Density Puzzle



Density Puzzle

There are six boxes (red, white, yellow, blue, navy and pink). Each box has a different mass (66.8 g, 42.7 g, 54.6 g, 46.2 g, 44.3 g, and 35.1 g) and a different volume (92.4 cm3, 52 cm3, 89.1 cm3, 9.4 cm3, 26 cm3, and 15.8 cm3). Based on this information and the clues, determine the mass, volume and density of each box. Summarize your findings in the chart on the opposite side.

1. One object has a volume of 26 cm3 and a density of 1.35 g/cm3.

2. The white object has a density of 0.75 g/cm3 and a volume of 89.1 cm3.

3. The pink object has a mass of 42.7 g and a volume of 9.4 cm3.

4. One object has a volume of 15.8 cm3 and a density of 2.804 g/cm3.

5. The yellow object has a greater mass than the navy object.

6. The density of aluminum is 2.7 g/cm3. The navy object is denser than aluminum.

7. The blue object has a mass of 35.1 g and a density of 1.35 g/cm3.

8. The density of water is 1.0 g/cm3. If the yellow object was placed in water, it would sink.

9. The white object has a greater mass than the blue object.

10. The volume of the white object is not 52 cm3 and it is also not 15.8 cm3.

11. The density of water is 1.0 g/cm3. If the red object was placed in water, it would float.

12. The volume of the red object is not 26 cm3.

Use this area for your scratch paper.

| |Mass |Volume |Density |

|Red | | | |

|White | | | |

|Yellow | | | |

|Blue | | | |

|Navy | | | |

|Pink | | | |

Density - Solutions

Make an observation of the flask.

1. There is a beaker of rubbing alcohol, water, and syrup.

2. The density of water is 1.00 g/mL, rubbing alcohol is .786 g/mL, and corn syrup is 1.36 g/mL.

Illustrate what you see in the graduated cylinder.

Using the data from above, explain why this occurs.

Order the densities of the liquids from lowest to highest.

If flavored water and maple syrup were placed in the beaker, predict the order you would expect them to be in?

What happens when water and oil are placed into a container together? Relate this is to the current topic.

Density - Calculating Volume

One component of density is volume. There are different ways to calculate volume depending upon the shape of the object. In this activity, you will be measuring the volume of different object. Remember to use units.

Use the table below to find the formulas needed to calculate volume.

|Shape |Formula |

|Box-Like |V = length x width x height |

|Cylinder |V = Лr2 x height |

|Graduated Cylinder |V = final – intial |

Volume:

Before you calculate the volumes, let’s look at why the unit is cm3 or mL.

Assuming a ruler was used to calculate the dimension of a box. The dimensions are 3 cm x 4 cm x 2 cm. To find volume, you would multiply all of the numbers together. 3 x 4 x 2 = 24.

You would also have to multiply the units. cm x cm x cm = cm3

This explains units of cm3.

Another way to calculate volume is with a graduated cylinder. A graduated cylinder initially has 5 mL of water. When you place an object into it, the water will rise. The rise in water is a result of the object’s volume. Therefore, the equation final – initial will tell you the volume of the object, or the difference caused by the volume of the object.

Measure the dimensions needed for each object and then calculate the volume for the object. You will not be using graduated cylinders for volume measurements, only rulers! Record the data in the table below. Remember units and use metric!

|Object |Formula |Volume |

|Gold Cylinder | | |

|Small Box | | |

|Block | | |

|Large Box | | |

Practice calculating volume if you were using a graduated cylinder. The initial volume is 15 mL and the final volume is 64 mL.

Density - Boxes

Calculate the density of the five boxes and answer the questions below. Fill in the table with your data.

| |Mass |Volume |Density |

|Clear | | | |

|Wood | | | |

|Silver | | | |

|Gold | | | |

|Copper | | | |

Compare the volume of each box.

Organize the boxes by increasing masses.

Organize the boxes by increasing densities.

Make a judgment regarding the effects of mass on density.

Graph the mass of each box on the x-axis and the density on the y-axis to provide evidence that supports your judgment above.

Discovering Density

Introduction

When scientific observations and measurements are made, patterns and trends sometimes emerge and relationships among different variables become evident. One of the best ways to recognize the existence of relationships involving numerical data is to plot the data on a graph.

Background

Mass is measured directly using a balance. The volume of an irregularly shaped solid, however, cannot be measured directly. Instead, its volume is usually measured by an indirect method called water displacement. The initial volume of a given amount of water is measured using a graduated cylinder. The solid is then carefully added to the water in the graduated cylinder and the new (final) volume is recorded. The volume occupied by the solid must be the same as the volume of water that has been displaced and is therefore equal to the difference between the final and initial volumes. See Figure 1 and Equation 1.

