**Measuring Density**

#### Background

All matter has mass and volume. Mass is a measure of the amount of
matter an object has. Its measure is usually given in grams (g) or
kilograms (kg). Volume is the amount of space an object occupies. There
are numerous units for volume including liters (l), meters cubed (m^3^),
and gallons (gal).

Mass and volume are physical properties of matter and may vary with
different objects. For example, it is possible for two pieces of metal
to be made out of the same material yet for one piece to be bigger than
the other. If the first piece of metal is twice as large as the second,
then you would expect that this piece is also twice as heavy (or have
twice the mass) as the first. If both pieces of metal are made of the
same material the ratio of the mass and volume will be the same.

We define density (*ρ*) as the ratio of the mass of an object to the
volume it occupies. The equation is given by:

$\rho = \frac{M}{V}$ (1.1)

here the symbol *M* stands for the mass of the object, and *V* the
volume. Density has the units of mass divided by volume such as grams
per centimeters cube (g/cm^3^) or kilograms per liter (kg/l).

## Sample Problem #1

A block of wood has a mass of 8 g and occupies a volume of 10 cm^3^.
What is its density?

## Solution

The density will be
$\frac{8g}{\text{10}\text{cm}^{3}} = 0\text{.}8\frac{g}{\text{cm}^{3}}$.

This means that every centimeter cube of this wood will have a mass of
0.8 grams.

#### Activity 1: (*Determine the density of an object with a regular shape.)*

Obtain a set of objects (cube, cylinder, sphere, etc.) made of the same
material. Calculate the density by measuring the mass and volume of your
samples.

####### Measuring the Mass

Measure the mass of your samples using the triple beam balance provided.
You will make this measurement three times and calculate the average.
Record your results in the table below.

  ----------------- -------------------------- --------------------------
  Trial             Sample 1                   Sample 2

  1                                            

  2                                            

  3                                            

  Avg.                                         
  ----------------- -------------------------- --------------------------

####### Measuring the Volume

To determine the volume of an object with a regular shape there are
standard equations that may be used. The equations for three common
shapes are given below.

![](media/image1.png){width="5.86875in" height="2.084722222222222in"}

Sphere Cube Cylinder

$V = \frac{4}{3} \cdot \pi \cdot R^{3}$ $V = L \cdot W \cdot H$
$V = \frac{\pi}{4} \cdot R^{2} \cdot H$ (1.2)

Measure the relevant dimensions of your sample and record the reading in
the tables below.

######### 

######### Sample #1

Calculate the volume of Sample #1 using equations (1.2). Show all work

Volume =
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

#########  Sample #2

Calculate the volume for Sample #2. Show all work

Volume =
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

####### Calculate the Density

+-----------------+----------------+-----------------+-----------------+
| Specimen        | Volume         | Mass            | Density         |
|                 |                |                 |                 |
|                 | (cm3)          | (grams)         | (gm/cm3)        |
+-----------------+----------------+-----------------+-----------------+
|                 |                |                 |                 |
+-----------------+----------------+-----------------+-----------------+
|                 |                |                 |                 |
+-----------------+----------------+-----------------+-----------------+

Even though both object have different shape and volume what did you
observe about the density of the samples:
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Unlike the mass and volume that may be different for each specimen, all
objects made of the same material will have the same density. Because of
this the density is often used to identify unknown substances or to
determine the percent composition. The densities of various substances
are given in Table 1.

**Table 1.** Density of solid substances. Densities are in g/cm^3^.

## Sample Problem #2

A block of wood has a mass of 4 g and occupies a volume of 5 cm^3^. What
type of wood can it be?

## Solution

The density will be
$\frac{4g}{5\text{cm}^{3}} = 0\text{.}8\frac{g}{\text{cm}^{3}}$.

From Table 1 the only wood with that density is Oak.

**Activity 2**: *(Determine the Density of an object with an irregular
shape.)*

Obtain a set of irregularly shaped samples. Calculate the density by
measuring the mass and volume.

####### Measuring the Mass

  ----------------- -------------------------- --------------------------
  Trial             Sample 1                   Sample 2

  1                                            

  2                                            

  3                                            

  Avg.                                         
  ----------------- -------------------------- --------------------------

*[Measuring the Volume]{.underline}*

The volume of an irregularly shaped object can be determined by
measuring the amount of water it displaces. Fill a graduated cylinder
about half way with water. Note the level of the water. Submerge your
sample and mark the new water level.

  ------------------------------------ ----------------- -----------------
                                       Sample 1          Sample 2

  Final volume of water                                  

  Initial volume of water                                

  Volume of sample                                       
  ------------------------------------ ----------------- -----------------

####### Calculate the Density

+-----------------+----------------+-----------------+-----------------+
| Specimen        | Volume         | Mass            | Density         |
|                 |                |                 |                 |
|                 | (cm3)          | (grams)         | (gm/cm3)        |
+-----------------+----------------+-----------------+-----------------+
|                 |                |                 |                 |
+-----------------+----------------+-----------------+-----------------+
|                 |                |                 |                 |
+-----------------+----------------+-----------------+-----------------+

###### 

###### Activity 3: *(Determine the Density of a liquid)*

Calculate the density by measuring the mass and volume of your liquid
sample.

####### Measure the Mass

  --------------------------- -------------------------------------------
  Trial                       Sample 1

  1                           

  2                           

  3                           

  Avg.                        
  --------------------------- -------------------------------------------

Measure the Volume

  ------------------------------- ---------------------------------------
  Trial                           Sample 1

  Volume                          
  ------------------------------- ---------------------------------------

####### Calculate the Density

+-----------------+----------------+-----------------+-----------------+
| Specimen        | Volume         | Mass            | Density         |
|                 |                |                 |                 |
|                 | (cm^3^)        | (grams)         | (gm/cm3)        |
+-----------------+----------------+-----------------+-----------------+
|                 |                |                 |                 |
+-----------------+----------------+-----------------+-----------------+

**Table 2.** Density of some liquid substances. Densities are in
g/cm^3^.

###### 

###### What is the composition of the liquid sample? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 

###### Activity 4: *(Determine the Density of a Gas)*

A gas can be compressed so the density of a gas can change.

![](media/image2.jpeg){width="6.0in" height="2.7444444444444445in"}

1.  Place a beaker inside a bath filled with water so that the beaker is
    about ½ filled with water and the other ½ air.

> (you might have to let some air out by tilting the beaker.)

2.  Add water to the bath.

    a.  What happens to the water level inside the beaker?
        \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

    b.  Has any air escaped the beaker? Has the amount of air inside the
        beaker changed?
        \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

    c.  What happens to the density of the air inside the beaker when
        you add the water?
        \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_