Week 32 – Moles and Molar Mass

This section of the lesson will serve as a review of working with moles.  Our textbook defines a mole as a counting unit used to keep track of large numbers of particles.  Just like one dozen represents 12 items, one mole represents 6.02 x 1023 items. Here are some examples:

• One mole of gold atoms is equal to 6.02 x 1023 gold atoms.
• One mole of glucose molecules is equal to 6.02 x 1023 glucose molecules.  The molecular formula of a molecule of glucose is C6H12O6.

How many carbon atoms are in one mole of glucose?  Since each glucose molecule includes 6 carbons, and we have 6.02 x 1023 glucose molecules (equal to 1 mole), then we have a total of 6 x 6.02 x 1023 carbon atoms, which is equal to 36.12 x 1023 carbon atoms.  For proper scientific notation, we need to move the decimal one position to the left which then increases the exponent by 1.  Therefore, we have 3.612 x 1024 carbon atoms per mole of glucose.  Because we also have 6 oxygen atoms per molecule of glucose, the same math applies, so we have 3.612 x 1024 oxygen atoms per mole of glucose.  Finally, since we have 12 hydrogen atoms per molecule of glucose, and 12 is 2 x 6, we can double the number of carbon (or oxygen) atoms per mole of glucose to determine the number of hydrogen atoms per mole of glucose: 2 x 3.612 x 1024 = 7.224 x 1024 hydrogen atoms.

How many moles of atoms are in one mole of glucose?  Well, for each glucose molecule, there are 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms.  That adds up to 24 atoms (6+6+12) per molecule of glucose.  That means there are 24 moles of atoms per mole of glucose molecules!  Of those 24 moles of atoms, there are 6 moles of carbon, 12 moles of hydrogen, and 6 moles of oxygen atoms per mole of glucose molecules.

Why does this matter?  Glad you asked!  The mole connects the microscale world (number of atoms or molecules) with the macroscale world (number of grams – something we can actually measure in the lab).  The number of grams per mole of a substance is the same as the number of atomic mass units (amu) of a substance.  For example:

• Gold, Au (element 79), has an average atomic mass of 197.0 amu.  Therefore, 1 mole of gold has a mass of 197.0 grams.  The molar mass of gold is 197.0 g/mol.
• Glucose, C6H12O6 has a molecular mass of 180.2 amu.  The molecular mass is calculated by multiplying the average atomic mass of each element by the number of atoms of that element and then adding them all up:
• carbon = 12.01 amu x 6 atoms = 72.06 amu
• hydrogen = 1.008 amu x 12 atoms = 12.096 amu
• oxygen = 16.00 amu x 6 atoms = 96.00 amu
• 72.06 amu + 12.096 amu + 96.00 amu = 180.156 amu
• 72.06 and 96.00 both have 4 significant digits, so we round 180.156 amu to 180.2 amu (which has 4 significant digits).
• Note: One formula unit of glucose has a mass of 180.2 amu.  One formula unit of glucose is the same thing as one glucose molecule.
• Therefore, 1 mole of glucose has a mass of 180.2 grams.  The molar mass of glucose is 180.2 g/mol.

Finally, imagine you have two samples: 100 g of C6H12O6 and 100 g of CO2.  Which sample has more carbon atoms?  Which sample has more oxygen atoms?  One way to solve this problem is to determine how many moles of each substance are in 100 g:

• From our work above, we know that C6H12O6 has a molar mass of 180.2 g/mol.  Therefore, 100 g x 1 mol / 180.2 g = 0.55 mol of C6H12O6
• For CO2, the molar mass works out to 44.01 g/mol.  We’ve calculated that in class many, many times, but you should also try the math yourself to be sure you get it.  Therefore, 100 g x 1 mol / 44.01 g = 2.27 mol of CO2

Next, we can determine how many moles of carbon are in each substance:

• 0.55 mol of C6H12O6 x 6 moles of carbon / mole of C6H12O6 = 3.3 moles of carbon in 100 g of C6H12O6
• 2.27 mol of CO2 x 1 mole of carbon / mole of CO2 = 2.27 moles of carbon in 100 g of CO2
• Therefore, C6H12O6 has more carbon atoms than CO2 in 100 g of each sample

Finally, we can repeat the process to determine how many moles of oxygen are in each substance.  Give it a try.  Then click here to check your work.

Time to move into the textbook:

1. Create a Google Doc titled Week 32 – Name (example: Week 32 – Pickles Swart)
2. Share the Doc with david.swart@g.highlineschools.org
3. Read Lesson 76 in the textbook and complete Exercise questions 4-7 in your Google Doc in a section labeled Lesson 76
4. Read Lesson 77 in the textbook and complete Exercise questions 3-8 in your Google Doc in a section labeled Lesson 77
5. Read Lesson 78 in the textbook and complete Exercise questions 1-8 in your Google Doc in a section labeled Lesson 78