Question #c2141

1 Answer
Jan 8, 2017

Answer:

Here's what I got.

Explanation:

In order to determine how many atoms of carbon you have in your sample, you must use a series of conversion factors to take you from

grams of sucrose #-># moles of sucrose #-># molecules of sucrose #-># atoms of carbon

To go from grams of sucrose to moles of sucrose, use the molar mass of the compound. Your sample will contain

#1.0 color(red)(cancel(color(black)("g"))) * ("1 mole C"_12"H"_22"O"_11)/(342.3color(red)(cancel(color(black)("g")))) = "0.0029214 moles C"_12"H"_22"O"_11#

Now, you can go from moles of sucrose to number of molecules of sucrose by using Avogadro's constant, which is essentially the definition of a mole.

Your sample will contain

#0.0029214 color(red)(cancel(color(black)("moles C"_12"H"_22"O"_11))) * (6.022 * 10^(22)"molecules C"_12"H"_22"O"_11)/(1color(red)(cancel(color(black)("mole C"_12"H"_22"O"_11))))#

#= 1.7593 * 10^(21)"molecules C"_12"H"_22"O"_11#

Now, as its chemical formula suggest, every 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"#

http://www.exploratorium.edu/cooking/candy/sugar.html

This means that your sample will contain

#1.7593 * 10^(21) color(red)(cancel(color(black)("molecules C"_12"H"_22"O"_11))) * "12 atoms C"/(1color(red)(cancel(color(black)("molecule C"_12"H"_22"O"_11))))#

# = color(darkgreen)(ul(color(black)(2.1 * 10^(22)"atoms of C")))#

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