Question #d45c9

1 Answer
Mar 31, 2016

Answer:

#6.76457 * 10^(25)"atoms"#

Explanation:

Your strategy here will be to

  • use glucose's molar mass to determine how many moles you have in that sample
  • use Avogadro's number to determine how many molecules you have in that many moles
  • use glucose's chemical formula to find how many atoms you get in that many molecules

So, glucose, #"C"_6"H"_12"O"_6#, has a molar mass of #"180.156 g mol"^(-1)#, which means that one mole of glucose has a mass of #"180.156 g"#.

Use the molar mass of glucose as a conversion factor to determine how many moles you have in your #"843.211 g"# sample

#843.211color(red)(cancel(color(black)("g"))) * overbrace(("1 mole C"_6"H"_12"O"_6)/(180.156color(red)(cancel(color(black)("g")))))^(color(blue)("molar mass of glucose")) = "4.68045 moles C"_6"H"_12"O"_6#

Now, Avogadro's number tells you how many atoms or molecules you get in one mole of a given substance. Since you know how many moles of glucose you have in your sample, you can use Avogadro's number as a conversion factor to help you go from moles to number of molecules

#4.68045color(red)(cancel(color(black)("moles"))) * overbrace((6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole")))))^(color(purple)("Avogadro's number")) = 2.81857 * 10^(24)"molec."#

To get the number of atoms you get in that many molecules of glucose, focus on figuring out how many atoms you get in one molecule first.

http://www.nutritionalhq.com/about-carbohydrates/about-glucose/

Each molecule of glucose is made up of

  • six atoms of carbon, #6 xx "C"#
  • twelve atoms of hydrogen, #12 xx "H"#
  • six atoms of oxygen, #6 xx "O"#

This means that one molecule of glucose will contain a total of

#6 + 12 + 6 = "24 atoms"#

The number of atoms present in your sample will thus be equal to

#2.81857 * 10^(24)color(red)(cancel(color(black)("molec."))) * "24 atoms"/(1color(red)(cancel(color(black)("molec.")))) = color(green)(|bar(ul(color(white)(a/a)6.76457 * 10^(25)"atoms"color(white)(a/a)|)))#

The answer is rounded to six sig figs, the number of sig figs you have for the mass of sucrose.