Question #54f82

1 Answer
Apr 10, 2016

Answer:

#"0.6777 moles C"_12"H"_22"O"_11#

Explanation:

Your strategy here will be to use Avogadro's number to convert the number of atoms of carbon to moles of carbon, then use the molecular formula of sucrose, #"C"_12"H"_22"O"_11#, to find how many moles of this compound would contain that many moles of carbon.

So, you know that you're dealing with a sample of sucrose that is known to contain #4.897 * 10^(24)# atoms of carbon, #"C"#.

In order to convert this to moles of carbon, use the fact that a mole of atoms is defined as a collection of #6.022 * 10^(23)# atoms.

#color(blue)(|bar(ul(color(white)(a/a)"1 mole atoms" = 6.022 * 10^(23)"atoms"color(white)(a/a)|)) ->)# Avogadro's number

You can say that the sample of sucrose contains

#4.897 * 10^(24)color(red)(cancel(color(black)("atoms"))) * "1 mole C"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms")))) = "8.132 moles C"#

Now that you know how many moles of carbon you have in your sample, use the fact that one molecule of sucrose contains

  • twelve atoms of carbon, #12 xx "C"#
  • twenty two atoms of hydrogen, #22 xx "H"#
  • eleven atoms of oxygen, #11 xx "O"#

https://www.indigo.com/molecular_models/molymod/kits/sucrose-chemical-structure-molecule-model-62115.html#.Vwmo3DHSlvo

The carbon atoms are shown here in black, the oxygen atoms in red, and the hydrogen atoms in white.

So, if one molecule of sucrose contains #12# atoms of carbon, it follows that one mole of sucrose will contain #12# moles of carbon.

This means that the number of moles of carbon you have here will be enough to make up

#8.132 color(red)(cancel(color(black)("moles C"))) * "1 mole sucrose"/(12color(red)(cancel(color(black)("moles C")))) = color(green)(|bar(ul(color(white)(a/a)"0.6777 moles sucrose"color(white)(a/a)|)))#

The answer is rounded to four sig figs.