isotope bromine 79 has an atomic mass of 78.9183 amu or atomic mass unit and we're given the relative percent abundance for that isotope we're also given the same information for isotope bromine 81. we have the atomic mass and the percent abundance so with this information how can we calculate the average atomic mass of the element bromine so there's a formula that we could use it's equal to the mass of the first isotope times its percentage as a decimal plus the mass of the second isotope times its percentage now if you have three isotopes this can continue or if you have four so it would be plus m3 p3 plus m4 p4 but we only have two so we can stop here in this case m1 is the mass of the first isotope so that's going to be 78.9183 p1 is the percentage for that isotope now we need to convert it to a decimal number and so we got to divide 50.69 by a hundred so that's going to be 0.5069 now the second mass is 80.9 163 and now we need to multiply by its percentage which is 0.4931 so you can also move the decimal point two units to the left if you're dividing that number by a hundred now let's plug these numbers into a calculator and let's get the answer so what i got is 79.90 and so this is the average atomic mass of the element bromine and you could check this answer out you can go to google images look up the average atomic mass for bromine using a periodic table and you should get about 79.9 and so that's how you can confirm your answer in this case so that's it for this problem now you know how to calculate the average atomic mass of an element now let's move on to our second example the average atomic mass of boron is 10.81 atomic mass units based on the stable isotopes b10 and b11 and we're given the mass of each of those stable isotopes part a calculate the relative percent abundance of each isotope so in the last problem we had the percent abundance of bromine 79 and bromine 81. it was about 50.69 and 49.31 respectively in this problem we need to calculate those relative percent abundances so basically we're working in reverse now we're going to use the same formula where the average atomic mass is equal to m1 p1 plus m2 p2 since we still have two isotopes we're dealing with if you go to the periodic table you should see this for boron it has an atomic number of 5 and an average atomic mass of 10.81 now it's important to understand that when you see this number it represents not the mass of an individual isotope of boron but rather the average mass of all the isotopes of boron on the earth so just keep that in mind on the left side we're going to plug in the average atomic mass which is 10.81 the mass of the first isotope we're going to say that m1 corresponds to b10 and m2 p2 corresponds to b11 so the mass of the b10 isotope is given to us is 10.0129 times its percentage now the percentage we don't know so we're looking for that let's call it x now the mass of the second isotope b11 is 11.0093 now what should be the percentage of the second isotope let's think about this let's assume that thirty percent of the boron atoms are b10 if there's only two stable boron isotopes that means that the other seventy percent has to be b11 because these two have to add up to 100 now we need to deal with decimal numbers and not percentage based numbers so 30 is basically 0.3 70 is 0.7 so if point three is x we could say that one minus x is point seven because one minus point three will give us point seven and that's what you need to understand when dealing with this problem so if p1 is x p2 has to be 1 minus x now it's time to do the math so on the right side we have 10.0129 x and we need to distribute this number to 1 and negative x so it's going to be 11.009 and then minus 11.0093 times x so let's go ahead and combine like terms so 10.0129 minus 11.00 that's going to give us negative 0.9964 x now our next step is to subtract both sides by 11.0093 so on the right side this is going to disappear so this is going to be let's see 10.81 minus that number is negative 0.1993 and so that's equal to negative 0.9964 x so let's get rid of some stuff here i'm just going to rewrite what i have above now what we need to do at this point is divide both sides by negative 0.9964 and so this will give us the value of x which is 0.2 so p1 was associated with x and p2 was associated with 1 minus x now if x is 0.20 that means that one minus x which is one minus point twenty that's point eighty so this tells us that twenty percent of all of the boron atoms is the b10 isotope and 80 percent of all of the boron atoms consist of the b11 isotope now does that answer make sense notice that the average is 10.81 the average atomic mass is closer to the mass of the heavy isotope the reason for that is because we have more of b11 and less of b10 so because b11 is more abundant the average atomic mass is closer to the mass of the b11 isotope now let's move on to