## Determination of Density

**Required materials provided in the Home Science Tools chemistry kit:** 100mL graduated cylinder, balance (scale)

**Required materials ****not**** provided in the Home Science Tools chemistry kit: **cell phone (with camera), metric ruler, 25-30 pennies, graph paper

### Objectives: *to find the density of regular-shaped and irregular-shaped substances including graphing techniques*

### Introduction: __Density__ is the intensive property of matter defined as the ratio of an object’s mass to its volume. In simpler words, density is the mass of an object divided by the volume which the object occupies. The term __intensive property__ means that it is *independent* of the amount of the substance. The density of any substance remains the same, no matter the shape and size of the sample. The density of water at 4°C is 1.000 g/mL regardless if the sample size is 1 cup or 1 swimming pool. Thus, density is one of the characteristic properties which allows us to identify substances; it is fixed and has a unit of g/mL. As such, it is a useful tool to identify an unknown metal. One can calculate the density of an unknown metal and can match the value against a standard density table for its identification.

The density of a substance does change with a change in temperature. This change in density is __inversely proportional__ to the change in temperature. This is to say, if the temperature rises, then the density decreases, and if the temperature falls, then the density increases. Cooling a substance causes its molecules to occupy a smaller volume, resulting in an increase in density. Hot water is less dense and will float on room-temperature water. Cold water is denser and will sink in room-temperature water.

Densities of various substances can be identified differently. For **regular **(shaped) **solids**, calculating the density is straightforward: simply weigh the solid and measure its dimensions, using a simple formula to calculate the volume. The density is calculated by dividing the mass by the volume. Each regular solid has its own formula for calculating its volume depending on the shape of the solid. The volume of a *rectangular* solid equals length times width times height. Note: 1 mL = 1 cm3. For **irregular **(shaped)** solids**, those that do *not* have a standard formula for calculating their volume, the volume can be determined by measuring the volume of liquid that the solid displaces. To do this, the solid is submerged in a liquid and the volume displaced is measured. This is done by taking an initial reading and a final reading and calculating the difference in volume. The mass of the object is then divided by this volume, and the density is determined.

Measuring the density of a liquid is very similar. Although the volume cannot be measured with a ruler, it can be determined using volumetric glassware, for instance, a graduated cylinder. The liquid’s mass is determined when this measured volume is weighed. Knowing the mass and volume, the liquid’s density may now be calculated.

Table 1 – Formulas for Calculating Densities

## Type of calculation

## Formula

density of a regular solid

D = M/V

where M is mass, and V is volume.

The unit is g/cm3.

V for a cube or rectangular solid = l × w × h

where l is length, w is width, and h is height.

V for a triangular pyramid = (area of triangular base × height)/3

V for a rectangular pyramid = (l × w × h)/3

V for a cylinder = r2h where = 3.14 and r is radius

density of an irregular solid

D = M/(V2 – V1)

where M is mass and (V2 – V1) represents the difference in volume due to the difference in mass of the object.

The unit is g/cm3.

density of a liquid (immiscible)

D = M/V where M is mass, and V is volume.

The unit is g/mL.

density by graphing technique

Using graph paper, plot a series of mass readings of the substance on the x-axis and a corresponding series of volume readings on the y-axis.

Using y = mx + b, one can find the slope (m) of the line created by plotting the datapoints. This slope equals the density (mass/volume) of the object.

### Experimental Procedures:

#### I. Density of a Regular Solid

1. Obtain an unknown regular-shaped solid. A cell phone, for example. Record the identity of the regular solid on the report sheet.

2. Weigh the item. Record its mass on the report sheet.

3. Measure its length, width, and height using the metric ruler. Record these values on the report sheet.

4. Calculate the volume of the solid.

5. Calculate the density of the unknown solid.

#### II. Density of an Irregular Solid

1. Weigh the irregular solid provided by your instructor. Record its identity and mass on the report sheet.

2. Fill the 100mL graduated cylinder between 50 mL and 70 mL with water.

3. Record this initial volume (V1) on the report sheet.

4. Gently place the irregular solid into the graduated cylinder. This is best accomplished by tilting the graduated cylinder and sliding the solid into the water. This will avoid splashing.

5. Record the new volume (V2) of water plus the irregular solid.

6. Determine the total volume displaced by difference (V2 – V1).

7. Calculate the density of the irregular solid by dividing the mass of the solid by the volume of water it displaced.

Table 2 – Density Values of Some Common Metals

Metal

Density (g/cm3)

Metal

Density (g/cm3)

Copper

8.96

Nickel

8.91

Iron

7.86

Gold

19.3

Tungsten

19.25

Silver

10.49

Lead

11.34

Palladium

12.02

Tin

7.27

Aluminum

2.70

Zinc

7.14

#### III. Finding the Density using Graphing Technique

*If you have a series of data, you can plot a graph of the mass vs the volume. * *The slope of the resultant line will give you the density.* *Slope = density (g/mL)*

#### *** A VIDEO RECORDING must be produced of the student executing the following steps of the lab experiment as the steps are performed. ***

[This video will either be (1) attached as a file to the report sheet for submission** or**

(2) provided as a link on the report sheet to a YouTube video.]

