Lesson 2-7

Density Calculations

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     Density is an important intensive property, which can be used to help determine the identity of an unknown substance.  While the mass or the volume of a substance will vary from sample to sample, the density will remain the same at a given temperature.  As you know, the density of a substance is a measure of how much mass is present in a given unit of volume.  The formula is shown below:

    In laboratory exercises, it is easy to find the mass and volume of most solids, so it is common to solve for density.  When dealing with gases, however, it is often easy to find the volume, but very hard to find the mass.  By looking up the density of a known gas in a reference table, and using the experimental volume, you can calculate the mass using the equation above.  As in any algebraic expression, we can solve for any of the three variables as long as the other two variables are given or known. 

Solving For Density

   When solving for density, you would use the formula exactly as it appeared above.  Here is an example where density is the unknown, and the steps for solving the problem:

1.  A student determines that a piece of an unknown material has a mass of 5.854 g and a volume of 7.57 cm³.  What is the density of the material, rounded to the correct number of significant digits?

First:  Write the correct formula at the top of your page, and list the knowns and the unknowns.

D = ?
M= 5.854 g
V = 7.57 cm³

Second: Substitute the known values in the problem

Third:  Calculate your answer, including units

                                                                          D = 0.77331571994 g/cm³  

Fourth:  Round to the correct number of significant figures

                                                                                  D = 0.773 g/cm³   

Solving For Mass

    When solving for mass, we must take the original formula, and isolate the unknown like so:

Multiply both sides by v

The "v's" cancel out

Isolate for mass

                                                                                     m = v x D                                 

Here is an example where we must solve for mass being the unknown

2.  Iron has a known density of 7.87 g/cm³.  What would be the mass of a 2.5 dm³ piece of iron?  

Notice that the density is given in the units g/cm³, but the volume is given in the units dm³.  Therefore, this problem requires an additional step.

First:  Change the question so that the volume is given in the same units as the density.

Use the factor label method:      

 
Second:  Write the original formula for density, and then isolate the unknown (mass).  List the "knowns" and the "unknown"

Original Formula

         Adjusted Formula

  m = v x D  

D = 7.87 g/cm³  
m = ? 
v = 2500 cm³

  
Third:  Substitute the known values in the problem

Now, here is an example of a density problem where volume is the unknown

3.  Mercury has a density of 13.5 g/cm³.  How much space would 50.0 g of mercury occupy?

   
First:  Write the original formula for density, and then isolate the unknown (Volume).  List the "knowns" and the "unknown".

Original Formula

Multiply both sides by volume

  m = v x D 

Divide both sides by density

Adjusted formula

D = 13.5 g/cm³  
M = 50.0 g  
V = ?

Second: Substitute the known values in the problem

Third:  Calculate your answer, including units

Fourth:  Round to the correct number of significant figures