Pre-Lab Questions

1. The volume of a metal cylinder was measured indirectly by water displacement three times. The following volume readings were recorded. Using Equation I from the Background section, determine the volume of the metal cylinder for each trial, and then calculate the average volume of the metal cylinder.

Note: Since the volume of a solid is being measured, use the unit cm3.

|Initial Volume (cm3) |Final Volume (cm3) |Cylinder Volume (cm3) |

|7.6 |19.3 | |

|8.0 |20.1 | |

|6.2 |18.4 | |

|Average | |

2. The metal cylinder in Question #1 has a radius (r) = 1.05 cm and a height (h) = 3.32 cm.

a. Calculate the volume (V) of the metal cylinder (V = πr2h).

b. How does the average measured volume compare to the calculated (accepted) volume?

c. Use the percent error equation shown below to calculate the percent error between the measured and accepted values for the volume of the cylinder.

[pic]

3. Describe the purpose of figure 3.

Safety Precautions

Although the materials in this experiment are considered nonhazardous, follow all normal laboratory safety guidelines. Always wear safety glasses when working with chemicals and glassware in the lab.

Procedure: Develop a procedure that you will use to determine the density of your unknown. Be detailed by including the names of all lab equipment!

Data Table: Create a data table for your sample. Be sure to include at least 10 trials and your sample number!

Name: Date: Block:

Density Lab Summary Sheet

Graphing the Data

Plot the mass and sample volume data for samples 1—4 on the following graph. Each sample will be represented by one point Use the horizontal (x) axis for the volume and the vertical (y) axis for the mass. Label each axis—don’t forget the UNITS—and make sure the scale is clearly marked.

[pic]

Post-Lab Questions

1. Does it make sense that any trend or pattern in the mass and volume data should include (0,0) as a point? Explain your reasoning.

2. What kind of trend or pattern is obvious from the plotted graph of the mass and volume data? Is there a consistent relationship between the volume and mass of each sample? Explain.

3. Use the following information to determine the probable identity of your metal. What type of metal do you have? Justify your answer.

|Metal |Gold |Silver |Copper |Brass |Iron |Zinc |Aluminum |

|Slope (g/cm3) |19.3 |10.5 |8.9 |8.5 |1.9 |7.1 |2.7 |

4. Assuming that the identification of your metal is valid, use Equation 2 from the Pre-Lab Questions to calculate the percent error in your determination of the slope and the physical property it represents. The percent error measures the accuracy of your results.

5. Comment on the accuracy of this procedure and discuss any possible sources of experimental error and their effect on the data.

6. Create a bar graph comparing the densities of the metals provided in the chart above.

1. Obtain 35—40 g of either silver- or gold-colored metal shot in a 100-mL beaker. In the Data Table, circle whether the metal is “silver” or “gold.

2. Use a pen or marker to label four weighing dishes 1—4.

3. Tare (“zero”) weighing dish #1 on the electronic balance and add about one-fourth of the metal shot to the dish. Measure the mass of sample #1 (it should be between 8 and 14 g). Record the mass of sample #1 in the Data Table.

4. Repeat step 3 to divide the original metal shot sample among the other three weighing dishes. Vary the sample sizes so they are not all the same mass. Thus, if the first sample is 8 g, make the next sample about 10 g, etc. Do not mix up the samples!

5. Obtain a clean, 25-mL graduated cylinder and add approximately 10 mL of water to the cylinder.

6. Measure the initial volume of water in the cylinder to the nearest 0.1 mL and record the value for sample #1 in the Data Table (see Figure 3). Note: Use the units cm3 for the volume measurements.

7. Carefully add sample #1 to the water in the graduated cylinder. The best way to do this is to tip the cylinder at a slight angle and gently slide the metal shot into the water so that the water does not splash or splatter (and the glass cylinder does not break). Lightly tap the cylinder to release any trapped air bubbles. Record the final volume (volume of water plus the sample) in the Data Table.

8. Subtract the initial volume from the final volume to determine the volume of sample #1. Record this value in the Data Table.

9. Repeat steps 6—8 for each of the remaining samples. Do NOT remove prior samples from the cylinder between measurements. Before adding a new sample to the cylinder, measure the new “initial” volume in the graduated cylinder. This may not always be precisely the same as the previous final volume reading. Record initial and final volume measurements and the volume of each subsequent sample in the Data Table.

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