eliminate answer choice b and d now what conditions will favor the formation of a gas high pressures or low pressures well if we start from the same position if we increase the pressure that means if we travel towards the positive y axis it's not going to turn into a gas but if you decrease the pressure the liquid will eventually become a gas the best way to illustrate this is the boiling of water at different elevations so let me draw a picture so let's say this is a mountain and here we have a valley and let's say this is sea level at sea level the atmospheric pressure is one atm on the top of a mountain it might be less maybe like 0.6 or 0.7 atm atmospheric pressure decreases with increase in elevation and at a valley the pressure is going to be higher maybe like 1.2 or 1.3 atm the boiling point of water at one atm is about 100 degrees celsius at 0.7 atm it's going to be less than 100 so i'm going to just pick a number that's less than 100 it may not be the exact number that corresponds to this pressure but for illustrative purposes let's say it's like 85 or 86 degrees celsius and at 1.3 let's say it's about 108 or 109 degrees celsius but the point is that as the pressure increases the boiling point of water increases and so it's harder to boil water at high pressures but it's easier to boil water at a low pressure so if you decrease the pressure it's a lot easier for a liquid to enter the gas phase because the boiling point has been reduced the energy required to vaporize a liquid is not as high as before you only have to reach a temperature of 86 to boil water at let's say the top of a mountain rather than 100 at sea level and so when you decrease the atmospheric pressure you make it easier for the liquid to enter the gas phase and so you're going to travel down on the phase diagram so 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 of the location of the gas phase in this phase diagram it exists towards the right that is towards high temperature and it doesn't exist at the top of the graph it exists at the bottom of the graph so at low pressure so gases tend to form under conditions of low pressure and high temperature solids tend to form under conditions of low temperature 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 you ever see a question like this a real gas behave like an ideal gas under conditions of low pressure and high temperature number five which of the following real gases will best approach the behavior of an ideal gas now keep in mind what we said earlier polo molecules will not behave like an ideal gas but nonpolar molecules will behave more like an ideal gas polar molecules tend to deviate from ideal gas behavior so which molecules are polar and which ones are not if you want to find out if you need to review polar and non-polar molecules you can search out video that i've created on youtube that can help you to distinguish it but typically if a molecule has hydrogen bonds it will be polar for the most part so whenever you see h hydrogen directly bonded to one of these elements nitrogen oxygen or fluorine then those bonds are polar so hf is a polar molecule fluorine is very electronegative and so it tends to pull the electrons toward itself so as a result fluorine acquires a partial negative charge and hydrogen acquires a partial positive charge and so whenever you have a molecule where one side is partially positive and the other side is partially negative and if there's a net dipole moment then the molecule is going to be polar so hf is not going to behave like an ideal gas due to the forces that it will exert on other hf molecules nh stream is another polar molecule as you can see we have hydrogen bonds between ammonia molecules and so we can eliminate this one as well it's not going to behave like an ideal gas now what about carbon dioxide is it polar or is it nonpolar carbon dioxide has polar bonds to determine if a bond is polar you need to look at the difference in the electronegativity values carbon has an electronegativity value of 2.5 and oxygen is 3.5 if you type in electronegativity chart in google images you could 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 the dipole moments which are arrows that you draw from a positive atom to a negative atom notice that the arrows they point in opposite directions and so the net 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's composed of just one element it's always going to be nonpolar so the two oxygen atoms in an oxygen molecule they will share the electrons equally because they're chemically the same and so you're not going to have a positive atom and a negative atom it's just not going to happen in this case so the o2 molecule is nonpolar and helium it's just an atom it's electrically neutral the electrons are distributed evenly around that atom so it's going to be non-polar when electrons are not distributed evenly in the case of hf because fluorine pulls electrons towards the right that's why you have one side is negative and one side is positive and so that uneven distribution of electrons creates a polar molecule but in o2 the two atoms are the same so the distribution of electrons are equal which makes the molecule nonpolar so these three gases helium oxygen and co2 they will behave more ideally than hf or any stream but among these three gas molecules which one will behave most ideally compared to b c and d now the only type of intermolecular force that acts on a nonpolar molecule are london dispersion forces and those forces depend on the molar mass of the molecule so as the molar mass of the molecule increases the london dispersion forces will increase and an ideal gas is one that does not have any forces that are exerted between the gas particles so therefore we want to reduce this as much as possible the only way to do that 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's 32 based on the periodic table and helium is four so helium has the lowest molar mass so it has the lowest amount of intermolecular