The Mole

 

How many molecules are there in 6.8 mol of carbon monoxide, CO, gas?

 

Solution: The beginning point in problems of this kind should be the fundamental relationship 1 mole = 6.022 X 10­23 representative particles (in this case, molecules0. In this problem, however, you are asked to find the number of molecules in 6.8 mol. The problem should be set up so that units will cancel to give the correct unit in the answer.

 

6.8 mol CO      X         6.02 X 1023 molecules CO       =          40.936 X 1023 molecules CO

            1 mole CO                                          

 

Notice that the answer must have two significant figures since the original measurement (6.8 mol) contained only two. Written in standard scientific form the answer is 4.1 X 1024 molecules CO.

 

1. How many sodium ions are there in 0.482 mol of sodium sulfate (Na2SO4)?

 

 

 

 

 

 

 

How many moles are there in 6.32 X 1024 molecules of chloroform, CHCl3?

 

Solution: Begin with this fundamental relationship.

 

1 mol CHCl3 = 6.022 X 1023 molecules CHCl3

 

Then multiply the given number of molecules of chloroform by a conversion factor that will give an answer expressed in moles.

 

6.32 X 1024 molecules CHCl3 X           1 mol CHCl3                 = 1.05 X 101­ mol CHCl3

     6.022 X 1023 molecules CHCl3

 

The answer should contain three significant figures and should probably be written in a simpler form, 10.5 mol CHCl3.

 

 

 

2. A sample of silver metal contains 1.91 X 1021 atoms. How many moles of silver is this?


 

3. How many moles are there in 3.04 X 1023 molecules of hydrogen, H2, gas?

 

 

 

 

 

 

 

 

 

 

4. How many phosphorus atoms are there in 1.75 mol of calcium phosphate, Ca3(PO4)2?

 

 
Molar Mass

 

Find the molar mass of iron(III) sulfate, (Fe2SO4)3.

 

Solution: Each mol of (Fe2SO4)3 contains two moles of iron atoms, three moles of sulfur atoms, and 12 moles of oxygen atoms. You can find the molar mass of (Fe2SO4)3 by adding the molar masses of each of the three atoms that make up the compound.

 

2 mol Fe   X   55.85 g Fe   =   111.7 g Fe

   1 mole Fe

 

3 mol S   X   32.06 g S   =   96.18 g S

   1 mole S

 

12 mol O   X   16.00 g O   =   192.0 g O

   1 mole O

 

The molar mass of (Fe2SO4)3 = 111.7 g Fe + 96.18 g S + 192.0 g O = 399.9 g

 

 

2. What is the molar mass of sucrose, C12H22O11?

 

 

 

 

 

 

 

 

 

 

3. Find the gram molecular mass of -dichlorobenzene, C6H4Cl2.

 

 

 

 

 

 

 

 

 

 

4. What is the molar mass of calcium bisulfate, Ca(HSO4)2?

 


Solutions

 

The Mole

 

1. How many sodium ions are there in 0.482 mol of sodium sulfate (Na2SO4)?

 

0.482 mol Na2SO4   X   6.022 X 1023 formula units Na2SO4   X             2 Na+ ions______

1 mol Na2SO4                                  1 formula unit Na2SO4

 

= 5.80 X 1023 Na+ ions

 

* Formula units are like molecules; the only difference is that they’re used for different types of compounds

 

 

2. A sample of silver metal contains 1.91 X 1021 atoms. How many moles of silver is this?

 

1.91 X 1021 atoms Ag   X         _     1 mol Ag_____

         6.022 X 1023 atoms Ag                = 3.17 X 10-3 mol Ag

 

 

 

 

3. How many moles are there in 3.04 X 1023 molecules of hydrogen, H2, gas?

 

3.04 X 1023 atoms Ag   X          ___    1 mol H2_______

         6.022 X 1023 molecules H2          = 0.505 mol H2

 

 

 

 

4. How many phosphorus atoms are there in 1.75 mol of calcium phosphate, Ca3(PO4)2?

 

1.75 mol Ca3(PO4)2   X   6.022 X 1023 formula units Ca3(PO4)2   X   __ 2 atoms P_____

1 mol Ca3(PO4)2                              1 formula unit Ca3(PO4)2

 

= 2.11X 1024  Phosphorous ions

 


Molar Mass

 

2. What is the molar mass of sucrose, C12H22O11?

 

12 mol C   X   12.01 g C   =   144.12 g C

    1 mole C

 

22 mol H   X     1.0 g H     =   22.22 g H

     1 mole H

 

11 mol O   X   16.00 g O   =   176.0 g O

   1 mole O

 

The molar mass of C12H22O11= 144.12 g C + 22.22 g H + 176.0 g O = 342.3 g

 

 

3. Find the gram molecular mass of -dichlorobenzene, C6H4Cl2.

 

6 mol C   X   12.01 g C   =   72.06 g C

   1 mole C

 

4 mol H   X     1.01 g H     =   4.04 g H

   1 mole H

 

2 mol Cl   X   35.45 g Cl   =   70.90 g O

   1 mole Cl

 

The molar mass of C6H4Cl2 = 72.06 g C g C + 4.04 g H + 70.90 g O = 147.0 g

 

 

4. What is the molar mass of calcium bisulfate, Ca(HSO4)2?

 

1 mol Ca   X   40.08 g Ca   =   40.08 g C

   1 mole Ca

 

2 mol H   X     1.01 g H     =   2.02 g H

     1 mole H

 

2 mol S   X     32.06 g S     =   64.12 g H

   1 mole S

 

8 mol O   X   16.00 g O   =   128.00 g O

   1 mole O

 

The molar mass of (Fe2SO4)3 = 40.08 g C + 2.02 g H + 64.12 g S + 128.00 g O = 234.2 g