part b in a sample of 600 boron atoms how many b10 atoms are there let's find out so we know that twenty percent of the boron atoms will be the b10 isotope so we gotta multiply this by 20 so this is the same as 600 times 0.2 and 600 times 0.2 is 120. so in a sample of 600 boron atoms 120 out of those 600 boron atoms will be the b10 isotope in the case of b11 it's 600 times 0.8 and that's going to be 480 b11 atoms and as you can see the total adds up to 600. so if you had a sample of let's say a thousand boron atoms 800 will be b11 and 200 of those thousand would be the b10 isotope now let's move on to the next problem calculate the molar mass of each of the following substances well first we need to know exactly what the molar mass mean what is molar mass the molar mass of a substance is the mass in grams of one mole of the compound so let me give an example let's analyze carbon carbon has an atomic mass of 12.01 and so what this means is that carbon has a molar mass of 12.01 grams per mole that's how you could find the molar mass using the periodic table so if we had one mole of carbon we would have a mass of 12.01 grams now you might be wondering what is a mole a mole represents a quantity of something for instance when you hear the word dozen what do you think of a dozen is 12. so if you have a dozen pens you have 12 pence if you have a dozen eggs you have 12x well a mole is like a dozen it represents a number a quantity a mole is 6.022 times 10 to the 23. in this case one mole of carbon atoms is equal to 12.01 grams of carbon and so the molar mass gives us a conversion factor it tells us the connection between the quantity of carbon atoms and the mass of carbon so here is what you need to take from this when you're looking for the molar mass of a substance you need to find the atomic mass of the elements involved and the units will be grams per mole or you can express it in terms of atomic mass units i'm going to use grams per mole but you're going to find it based on a periodic table looking at the larger of the two numbers here so let's work on part a what is the molar mass of potassium fluoride so we need to add up the atomic mass of potassium and the atomic mass of fluorine so you need to get a periodic table and look up the numbers using that table so the atomic mass of potassium is 39.1 and atomic mass of fluorine is about 19. so if we add these two numbers 39.1 plus 19 that's going to give us 58.1 and the units will be grams per mole so that's how we could find the molar mass of a substance so what this means is that one mole of potassium fluoride has a mass of 58.1 grams so make sure you understand what is meant by the molar mass it tells us the mass of the substance if we have one mole of that substance now let's move on to part b so let's calculate the molar mass of sodium carbonate so what we have is two sodium atoms or in this case ions because it is an ionic compound we have a carbon atom and three oxygen atoms so the atomic mass for sodium is 22.99 and for carbon it's 12.01 based on the periodic table and for oxygen is 16. so all we need to do is basically just add these numbers up so go ahead and type this into your scientific device so you should get 105.99 grams per mole and so that's the molar mass of sodium carbonate so one mole of na2co3 has a mass of 105.99 grams now let's move on to part c so what is the molar mass of aluminum sulfate so i'm just going to rewrite the chemical formula so you can see it more clearly in this formula we have two aluminum atoms we have three sulfur atoms there is an invisible one here if you don't see it so if it's not there it's assumed to be one so it's basically one times this subscript of three and that gives us three sulfur atoms now how many oxygen atoms do we have in this compound so in this case it's going to be four times three because we have three sulfate units and each sulfate carries four oxygen atoms so we have a total of 12 oxygen atoms now the atomic mass for aluminum is 26.98 and the atomic mass of sulfur is 32.06 and for oxygen we know it's 16. so let's go ahead and plug these numbers in and see what answer we get so i got 342.14 grams per mole so that's the molar mass of aluminum sulfate now let's move on to the next problem how many moles are in 72 grams of methane in order to do these problems and those that are coming up next you need to become proficient at converting units and for those of you who might need help in this regard i have another video entitled converting units with conversion factors and i'm gonna post a link in the description section of this video so you can find it there if you don't want to search on youtube but i recommend watching that video so you can get good at converting units because every other problem that's gonna come after this one we're going to do a lot of unit conversion so make sure you understand that topic before