SCH 3U/4C - Molar Mass & the Number of Particles

***Be sure you have your "The Official Sandwich Secondary School Periodic Table of the Elements" for this and every lesson from here onward.  This will be the table I exclusively use.***

Atomic Mass & Molar Mass

We can use the atomic mass (which is found on the periodic table for each element) to determine the molar mass for atoms or molecules.

Let's begin with a few definitions, just so we are all speaking the same language:

• atomic mass is the mass of a single atom of an element (you have known this since grade 9 - it is found in the box for each element on the periodic table, along with the atomic number)
• molecular mass is the mass of a single molecule of a compound
• molar mass (given the symbol, M & units of g/mol) is the mass of a mole (6.02 x 10²³) of a substance
  

	Particle (Atom/Molecule) Atomic Mass/Molecular Mass (u = 1.66054 × 10-24 g) Molar Mass (g/mol) sodium (Na) 22.99 u 22.99 g/mol chlorine (Cl) 35.45 u 35.45 g/mol water (H2O) (1.008 x 2) + 16.00 = 18.02 u 18.02 g/mol carbon dioxide (CO2) 12.011 + (2 x 16.00) = 44.01 u 44.01 g/mol

   

Notice that the only difference between atomic/molecular mass and molar mass is the unit (u and g/mol, respectively). Therefore, the mass of 1 mole of an element or compound is its molar mass.  So if we have 6.02 x 10²³ particles or 1 mole of lead, it will have a mass of 207.2 g and thus, it's molar mass would be 207.2 g/mol.

Mole & the Number of Particles 

• Measuring 1 mole of a substance means that you have 6.02 x 10²³ particles of that substance.  
•  However, we can also measure out multiples and fractions of a mole.

     N = nN_A 

where N is the number of particles (particles), n is the number of moles (mol) and N_A is Avogadro’s number (6.02 x 10²³ particles/mol)

• Be sure to show all calculations with proper format (equation, substitution, answer, units, sig digs)

ex. calculate the number of Pb(IO₃)₂ molecules in 1.00 mole of Pb(IO₃)₂

N = nN_A      
N = 1.00 mol(6.02 x 10²³ molecules/mol) 
N = 6.02 x 10²³ molecules

*Note:  If we do unit analysis, the "mol" cancel out, leaving us with "molecules."

ex. calculate the number of Li₂CO₃ molecules in 2.0 moles of Li₂CO₃

N = nN_A      
N = 2.0 mol(6.02 x 10²³ molecules/mol) 
N = 1.2 x 10²⁴ molecules

ex. calculate the number of S atoms in 0.50 moles of Na₂SO₄ 
N = nN_A 
N = 0.50 mol(6.02 x 10²³ molecules/mol)(1 atom/molecule)
N = 3.0 x 10²³ atoms

*Note: Since we want the number of S atoms this time, instead of the number of molecules like in the previous two examples, we have added the "(1 atom/molecule)" term because there is 1 S atom per molecule of Na₂SO₄.  Had we been asked to find the number of Na atoms, this term would have been "(2 atom/molecule)" or if we had to find the number of O atoms,  the term would become "(4 atom/molecule)."  Also, notice that if we do unit analysis, the "mol" cancel out, the "molecules" cancel out, leaving us with "atoms."

ex. calculate the number of H atoms in 4.120 moles of (NH₄)₂S 
N = nN_A
N = 4.120 mol(6.02 x 10²³ molecules/mol)(8 atoms/molecule)
N= 1.98 x 10²⁵ atoms

Homework: 

1. Find molar mass of (a) xenon, (b) oxygen, (c) hydrogen acetate, (d) ammonium sulfate, (e) sugar, (f) lithium phosphide, (g) methane, (h) lead (II) carbonate, (i) barium nitrate, (j) cesium chlorate.

2. Particle Worksheet

 Answers:

Student Questions:

 

1.  What does N = nN_A mean in all the examples?

 

Did you read today's lesson?  Remember that N = nN_A is the equation we use to determine the number of particles (N) in a given number of moles (n) of a sample, using Avogadro's number (N_A = 6.02 x 10²³ particles/mol).  

 

See this video for guidance.  Note that in the latter part of the video, I misspeak and say "number of phosphate atoms" when I clearly mean "number of phosphorus atoms."  Oops.