so we've talked about moles we've talked about mass we've talked about atomic mass we've added up how do we find the atomic mass off the table we've even looked at how to add up molar mass off of the table looking at water and aluminum phosphate so molar mass what is molar mass why do we care and why are we going to use it for the rest of our general chemistry career molar mass is the mass of one mole it's mass per mole it's called molar mass and it can be used to convert from grams to moles to moles to grams other terms that you're going to see for molar mass include molecular weight formula weight and formula mass oh and of course molecular mass um so again molar mass is just the mass of one mole of a substance so the molar mass of carbon is 12.01 grams exactly 12.01 grams of carbon is exactly one mole of carbon which contains exactly 6.022 times 10 to the 23rd carbon atoms a very useful conversion that you're going to use a lot for molar mass is this molar mass is equal to your mass over your moles molar means per mole so this is supposed to be like a script m i can't find that in the font but what i mean by a script um and the way i write this personally is i write an m like this with a tail on it this is your number of grams divided by the number of moles there's a number of times that so often throughout the semester you're going to have to use molar mass to convert from grams to moles of something for a specific reason we have to compare things through moles because remember mole is a number word if we're comparing how many moles of something react with how many moles of something else we're actually looking at the number of each species that's reacting mass is not the same thing because every atom has a different weight or a different mass because it's dependent upon the number of protons neutrons and electrons for that specific atom even within the same element we now know they can have a different mass because of isotopes which is why we need to use molar mass the other reason though i really emphasize this is because one question i love to ask and i can ask a variety of questions throughout the entire year is giving you the mass of something and giving you some information to determine the moles of something and then asking the identity of that species and students more often than not get tripped up by this i'm not asking you this to trip you up i'm not trying to trick you i'm not trying to make it difficult i'm trying to make you remember the basis of what you know about chemistry and that basis is if you know the number of grams you have and you can use that number of grams to determine the number of moles you have through some other form or some other calculation you can then determine the molar mass and that molar mass can lead you back to the identity of that species so let's go ahead and add some up what is the molar mass of ammonium nitrate nh4no3 is ammonium nitrate if you are filling this out along with the student notes you see in the notes i wrote out the words ammonium nitrate you haven't learned naming quite yet it comes in the next chapter so that's why i went ahead and put these in formula but in your notes i left it as ammonium nitrate because it's really good to see even before you learn naming to start to see these things correlated together sometimes when i'm speaking i would say um sometimes while speaking i would actually say nh4nl3 other times i'll say ammonium nitrate sometimes it depends on the compound um sometimes it just depends on what my brain thinks for that moment but i correlate them back and forth very quickly they mean the same thing saying ammonium nitrate or nh4nl3 tells me it's still ammonium nitrate so that just comes back to terminology but enough of that how do i find the molar mass well i need to add up what each one of these atoms weighs based on the mass on the periodic table and figure out what an overall mole of this entire thing would weigh i see here i've got two nitrogen atoms i've got four hydrogen atoms and three oxygen atoms if i look at the table this means i have two times the atomic mass of nitrogen and the atomic mass of nitrogen according to the periodic table is 14.01 grams per mole this gives me a value of 28.02 grams per mole i have four hydrogens the atomic mass of hydrogen is 1.008 grams per mole this gives me a mass of 4.032 [Music] grams per mole note i'm leaving these with the correct number of sig figs in them that's why i've written the one outs of two decimal places and one out to three it's just the number of sig figs i have for the numbers and three oxygens oxygen is 16.00 grams per mole so this equals out to 48.00 grams per mole but i'm not quite done i need to sum these together the sum of all of this is 80.052 grams per mole but that is my calculated answer i need to look back and see where are my 6x since i'm doing addition subtraction you look at number of decimal places i have two i have three and i have two i'm going to round this to the second decimal place and so i would say the molar mass is 80.05 grams per mole for ammonium nitrate now why did i write the identity of the species here do i need and do i need to not technically you don't need to but very soon we're going to be converting between different