moving forward so let's work on part a how many moles are in 72 grams of methane so what we need to do is we need to convert grams to moles and the only way we can do that is by using the molar mass so that's the first thing we need to do we need to find the molar mass of methane so methane contains one carbon atom and four hydrogen atoms now the atomic mass of carbon is 12.01 and for hydrogen it's 1.008 [Music] so let's go ahead and plug these numbers in so you should get a molar mass of 16.042 grams per mole now what we need to do is take this information and convert it into a conversion factor so what this means is that one mole of methane has a mass of 16.042 grams so this is our conversion factor so now what we are going to do is we're going to start with the information that we're given and that is 72 grams of methane and we're going to use our conversion factor to convert it from grams to moles so the conversion factor will be placed in the second fraction so because we have grams on the top left we need to make sure that grams of methane will be on the bottom right so that those units will cancel and if grams is on the bottom then moles of methane must go on the top now the number that's in front of the moles of methane is a one and the number in front of the grams is 16.042 so that's the way we need to set it up now we need to divide because we have a number on top and a number on the bottom if we had two numbers on top then we would multiply so to get the answer it's going to be 72 divided by 16.042 and so it's 4.488 moles of methane so that's how you can convert from grams to moles part b how many grams are present in a sample of 2.5 moles of no2 so this time we're going backwards we need to convert from moles to grams so let's start with what we're given 2.5 moles of no2 now just like before in the next fraction we need to put the conversion factor so in order to convert from moles to grams we need the molar mass of no2 and so we have one nitrogen atom and two oxygen atoms so the atomic mass for n is 14.01 and for oxygen is 16. so 2 times 16 that's 32 plus 14.01 that's going to give us a molar mass of 46.01 grams per mole so from this let's write our conversion factor and that is that one mole of nitrogen dioxide contains 46.01 grams of no2 so this right here is our conversion factor now how should we take this information and how should we place it in this fraction so looking at the unit on the top left we have moles of no2 so we need to make sure that it's on the bottom right and so on the top we're going to put grams of no2 now the number that's associated with moles is one and the number associated with the grams is 46.01 so this time because we have two numbers that are both on top of the fractions we need to multiply those two numbers so it's going to be 2.5 times 46.01 and so the answer is 115.00 grams of no2 and so that's how you can convert moles to grams that's how you can set up the conversion process and make sure that these units cancel now let's move on to part c how many atoms of carbon are present in 7.2 moles of carbon so in this problem we need to convert from moles to atoms if you want to go from moles to atoms or atoms to moles here's what you need to know we talked about this earlier one mole of something it could be atoms molecules pens books it doesn't matter one mole of something is equal to 6.022 times 10 to the 23. which you know it as avogadro's number and so this is the conversion that we're going to use to go from moles to atoms so as always let's start with what we're given and that is 7.2 moles of carbon now what should we write in the next fraction since we have moles of carbon on the top left we're going to put that on the bottom right so one mole of carbon is going to equal 6.022 times 10 to the 23 atoms of carbon and so make sure you set it up in such a way that the units moles of carbon cancel so what we need to do in this case is we need to multiply 7.2 by avogadro's number and so you should get 4.3358 times 10 to the 24 atoms of carbon and so that's how you can convert from moles to atoms by using avogadro's number now let's move on to the last part of this question how many moles are in 4.6 times 10 to the 23 atoms of nickel so let's start with the information that we're given let me write atoms of nickel when you're converting this three things that you need you need the number you need the unit it could be grams moles atoms molecules and you need the substance right now in the problems that we're dealing with we're only changing the unit of course we get a different number of course but we haven't changed the substance yet in other problems that's going to be something you need to be aware of so not only do you need to convert the unit you may need to convert from one substance to another so just keep that in mind so once again we're going to use the same conversion one