forces among helium atoms therefore it's going to behave most ideally now you could look at this problem from another perspective recall 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 least amount of volume will behave more ideally as well now if we look at the case of oxygen oxygen is composed of two oxygen atoms carbon dioxide is composed of three atoms and helium is composed of a single atom and helium is a lot smaller than oxygen or carbon so therefore 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 less forces and at the same time takes up less space or less volume which makes it behave more ideally so there's two reasons why substances will look um with a small molar mass will behave ideally less forces and less volume number six which of the following graphs shows the relationship between pressure and volume so think of boyle's law which graph is associated with boyle's law so if you increase the volume of a container what happens to the pressure according to boyle's law the pressure would reduce we have an inverse relationship so it's not going to be b and it's not going to be a because as we increase the volume as we move towards the right the pressure is increasing and so those two can be eliminated so is it going to be c or is it going to be d it's not going to be d the answer is c there's only two graphs that you need to be familiar with this is the graph of boyle's law it's a curved graph it doesn't decrease that leaner rate the other laws look like this it's a straight line so for charles law if you increase the temperature the volume will increase so it has this shape and then you have galu stack's law where if you increase the temperature the pressure will increase it also has the same shape and then finally avogadro's law where if you increase the moles the volume will increase so here's n and here's v number seven which are the following gases contained and the two liter vessel will exert the greatest pressure with the walls of the container is it going to be the sample of xenon gas fluorine gas or sulfur dioxide gas now 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 that the temperature is the same because each container is at 300 kelvin the only thing that's different is the moles and the pressure is proportional to the number of moles if you increase the moles of gas within the container the pressure will increase and the reason why the pressure goes up is because if you have more molecules inside a container there will be more collisions with the walls of the container and every collision exerts a force on that container and pressure is force per unit area so if you increase the number of molecular collisions the pressure will increase so therefore the right answer is so2 because we have the greatest quantity of molecules in that container so c is the right answer because it has the highest number of moles number eight which of the following is a true statement so let's look at each one heavy gas molecules exert more pressure with the walls of the container since they exert more force is that true or false now you might think a heavy object when it collides with something might 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 with light gas molecules heavy gas molecules even though they have more mass they move more slowly and later gas molecules even though they have less mass they tend to move faster and so these two they sort of balance each other out and it turns out that they exert the same pressure pressure doesn't depend on the molar mass of a gas so it doesn't really matter if the gas is heavy or light the heavy gas particles move slow and the light gas particles will move fast and so it turns out that they average out to be the same the average kinetic energy between heavy gas molecules and light gas molecules is the same it only depends on temperature so both a and b are false statements even though lighter gas molecules will have a higher average velocity which would typically yield a greater pressure the mass is less and so if you have less mass you have less force even though you have it's moving at a higher speed and here there's more mass which means there's more force but the speed is less so it turns out that the pressure is going to be the same so pressure does not depend on the molar mass of a gas now what about the density is the density directly proportional to the kelvin temperature density is equal to the pressure times the molar mass divided by rt now notice that the temperature is in the bottom of the equation anytime you increase the denominator of a fraction the value of the whole fraction goes down 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 goes down and density is mass divided by volume so the mass of the gas will be the same but any time you increase the volume of an object the density goes down and so temperature leads to an increase in volume according to charles law and that leads to a decrease in the density of the gas so the density is inversely proportional to the kelvin temperature which means c is a false statement now density is directly related to pressure and molar mass if you increase the pressure of a gas the density of that gas will increase and if you increase the molar mass of the gas the density will increase so if you're comparing two substances like co2 versus neon where everything else is the same co2 will have a higher gas density because it has a higher molar mass now what about d the average velocity of gas molecules increases with temperatures that's true or false so recall 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 speed will increase so d is a true statement if you increase the molar mass the speed will decrease as we said before heavy gas molecules move slower lighter gas molecules move faster now what about e the pressure is independent with the collision frequency of a gas and the walls of the container that's a false statement the pressure depends on the number of collisions between the gas