species and it's always better to label what you have now so that you're in the habit of it so when you start converting between species that you don't get lost on what you're actually looking at okay how about the molar mass of calcium permanganate so this calcium permanganate what is the molar mass here i have one calcium so 1 times 40.08 grams per mole i have two manganese there's a two out here that's distributed through the entire compound because permeate is a polyatomic so i have two manganese looking up manganese on the periodic table maybes is one of your transition metals calcium is one of your alkaline earth metals group two magnesium is a transition metal so 54.94 grams per mole and permanganate itself has four oxygens but this compound has two permanganates for every one calcium which means that i have eight oxygen atoms eight times 16.00 grams per mole this gives me 40.08 grams per mole one hundred and nine point eight eight grams per mole i'm going to underline that first eight that's where my sig figs are at and 128.0 grams per mole go ahead and sum this up and when you sum this up you should get a value of 277.96 grams per mole go back and look at your sig figs click two decimal places one decimal place one decimal place i'm going to round this to the first decimal and i'm going to say 278.0 that point zero matters that is your significance your precision your measurement grams per mole for calcium permanganate how about how many moles of carbon are in 25 grams of carbon now i'm converting from grams to moles let's go ahead and look at that how do i do that well for carbon i'm going to need its atomic mass the atomic mass of carbon is 12.01 grams per mole i'm going to write down first what do i want to know i want to know the number of moles of carbon next i'm going to write down what i'm given i'm told that i have 25 grams of carbon i want to convert this to moles so i'm going to put what i want to convert to in my numerator because that's going to be my numerator here and then i'm going to divide by what i'm trying to cancel out and to do that i know that 12.01 grams of carbon weighs or 12.01 grams of carbon is exactly one mole of carbon and that also cancels out my grams of carbon when i calculate this out i get an answer of 2.08 moles of carbon does that answer make sense to you um some of these answers are hard to correlate especially when you get into scientific notation which we're going to do in the next example but in this example it absolutely makes sense to me i know 25 i'm starting with 25 grams of carbon i know one mole of carbon weighs about 12 grams that means two moles of carbon weighs about 24 grams i have 25 grams i have 2.08 moles yep that answer makes sense to me how many iron atoms are in 675 grams of iron find iron on your periodic table it's in the first row of your transition metals elemental symbol f e so now i want the number of atoms and the atomic weight of iron is 55.85 grams per mole i want number of atoms and i'm given grams so i have 675 grams of iron how the heck can i get to atoms i need to convert through moles i know that one mole of iron weighs 55.85 grams this cancels my grams of iron if i was to stop right here i would be able to tell you how many moles of iron i have but i don't want to know a number of moles i want to know how many iron atoms so i'm going to continue the calculation and use avogadro's number 6.022 times 10 to the 23rd iron atoms contained in one mole of iron this cancels out my moles of iron and leaves with iron atoms and when i calculate this out i get 7.28 times 10 to the 24th iron atoms now again these numbers are harder for me to mentally check and say does that never make sense to me um i know it's bigger than avogadro's number i know that 675 grams is bigger than one mole that's about the best that my mind can correlate though to see if that ever makes sense and last example for this section how many water molecules are in 675 grams of water first we need the molar mass of water remember to add this up you would look up how much does two hydrogens weigh and one oxygen so two times 1.008 grams per mole and one times 16 grams per mole go ahead and add that up and you should find the molar mass to be 18.02 grams per mole now we're going to set this up just like we did the last example this time though instead of iron atoms we're looking for water molecules notice the difference in terminology an iron atom is a single atom of iron a water molecule is a molecule of water i'm starting with 675 grams of water i cannot convert directly to molecules from grams but i can convert to moles i know one mole of water weighs 18.0 grams that cancels out my grams and gives me moles of water now i can use avogadro's number to find the number of water molecules 6.022 times 10 to the 23rd water molecules to one mole of water and when i calculate this out i get 2.26 times 10 to the 25th water molecules again that number is very large for me it's hard for me to correlate does that make sense but i do know that 675 is a lot larger than 18.02 um which 18.02 grams is exactly one mole and i see that my answer is bigger than avogadro's number so i say yes my answer does make sense and that's how you use molar mass in your calculations