Density & Moles

Density:

•  density is a measure of mass per volume
• d = m / V
• measured in g / L or g / mL
• Mass <----> Density           

               d = m / V

Example: 

• Water has a density of 1.0 g / mL. Determine the mass of 11.5 mL of water.
• How many moles are in 11.5 mL of water? 
• 11.5 mL x (1.0 g / 1 mL) = 11. 5 g
• 11.5 g x (1 mol / 18 g) = 0.639 mol

Example:

• An unknow compound has a molar mass of 65.0 g / mol. If 0.25 mol occupies a volume of 50 mL determine the compound density.
• (65.0 g / 1 mol) x (0.25 mol / 1) x (1 / 50 mL) = 0.33 g / mol

Example: 

• The density of aluminium is 2.70 g / mL. A solid piece of aluminium has a volume of 45.0 mL. Determine the number of aluminium atoms present.
• Density ---> Mass ---> Moles ---> Atoms
• 45.0 mL x (2.70 g / 1 mL) x (1 mol / 27.0 g) x (6.02 x 10²³ atoms / 1 mol) = 2.7 x 10²⁴ atoms
 

Example:

• Copper has a density of 8.96 g / mL. Determine the number of atoms in copper key that has a volume of 20 mL.
• Mass ---> Mol ---> Atoms
• 20 mL x (8.96 g / 1 mL) = 179.2 g
• 179.2 g x (1 mol / 63.5 g) x (6.02 x 10²³ atoms / 1 mol) = 1.7 x 10²¹ atoms

Density of Gases:

• the density of gases varies with temperature
• at STP we can find density by:

               MM           Molar mass
          ----------- 

              22.4 L/ mol         Molar volume


                  g
                ----
                mol                 g                 L                g           mol            g
           ---------= ------- / ------- = ----- x ----- = ----
                  L                  mol             mol            mol          L               L
                ----- 
                 mol 

 Example:  

• Calculate the density of O2 at STP

                         32 g
                        -------
                          mol
                      --------- =   1.4 g / L
                           22.4 L
                        ----------
                           mol 

Example: 

• Determine the density of the methane (CH4) at STP

                       16 g
                     --------
                        mol  
                 ---------  =  0.71 g / L
                22.4 L
                     ---------  
                 mol 



-Eva 

Multiple Conversions

Example:

•  11.5 grams of H2 gas placed in a balloon at STP. Determine the volume of the volume of the balloon.

1.  11.5 grams x ( 1 mol / 2.0 grams ) = 5.75 mol

        5.75 mol x ( 22.4 L / 1 mol ) = 128.8 L = 129 L

    2.  11.5 grams x ( 1 mol / 2.0 grams ) x ( 22.4 L / 1 mol ) = 129 L



Example: 

•  A car tire contains 25.0 L of Nitrogen (N2) gas at STP. How many grams of Nitrogen is this?

•   25.0 L x (1 mol / 22.4 L) x (28 grams / 1 mol) = 31.25 grams  =  31.3 g

Example:

•  How many Formula Units are there in 3.5 grams of Nickel (ll) Oxide ?
•  Ni 2+  O 2-  
•  NiO
•  3.5 x (1mol / 74.7 grams) x (6.02 x 10²³  F.U. / 1 mol)  = 2.8 x 10²² F.U.

Example:

•  A sample of Oxygen (O2) contains 3.5 x 10²¹ molecules. How many grams of Oxygen is this ?
• 3.5 x 10²¹  molecules x (1 mol / 6.02 x 10²³ molecules) x (32 grams / 1 mol) = 0.19 grams

Example:

•  A container of Oxygen holas 35.0 L of methane (CH4) gas at STP. How many molecules of methane is this?
• 35.0 L x (1mol / 22.4 L) x (6.02 x 10²³ molecules / 1 mol) = 9.41 x 10²³ molecules

Example:

•  A sample of NO2 occupies 7.50 L. How many oxygen atoms are present in this sample?
• 7.50 L x (1 mol / 22.4 L) x (6.02 x 10²³ molecules / 1 mol) x (2 atoms / 1 molecules) = 4.03 x 10²³ atoms

Example:

•  Determine the mass of 10 molecules of Carbon Dioxide.
•  CO2
•  10 molecules x (1 mol / 6.02 x 10²³ molecules) x (44 g / 1 mol) = 7.3 x 10^-22 grams  

-Eva