today I want to give you the formulas and equations that you need to know if you're currently studying the gas laws in electri chemistry now this is going to be a fast-paced video so I'm going to give you a lot of formulas in a short time let's begin the first one you need to know is the definition of pressure pressure is force divided by area now in physics the standard unit of pressure is the is pascals and the standard unit of force in physics is Newtons and area is square meters so one pascal is 1 Newton per square meter so that's the standard unit of pressure but now in chemistry pressure is going to be in units of ATM typically you need to know that 1 atm is equal to 10,300 pluss which is 101.3 kilop pascals Now 1 atm is also equal to 764 which is also equal to 760 mm of mercury and this is also equal to 14.7 psi pounds per square inch in chemistry typically you'll be using these three conversion factors the other ones are less common but you could still use them in certain problems now the first Formula we're going to talk about is the idog gas law PV is equal to nrt in this equation R is the gas constant which is 8 206 and the units are lers time ATM per Mo per Kelvin so the units of R tell you the units that you need to use in this formula so in order for this formula to work the pressure has to be in ATM the volume has to be in liters n is the number of moles and T is the temperature as you could see in kelvin if you need to calculate the Kelvin temperature you could use this formula if you know the Celsius temperature it's the Celsius temperature plus 273.15 if you're given the Fahrenheit temperature you can calculate the Celsius temperature using this formula now there's another value for r as well R also equals 8.3145 jewles per mole per Kelvin now with the ideal gas law equation 95% of the time or even more you'll be using this value for r i want you to understand if you use the second value for R the units will be different so if you want to use that one you need to use basically the physics units for pressure which will be in pascals for volume instead of using liters you need to use cubic met the temperature will still be Kevin and will still be in moles so that's the difference between the two R values so if you're going to use this r value make sure the pressure is in ATM and the volume is in liters if you're using the second r value make sure the pressure is in pascals and volume is cubic meters now going back to this equation if we were to solve for R we would get EV over NT and if we write it twice but with a different subscript this will give us a variant of the combined gas law so let's start with this P1 V1 over N1 T1 equals P2 V2 over N2 T2 to get the combined gasa equation the moles have to be the same so if the moles are held constant you can get rid of N and you'll get this formula T1 V1 over T1 is equal to T2 V2 over T2 so that is the combined gas log in order for this equation to work pressure has to be in the same units so if P1 is in ATM P2 has to be in ATM if P1 is in tour P2 has to be in tour if P1 is in millimeters of mercury P2 has to be in millimeters of mercury the same is true for the volume if V1 is in liters V2 has to be in liters if V1 is in milliliters V2 has to be in milliliters you could use both units but they have to match the temperature has to be in kelvin for this to work you can't use Celsius or Fahrenheit even if if they match for temperature pressure and volume you can use different units but they have to match for temperature it has to be in kelvin only so that's the first equation that we can get from this equation now the next equation is going to be boils law if we hold the moles and the temperature constant we're left with what we have on top which is P1 V1 is equal to P2 V2 so that's Bo's law his law describes the relationship between volume and pressure which is an inverse relationship as you increase the volume the pressure decreases now let's move on to Charles law the Charles law we're going to hold the pressure and the moles constant so we're left with V1 over T1 is equal to V2 over T2 so his law describes the relationship between the volume of a gas and a temperature as you incre increase the temperature the volume of the gas is going to increase it's going to expand and so that relationship is associated with Charles law next up we have gusak law which shows the relationship between pressure and temperature so holding volume and moles constant we get P1 over T1 is equal to P2 over T2 so that's Galu sax law if we were to plot a graph for this placing temperature on the x-axis pressure on the Y AIS this too shows a direct relationship between the two much in the same way as Charles law as the temperature goes up pressure goes up so imagine having a gas in a rigid container if you heat up the gas the pressure on the inside is going to build now the next one has to do with AOG godel's law for this one we're going to hold the pressure and a temperature constant so we get a relation between volume and moles so we get V1 over N1 is equal to V2 over N2 so if we were to plot the number of moles on the x- axis and the volume on the Y AIS as we increase the moles the volume is going to increase so in other words the more moles of gas that you have the greater the volume that that gas will occupy so imagine blowing more air inside a balloon the balloon is going to expand now let's go back to this formula PV is equal to nrt the ideal gas law equation we know that the moles is equal to the mass / the molar mass or the molecular weight of the gas so what I'm going to do is I'm going to replace n with M over MW and then multiplying both sides by the molar mass we get this equation so the pressure times the volume time the M mass or the molecular weight of the gas is equal to the mass of the gas time r time T So this formula is very useful if you need to calculate the molar mass of a gas I mean you could use a combination of these two formulas but if you want to write this down in your list it'll be helpful if you need to calculate the mass or the molar