# Graphing the Density of Lead

## Background:

The relationship between two measurements can be shown on a graph. Density is the relationship between mass and volume. It is a measure of how much matter (mass) is packed into a certain amount of space (volume). The density of a substance doesn't change with sample size. If you have more of it (mass), it has to take up more space (volume). To calculate the density of a substance divide the mass by the volume. Typical units are: g/ml or g/cm^{3}. Here is an example:

mass of gold sample 38.6 g Density of gold = -------------------- = ------- = 19.3 g/cm^3 volume of gold sample 2.0 cm^3

Sample Number | Mass (g) | Volume (ml) |
---|---|---|

1 | 5.00 | 0.443 |

2 | 15.0 | 1.33 |

3 | 24.0 | 2.12 |

4 | 52.0 | 4.60 |

5 | 64.0 | 5.66 |

6 | 81.0 | 7.17 |

7 | 95.0 | 8.41 |

8 | 101 | 8.94 |

9 | 142 | 12.6 |

10 | 153 | 13.5 |

## Data:

The data table to the right shows mass and volume data for ten samples of lead.

## Graphing:

Use the data to make a graph that shows the relationship between the mass (y-axis) and volume (x-axis) of the lead samples. Include an appropriate title, label and number the axes correctly. Connect the data points with a single straight line (use a ruler to draw ONE line - do not connect the dots). Position the line as close as possible to as many of the dots as possible.

## Questions:

Use your graph and the information you were given about density to answer the following questions. Where appropriate, answer in well-written, complete sentences.

- Describe in words the equation used to determine the density of an object.

- What is the density of sample number 3? Show your work.

- What is the density of sample number 7? Show your work

- Use the graph to find the volume of a lead sample with a 120 g mass.

- For a sample of lead with a volume of 14 ml, use the graph to find its mass.

- Describe how you can use your graph to find the volume of a sample if you only know its mass?

- Why doesn't every data point lie exactly on the line of your graph?

- Algebra bonus: What is the slope of the lead density line? Be sure to include the appropriate units.