To begin, the chemical formula for carbon dioxide is #CO_2#.
After knowing this, we first need to find how many moles of carbon dioxide there are in #"100g"#. We accomplish this from dividing #"100g"# by the mass of #1# mole of #CO_2#.
#100/(C+2xxO)=100/(12.01+2xx16.00)=100/44.01="2.272 moles"#
In #CO_2#, for every #1# mole of carbon dioxide molecules, there is #1# mole of carbon atoms.
This tells us that if there's #2.272# moles of carbon dioxide molecules, there are also #2.272# individual carbon atoms.
Then, we can just find the mass of #2.272# carbon atoms by multiplying #2.272# by the mass of #1# mole of carbon:
#2.272 xx 12.01 = "27.29g"#
Since there was #1# significant figure in the question, our answer is #"30g"#.
Another way to solve this problem is by using the mass percent! The percentage of carbon, by mass, in carbon dioxide is:
#12.01/(12.01+2xx16.00) = 0.2729 = 27.29%#
This means that, for any mass of carbon dioxide, #27.29%# of that will be pure carbon. It also means that in #"100g"#, #0.2729 xx "100g" = "27.29g" = "30g"# will be carbon. :)