mole is equal to 6.022 times 10 to the 23. so this time i need the unit atoms on the bottom so i can say that there's 6.022 times 10 to the 23 atoms of nickel for every one mole of nickel because what's on the top must equal what's on the bottom in the conversion fraction so these units will cancel and now we're going to get what's left over the unit on the top that is moles of nickel so this time because we have a number on the top and one on the bottom we need to divide instead of multiplying so it's 4.6 times 10 to the 23 divided by 6.022 x 10 to the 23 and so you should get 0.7639 if you round it moles of nickel and so that's it for this problem now let's consider number five how many atoms of iron are in a sample of 235 grams of fe so in this problem we need to convert from grams to atoms but we can't do so directly what we need to do is convert from grams to moles we know how to do that using the molar mass and then once we have the number of moles we could use avogadro's number to convert to atoms so this is a multi-step process now the first thing we need to do is look up the molar mass of fe so using the periodic table you should get 55.85 grams per mole so what this tells us is that one mole of fe is equal to 55.85 grams of fe so this is our first conversion factor that we need to use the second one is just avogadro's number we know that one mole of fe contains 6.022 times 10 to the 23 atoms of fe so let's begin always start with what you're given in this case 235 grams of fe now let's use the first conversion factor to convert it from grams to moles so we need to put grams on the bottom one mole of fe has a mass of 55 point grams of fe so we could cancel the unit grams of fe now the next thing that we need to do is use the last conversion factor we need to convert from moles to atoms so since we have moles on the top let's put it on the bottom so one mole of fe contains 6.022 times 10 to the 23 atoms of fe so now let's perform the calculation so what we're going to do first is we're going to take 235 and divide it by 55.85 go ahead and type that in so you should get at this point 4.2077 and then take that result and multiply by this number so the final answer that i got is 2.53 times 10 to the 24 atoms of fe and so that's it for this problem that's how you can convert from grams to atoms without changing the substance now if you look at part b the substance is going to change part a and part b are similar because we're given the grams of um excuse me of this substance that could be glucose or fructose c6h12o6 and we want to convert it to the atoms of carbon so both in part a and part b we're going from grams to atoms but let me show you the difference between the two because when you're working out these problems you need to pay attention for this so in part a we've converted the grams of fe to the atoms of fe and in part b what we need to do is go from the grams of let's say glucose to the atoms of carbon so the difference between part a and part b is that in part a the substance is not changing however in part b we need to change the substance so part b requires an extra step relative to part a so let's begin well first let's write out a map of what we need to do or an outline so we're going to start with the grams of c6h12o6 and then using the molar mass we're going to convert it to moles and then once we have the moles what we could do is convert it to the atoms of glucose and then once we have that now we need to change the substance so we're going to convert glucose into carbon so the first step we need to use the molar mass for the second step avogadro's number for the third step we need to use the formula that we have here so let's go ahead and begin so let's start with what we're given and that is 356 grams of glucose or fructose they have the same molecular formula now let's convert it to moles so we need the molar mass we have six carbon atoms 12 hydrogen atoms and six oxygen atoms so the atomic mass of carbon is 12.01 and for hydrogen it's 1.008 and for oxygen it's 16. so let's go ahead and type this in so you should get 180.156 grams per mole so what this means let me see if i can use less space is that one mole of glucose has a mass of 180.156 grams now we could cancel grams and glucose so now let's use avogadro's number so let's use the fact that one mole is equal to 6.022 times 10 to the 23. so we could say one mole of glucose has 6.022 times 10 to the 23. now we can't say atoms because c6h12o6 that entire particle is not an atom but rather it's a molecule a molecule is a particle that it's made up of many atoms so we need to say we have this many molecules of glucose let's see if i can fit it in here and run out of space so now we could cancel the unit moles of glucose now the last step to change the substance we need to use the chemical formula of glucose in other problems later in this video we