A sample of propane gas contains #9.36xx10^24*"hydrogen atoms"#. What mass with respect to carbon, and hydrogen, AND propane, does this quantity represent?

1 Answer
Aug 30, 2017

Answer:

You gots propane, i.e. #C_3H_8#.

Explanation:

Now if I specify a mole of propane I specify #6.022xx10^23# individual propane molecules. Why should we use such an absurdly large number? Well, because it is a fact that #6.022xx10^23# individual carbon atoms have a mass of #12*g# (or near enuff), and #6.022xx10^23# individual hydrogen atoms have a mass of #1*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 #3xx6.022xx10^23# carbon atoms, and #8xx6.022xx10^23# 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^-1#

That is the background. It is specified that there are #9.36xx10^24*"hydrogen atoms"#, and thus represents a molar quantity of ..................

#(9.36xx10^24*"hydrogen atoms")/(6.022xx10^23*"hydrogen atoms"*mol^-1)=15.54*mol#

And clearly, we can divide this by 8 to give the molar quantity of #1.94*mol# WITH RESPECT TO PROPANE. Do you agree?

And so (finally), there are.....

#1.94*molxx3*"carbon atoms"xx6.022xx10^23*mol^-1#

#=3.51xx10^24*"carbon atoms"#.

And as to the mass of the sample, I take the product...

#"Number of moles"xx"molar mass of propane"#

#=1.94*molxx44.1*g*mol^-1~=90*g#, i.e. I get an answer in grams as required.