particles and the walls of the container as the collision frequency 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 need to understand why they work the way they do so let's start with boyle's law if we decrease the volume we know that the pressure will increase the question is why does that happen go ahead and explain it feel free to pause the video and write out an explanation if you want to so let's say if we have a container this large and it contains some gas particles now if we reduce the volume why does the pressure increase when dealing with pressure you need to describe it in terms of the collisions as you reduce the volume notice that there's less space and so those particles will collide more frequently with the walls of the container and that's why the pressure goes up in the case of boyle's law so make sure you understand that when you reduce the volume the collision frequency goes up as the particles collide more often with the walls of the container the pressure goes up now the next thing we need to talk about is galoo sachs law actually let's go over avogadro's law first if we increase the moles the volume increase so let's say if we have a balloon and there's only one mole of gas particles inside the balloon if we add more gas we know the balloon will expand the question is why why does the balloon expand well for one thing as you increase the number of moles of gas particles initially the pressure is going to go up so i'm going to have to draw this visually so before the volume increases the instant you add more gas particles you're going to have more collisions between the gas particles and the inside wall of the balloon so the pressure goes up now let's say before that happen the outside pressure is one atm the pressure on the inside is also one atm so the volume doesn't change but as soon as you add more gas particles in the balloon the pressure is going to increase the inside pressure might be two the outside pressure might be one and so the forces on the inside exceed the forces on the outside and as a result due to this lack of equilibrium the balloon is going to expand and it's going to expand at until it reaches equilibrium so you're still going to have more gas molecules inside this balloon but the volume is going to double to bring back the pressure down to one atm so the volume will no longer increase when the inside pressure is equal to the outside pressure and so that's why the volume goes up so let's just review what we just said as you increase the number of moles in a container like a balloon like a flexible container initially the pressure goes up it went up from one to two and as the pressure increases the internal pressure exceeds the external pressure and so the volume will increase and according to boyle's law as you increase the volume the pressure will decrease so the net result is that there's no change in pressure the pressure goes up and then it goes back down so then that change in pressure is zero so as you increase the moles the final result is that the volume goes up it goes up due to a change in pressure but in the end the pressure goes back to its normal level when the inside pressure is equal to the outside pressure the volume will not increase or decrease it's going to stay the same when you increase the moles the pressure goes up which causes the volume to go up until equilibrium is reestablished and then the pressure goes back down so the net result is 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's going to happen if you increase the temperature to let's say 500 kelvin now the number of particles will not change however we know that the speed the root mean square velocity is dependent on the temperature so as you increase the temperature the average speed will increase and so the particles will be moving a lot faster so if they're moving faster they will collide more frequently with the walls of the container and if you can increase the collision frequency then the pressure will increase and so that's how an increase of 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 law which is a combination of the other laws as the temperature goes up the volume goes up now let's talk about why and let's use a balloon for this example well if you increase the temperature we know that the average speed of the molecules will increase and this will lead to a greater collision frequency and as a result the pressure will go up so let's say if we have a balloon and the inside pressure is one atm and the outside pressure is one atm at 300 kelvin now as we increase let's say the temperature to 600 kelvin the molecules inside the balloon will be moving faster and so instantly the pressure is going to go up from 1 atm to 2 atm now because the internal pressure exceeds the external pressure the gases on the inside will exert more force compared to the gases on the outside and so the balloon will expand as it expands the internal pressure will decrease and it's going to stop expanding until the pressure is equal to the outside pressure so it's going to continue to expand until the inside pressure is back to one atm so once the inside and the outside pressure the same it will stop expanding the volume will no longer change and so that increase in pressure will lead to an increase in volume which brings back the pressure back to one atm or to the atmospheric pressure so this increase in pressure and then a decrease in pressure negates each other so the net effect is that the pressure remains the same as we can see but the volume increases so an increase in temperature leads to an increase in volume if you have a container that is flexible that is 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 doesn't expand but if the container is allowed to expand the pressure will reduce allowing the volume to expand and so we have charles law so that's the difference between galux saxon law and charles 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 so we have charles law you