now that we understand that moles are a way of converting from atomic mass units to grams so that we can discuss macroscopic samples of a substance in terms of a numerical quantity of molecules we are going to have to learn how to convert between grams and moles let's start with something easy and look at pure elements take for example potassium if we have 4.7 grams of potassium how many moles do we have this is important to be able to calculate because we may need to know how many moles of some other substance to react with the potassium in order to obey stoichiometry luckily it's quite simple we just use dimensional analysis to convert this quantity in grams by using the molar mass of the element if we look at the periodic table we can see that the atomic mass of potassium is 39.1 atomic mass units therefore by definition the molar mass of potassium is 39.1 grams per mole we express this as 39.1 grams per mole because there are 39.1 grams in every mole of potassium atoms multiplying our quantity by this conversion factor let's be careful to use the conversion factor in such a way so as to allow the grams to cancel so that we get the desired unit as a result moles and we can see that 4.7 grams times one mole over 39.1 grams does allow grams to cancel and gives us 0.12 moles as our answer we can also convert from moles to grams let's say we want to know the mass of argon in a certain container we might know from some other calculation that there are 9.2 times 10 to the negative 4 moles of argon atoms in the container which is a number of atoms but what mass does this represent once again since the atomic mass of argon is 39.95 atomic mass units the molar mass of argon is 39.95 grams per mole multiplying our value for moles by this conversion factor this time putting grams on top and moles on the bottom we will get 0.037 grams of argon this seems like a reasonable mass for a quantity of gaseous particles in a container and now we can convert between grams and moles for any element