can use the coefficients of a balanced chemical equation to change the substance and we'll talk more about that later but for now we need to use the formula of glucose so which is c6 h12o6 so according to this formula we could say that one molecule of glucose contains six atoms of carbon do you agree with that so this is our conversion factor for the last step so since we have molecules on the top we need to put it on a bottom so i could say that one molecule of glucose contains six atoms of carbon so now every unit has been cancelled except the unit that we want to get which is atoms of carbon so now we just got to do the math so it's going to be 356 divided by 180.156 take that result and then multiply it by avogadro's number and then multiply that by 6. so the final answer that i have is 7.14 times 10 to the 24 atoms of carbon so that's how you can go from the grams of let's say substance a to the atoms of substance b now let's move on to part c what is the mass of a sample in grams that contains 3.5 times 10 to the 24 molecules of so3 so as always let's start with what we're given and let's plan out what we need to do so we just need to find the mass of the sample so right now we have molecules of so3 so3 is a molecule it's consistent of i mean it's made up of many atoms so once we have molecules using avogadro's number we can convert from molecules to moles and then using the molar mass we can go to grams of so3 now we don't need to do anything else because once we have the mass in grams that's it we're done so we don't have to change the substance in this example so using avogadro's number we could say that there's 6.022 times 10 to the 23 molecules of so3 for every one mole of so3 so we could cancel these units and now for the last step which i'm going to rewrite here we need the molar mass so we have one sulfur atom and three oxygen atoms sulfur has an atomic mass of 32.06 and for oxygen is just 16. and so you should get 80.06 grams per mole so what this means is that one mole of sulfur trioxide has a mass of 80.06 grams and so since we have the unit moles of so3 on the top left in the third fraction it has to be on the bottom right so that they will cancel and now let's perform the calculations so it's going to be this number 3.5 times 10 to the 24 divided by avogadro's number and right now you should have like 5.812 and then we're going to multiply by 80.0 and so the final answer is 465.3 grams of so3 and so that's it for this example now let's move on to part d the last part of this problem calculate the mass in grams of a sample of silicon tetrafluoride that contains 2.8 times 10 to the 23 atoms of fluorine i know i marked over it but that's atoms of fluorine feel free to pause the video if you want to try this problem so we're given the atoms of fluorine and we need to convert it to molecules of sif4 so first let's go from atoms to molecules and we're going to change the substance and then we're going to go from molecules to moles using avogadro's number and then using the molar mass we're going to go from moles to grams so it's helpful if you can write out like an outline of what you need to do with regard to your conversion process so let's start with what we're given 2.8 times 10 to the 23 atoms of fluorine now in silicon tetrafluoride we can say that there's four atoms of fluorine for every one molecule of silicon tetrafluoride so this is the conversion factor for the next step and so i need to put the atoms of fluorine on the bottom and on top one molecule of sif4 so i could cancel these units atoms of fluorine now the next conversion factor that we need is this one we could say that one mole of silicon tetrafluoride contains 6.022 times 10 to the 23 molecules of silicon tetrafluoride so i need to put this part on the bottom and so i could cancel these units and on top of the third fraction i'm going to write one mole of silicon tetrafluoride now the last step is to convert from moles to grams and so i need the periodic table for that so in sif4 i have one silicon atom and four fluorine atoms silicon has an atomic mass of 28.09 and fluorine has an atomic mass of 19. and so if we add these values this will give us 104.09 grams per mole so what we can write in the next fraction is that one mole of silicon tetrafluoride has a mass of 104.09 grams and so now we could cancel the unit moles of sif4 so to do the math it's going to be this number divided by four which is seven times ten to the twenty-two take that result divided by avogadro's number and right now you should have point one one six and then multiply it by 104.09 so the answer that i have is approximately 12.1 grams of silicon tetrafluoride and so that's it for this problem so now you know how to go from grams to atoms and atoms to grams and at the same time changing the substance from one element into a compound number six calculate the mass of 25 