mass of a gas now starting from that formula I'm going to divide both sides by V so I get pressure time the M mass is equal to to m / V * RT m/ V Mass / volume is density so we get this and then dividing both sides by RT we get the formula that will help us to calculate the density of a gas which is this the density of a gas is equal to the pressure time the M mass of the gas / RT so if you know the M mass of the gas you can calculate the density of that gas if you need to determine the identity of the gas you could use a density calculate the molar mass and with the m mass that can help you identify what kind of gas you have so make sure you add these two formulas to your list now you need to be familiar with the term St P STP stands for standard temperature and pressure at STP the standard temperature is 270° I mean let me say that again I said it too fast 273° Kelvin which is the same as 0° C the standard pressure is 1 atm or 760 T now another fact that you want to to keep in mind is that at STP one Mo of gas occupies a volume of 22.4 l so this is very useful when dealing with uh gas through geometry problems at STP you can convert from moles to liters easily and I do have some practice problems in the description section that explains how to do that so feel free to take a look at that when you get a chance now the next thing we need to talk about is Dalton's law of partial pressures the total pressure inside a container is the sum of the individual partial pressures um by exerted by each gas so imagine if you have a container with the the gases nitrogen oxygen and carbon dioxide the total pressure will be the sum of the partial pressures of each of these gases so in this container nitrogen will exert a certain amount of pressure on that container oxygen will exert a certain amount of pressure and the same thing is true for carbon dioxide so each substance will exert their own partial pressure on that container and when you add it up you get the total pressure exerted by all of the gases in that container now the partial pressure of substance a is equal to the mole fraction of that substance times the total pressure and the mole fraction is basically the moles of that substance divided by the total moles mole fraction is also equal to the partial pressure of that substance divid by the total pressure now the sum of all the mole fractions for all the substances inside a container is going to add up to one so those are some other formulas you want to add to your list the next thing you need to know is that the average kinetic energy of a gas is directly proportional to temperature now for this formula you want to use 8.3145 Jew per mole per Kelvin for the value of R when you do so the kinetic energy will be in jewles and a temperature has to be in kelvin so this equation helps us to see the relationship between the average kinetic energy of a gas with the temperature so if you increase the temperature of a of a sample of gas the average kinetic energy will increase the next formul need to be familiar with is the root mean Square velocity of a gas and that's going to be equal to the square root of 3 RT over the molecular weight of that gas for this Formula 2 R is going to be 8.3145 jew per mole per Kelvin when you use that particular value of r the velocity that you get is going to be in me/ second now the molecular weight is not going to be grams per mole it's going to be kilog per mole in order for this formula to work so for instance O2 when you use a periodic table it has a m mass of 32 G per mole converting G to kilog you need to divide by 1,000 so that's going to be 032 kilg per mole now the next thing we're going to talk about is Graham's law of infusion the basic concept of infusion imagine if you have a container my drawn is not perfect but we'll make do of it let's say there's a hole in this container and you want to find out the rate at which nitrogen gas escapes this hole as it leaves that hole this is related to the concept of effusion it euses out of that container now the rate of effusion is inversely related to the square root of the molecular weight of the gas so you'll see this formula associated with Graham's law of a fusion R2 R1 is equal to the square Ro T of MW 2 mw1 I mean mw1 over MW2 so if you know the rate of diffusion of one gas and you know it's molecular weight you could find the rate of diffusion of another gas if you know it's molecular weight so as the molecular weight of a gas increases the rate of a fusion decreases and it makes sense because heavy gases they tend to move a lot slower lighter gases move faster this equation is based on this formula as you could see if you look at the relationship between velocity and molecular weight they're inversely related the molecular weight is on the bottom of the fraction and it's inside of the square root much in the same way as we see this formula is so the more mass that a gas particle has the slower it's going to be when moving so that's the basic idea behind Gram's law of a fusion now you might see some problems that may ask you how long it's going to take for a certain gas to diffuse so they'll introduce elements like time instead of rate we need to know that time is inversely related to rate in other words a gas particle that can move faster is going to take a shorter time to ause out of that container a gas particle that's heavier and moves slower is going to take a longer time to ause so the rate of effusion is inversely related with time so knowing that R2 over R1 is going to equal T1 over T2 so time and rate they're inversely related but time and molecular weight they're somewhat related so those are the formulas you could use when dealing with Graham's law of infusion and I do have practice problems on this topic so if you want to see how to use this formula feel free to check out the links in the description section below I have a ton of videos on the gas laws that you know you could really see how you can put these equations to use so feel free to take a look at that when you get a chance and thanks for watching