Now if I specify a mole of propane I specify 6.022xx10^236.022×1023 individual propane molecules. Why should we use such an absurdly large number? Well, because it is a fact that 6.022xx10^236.022×1023 individual carbon atoms have a mass of 12*g12⋅g (or near enuff), and 6.022xx10^236.022×1023 individual hydrogen atoms have a mass of 1*g1⋅g. These molar masses are listed on the Periodic Table, and there should be a copy beside you now.
Now it follows that a mole of propane SPECIFIES 3xx6.022xx10^233×6.022×1023 carbon atoms, and 8xx6.022xx10^238×6.022×1023 hydrogen atoms, and so we multiply thru by the molar masses to give a molar mass for the propane molecule as....
3xx12.011*g*mol^-1+8xx1.00794*g*mol^-1=44.10*g*mol^-13×12.011⋅g⋅mol−1+8×1.00794⋅g⋅mol−1=44.10⋅g⋅mol−1
That is the background. It is specified that there are 9.36xx10^24*"hydrogen atoms"9.36×1024⋅hydrogen atoms, and thus represents a molar quantity of ..................
(9.36xx10^24*"hydrogen atoms")/(6.022xx10^23*"hydrogen atoms"*mol^-1)=15.54*mol9.36×1024⋅hydrogen atoms6.022×1023⋅hydrogen atoms⋅mol−1=15.54⋅mol
And clearly, we can divide this by 8 to give the molar quantity of 1.94*mol1.94⋅mol WITH RESPECT TO PROPANE. Do you agree?
And so (finally), there are.....
1.94*molxx3*"carbon atoms"xx6.022xx10^23*mol^-11.94⋅mol×3⋅carbon atoms×6.022×1023⋅mol−1
=3.51xx10^24*"carbon atoms"=3.51×1024⋅carbon atoms.
And as to the mass of the sample, I take the product...
"Number of moles"xx"molar mass of propane"Number of moles×molar mass of propane
=1.94*molxx44.1*g*mol^-1~=90*g=1.94⋅mol×44.1⋅g⋅mol−1≅90⋅g, i.e. I get an answer in grams as required.