carbon atoms in amu or atomic mass units and in grams so what do you think we need to do in this problem how can we get the answer well first let's calculate the answer in amu now using the periodic table you'll find that the atomic mass of carbon is this number on the bottom 12.01 so we can write a conversion factor we could say that one carbon atom has a mass of 12.01 amu atomic mass units so if that's the case how many atomic mass units are present in 25 carbon atoms so we're going to set it up as a conversion problem so we're going to start with what we're given 25 carbon atoms and then use this to convert it to amu so each carbon atom has a mass of 12.01 amu and so we could see the units carbon atoms cancels and so it's just going to be 25 times 12.01 so the answer for the first part of the problem is 300.25 amu now let's convert this to grams another conversion factor that you want to know is that 1 gram is equal to 6.022 times 10 to the 23 atomic mass units so what we could do is start with 300.25 amu and then in the next fraction we could say that one gram is equal to this many atomic mass units and so amu will cancel and it's just going to be 300.25 divided by avogadro's number and so this will give us this answer 4.986 times 10 to the negative 22 grams and so that's how you can convert from atomic mass units to grams now another way in which you could have done this problem let's say if you just want to go from atoms to grams you could start with 25 carbon atoms and then using avogadro's number you can convert it to moles so one mole of carbon is equal to 6.022 times 10 to the 23 atoms of carbon so we could cancel these units and then we have the molar mass of carbon one mole of carbon has a mass of 12.01 grams and so this will give us the same answer and that is 4.986 times 10 to the negative 22 grams of carbon so as you can see there's different ways in which you can arrive at the same answer number seven calculate the percent composition by mass of each element in the compound c6 h12o6 so how do we find the mass percent of an element in a compound here's the formula that you need to know so let's say we want to find a percent by mass of the element carbon what we need to do is take the mass of carbon this could be just the molar mass of carbon and divided by the total mass or the total molar mass of the compound which is c6h12o6 and then we're going to multiply that by 100 and so that's how you find the mass percent of an element in a compound it's just the mass of that element divided by the mass of the compound times 100 so if you want to try this problem feel free to pause the video and work on it yourself and then you could play the video again and see if you got the right answer so let's start with carbon the molar mass of carbon is 12.01 now in this compound we have six carbon atoms so we need to multiply the molar mass by six now on the bottom we're going to put the total motor map excuse me the total molar mass of the entire compound and so that's six carbon atoms plus 12 hydrogen atoms where each hydrogen atom has an atomic mass of 1.008 and then we have the six oxygen atoms and then we're going to multiply this whole thing by a hundred percent so six times 12.01 that is 72.06 and i'm going to type in this whole thing and let's see what i'm going to get so the molar mass for the entire compound that is glucose or fructose is 180.156 and the units grams per mole or you could say atomic mass units now remember this number because we're going to use it when calculating the mass percent of hydrogen and of oxygen later in this problem so 72.06 divided by 180.156 times 100 so that gives me 39.999 which i'm going to round it and say it's about 40 so that's the mass percent of carbon in this compound now what about the mass percent of hydrogen so what we're going to do is take the total mass of hydrogen so we have 12 hydrogen atoms each with an atomic mass of 1.008 and then we're going to divide it by the molar mass of the compound which is 180.156 and then multiply everything by a hundred percent and so you should get six point seven one four percent so i'm going to round that and say it's 6.7 now the last one is oxygen so in the compound c6h12o6 there's six oxygen atoms each with an atomic mass of 16 and once again we're going to divide it by the total molar mass of the compound which is 180.156 and then multiply it by 100 percent the answer that i got is 53.3 so that is the mass percent of oxygen now notice that if you add up these three numbers you should get a hundred percent that has to be the total any time you're calculating the percent by mass of every element in a compound it should all add up to 100. if it doesn't that means somewhere along the lines there's a mistake and you need to look for it so that's it for this problem now you know how to calculate the mass percent of an element in a compound you