1. Fill the 100 mL graduated cylinder with about 50-55 mL of water and record this initial volume on the report sheet.

2. Weigh 5 pennies on the balance and record the mass (M1).

3. Add the 5 pennies slowly into the graduated cylinder. Remove any air bubbles by tapping the sides and record the volume (V1).

4. Leave the water and these 5 pennies in the cylinder.

5. Weigh another 5 or 6 pennies. Add this mass to the mass (M1) of the first 5 pennies for the combined mass of total pennies used so far. Record this combined mass (M2) on the report sheet.

6. Add these additional five or six more pennies (total of 10 or 11 pennies including the first 5 pennies) to the graduated cylinder. Record this new volume (V2).

7. Repeat steps #5 and #6 for a total data set of 5 mass readings (M1, M2, M3, M4, and M5) and 5 volume readings (V1, V2, V3, V4, and V5), recording all the data on the report sheet, completing Data Table 3.

8. Using the graph paper, draw a graph with the x-axis representing Mass and the y-axis representing Volume.

9. Plot all the sample readings on the same graph with the first datapoint (M0, V0) consisting of a mass (M0) of *zero grams* which represents the mass before adding any pennies and the volume (V0) measured in Step #1 before adding any pennies.

10. Continue plotting the measured values as follows: (M1, V1), (M2, V2), (M3, V3), (M4, V4), and (M5, V5). This creates a total of **six** datapoints on the graph.

11. Draw a* straight* line (line of best fit) through these six datapoints. **Do NOT draw a zig-zag line.** Try to pass the line (as close as possible) through all six datapoints. If the line drawn does not pass perfectly through all six points, it is okay. Still, try to do as best as possible.

12. Determine the density by calculating the line’s slope. To find the slope, choose any two data points on the graph and find differences of mass and volume for the two selected points. Slope = (Δ g / Δ mL) = density. [**Note:** The Greek letter delta, Δ, is generally used in math and chemistry to denote the difference between two values. In this example, “Δ g” is the difference in mass, and “Δ mL” is the difference in volume.

For example, using the data points (M2, V2) and (M4, V4):

slope = = density

13. Record the density on the report sheet.

14. Identify the type of metal which comprises a penny from the list of metals and their density above (**Table 2 –** **Density Values of Some Common Metals**).

15. Record the identity on the report sheet.

16. Attach the video recording of the student performing this section of the lab experiment to the report sheet either as a file attachment or as a link to a YouTube video**.** **Failure to provide this video will result in a grade of ZERO on this lab assignment**__.__

17. In addition to the video recording, attach a photo of the hand-drawn graph to the report sheet. **Failure to provide this photo will result in a grade of ZERO on this lab assignment**__.__

__IV. Procedure to find Density (slope) using Excel__

*** video tutorial on how to create a Scatterplot using Excel ***

(CTRL + click to follow link)

1. Open a new Excel spreadsheet and input your data (from Section** III. Finding the Density using Graphing Technique**) as shown in the example below of “Cross Section vs Circumference”, changing the left column (x-axis) heading from “Cross section (cm)” to “Mass (g)” and the right column (y-axis) heading from “Circumference (cm)” to “Volume (mL)”. Make sure to include the first datapoint values (M0 and V0) representing the starting point of the experiment.

**Cross Section vs Circumference**

2. Select the data to be used in the graph. To do this, click on any of the data cells and press **CTRL + A **to select the current region around the active cell.

3. Click the **Insert **tab located near the top of the page.

4. From the **Charts** group, select the “Scatter” chart option. A chart should now appear embedded in the center of the screen.

5. Click on the Chart Title and change the title’s name to read, “Mass vs Volume”.

6. Click on the chart and locate the **Chart Elements **button (with the plus sign icon) to the upper-right of the chart.

7. From the **Chart Elements **menu, check the box labelled, “**Axis Titles**”.

8. Change the title of the y-axis (vertical axis) to “Volume (mL)”.

9. Change the title of the x-axis (horizontal axis) to “Mass (g)”.

10. Again, from the **Chart Elements **menu, check the box labelled, “**Trendline**”. A line should now appear on the chart. [**Note:** A trendline is also known as “the line of best fit”.]

11. With the cursor still over the word “**Trendline**”, highlighting the word, click the black arrow located just to the right.

12. From this sub-menu, click “**Linear**” to ensure a straight line is generated as the trendline.

13. From the same Trendline sub-menu, select “**More Options…**”. A side menu titled “**Format Trendline**” should appear on the right side of the screen

14. Scroll to the bottom of the “**Format Trendline**” and check the box, “Display Equation on chart”. An equation in the style of y = mx + b should now appear on the chart. This equation expresses the mathematical description of the line generated. The value of “m” (the coefficient of x) represents the slope of the line. This calculated value of the slope *is* the value of the density of the pennies. Record this calculated density on the report sheet.

15. Using **Table 2 –** **Density Values of Some Common Metals**, identify the type of metal from which a penny is composed. Record the type of metal on the report sheet.

16. Attach a copy of the scatter chart created using Excel to the report sheet. **Failure to provide this photo will result in a grade of ZERO on this lab assignment**__.__

**Waste Disposal: **

· Clean and dry all pennies and glassware immediately for use in other labs.

· Clean the balance, making sure it is completely dry.