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# A Chemistry Calculation Challenge (2 Favorites)

LAB in Density, Identifying an Unknown, Measurements, Scientific Notation, Error Analysis. Last updated July 8, 2020.

### Summary

Students will apply their knowledge to solve four challenging chemistry-based calculation problems involving mass, volume, density, and number of molecules.

### Grade Level

Middle School

### NGSS Alignment

This lab prepares students to meet performance expectations in the following standards:

**Scientific and Engineering Practices**:- Using Mathematics and Computational Thinking
- Planning and Carrying Out Investigations
- Analyzing and Interpreting Data
- Engaging in Argument from Evidence

### Objectives

By the end of this lab, students should be able to:

- Solve problems involving density, mass, and volume.
- Identify an unknown substance using density.
- Complete error analysis in an investigation.

### Chemistry Topics

This lab supports students’ understanding of:

- Measurement
- Mass
- Volume
- Density
- Number of Molecules
- Identifying an Unknown
- Error Analysis

### Time

**Teacher Preparation**: 30 minutes**Lesson**: 90-120 minutes

### Materials (per student group)

- Ruler
- Digital scale or triple beam balance
- Aluminum foil, cut into rectangles (4-6 inches by 12 inches is an option)
- Sugar cube
- 100 mL graduated cylinder partially filled with water
- Unknown metal in powder, rock, pellet, or other irregular solid form (Ex: Al, Zn, Fe)
- Caliper (Part 4 only)
- Pre-1982 pennies
- Post-1982 pennies

### Safety

- Always wear safety goggles when handling chemicals in the lab.
- Students should wash their hands thoroughly before leaving the lab.
- When students complete the lab, instruct them how to clean up their materials and dispose of any chemicals.

### Teacher Notes

- This project was originally designed as an activity for high school students,
*Chemistry Composition Challenge*. This lab is a modification, inspired by that resource, for use in the middle school classroom as part of the AACT Strategic Plan and the work of the AACT Grade-Level Ambassadors. - Students will be tasked with designing a method to solve the following problems:
- Problem 1: Determine the thickness of a piece of aluminum foil and compare that value to an actual value.
- Problem 2: Determine the number of sugar molecules in a sugar cube.
- Problem 3: Determine the identity of an unknown metal. Determine the length, in centimeters, of one side of a cube that contains 1,000 grams of the identified metal.
- Problem 4: Determine the densities of two versions of the United States penny and compare those values to the actual values.

- There are separate worksheets for each problem, and they can be done together or separately.
- This lab should be conducted after students have been introduced to density and the particle model of matter. Students should know how to calculate density given mass and volume.
- This lab can be conducted in middle school physical science classrooms where students are comfortable making measurements and using data to calculate different quantities. It is also appropriate for introductory high school physical science and chemistry classrooms.
- This lab can be completed individually, but works best in groups of 2 to 4 students.

__Clarifications, Solutions, Hints, and Post Lab:__

*Problem 1: Thickness of a Piece of Aluminum Foil*Students need to find the thickness of a piece of aluminum foil__Clarifications:__folding it. Many students incorrectly attempt to solve the problem by folding the foil several times, measuring the height of the folded foil, and then dividing by the number of times they folded the foil.__WITHOUT__Students should mass the foil and use the mass and the density of aluminum to solve for the volume of the piece of foil using the density equation (D =m/V). The students should then measure the length and width of the foil, and use the calculated volume to solve for thickness, Volume = Length x Width x Thickness. The actual thickness of the foil can often be found on the packaging. If not, standard foil thickness is typically 0.0016 cm, heavy duty is 0.0024 cm.__Solution:__The density of aluminum and the necessary equations are given at the beginning of the activity.__Hint:__The lab can be followed up with a discussion of error analysis and calculating the percent error using the appropriate equation. Error can be introduced into the lab by purposely crinkling the foil prior to distribution. This will cause the measured length and width to be lower than the true value and result in greater calculated thickness.__Post Lab:__

*Problem 2: Sugar Cube Challenge*Students must find the number of sugar molecules in a sugar cube.__Clarifications:__To find the number of sugar molecules in the cube, students should mass the cube and convert the mass of sugar in the cube to the number of sugar molecules in the cube using one of these equivalent statements:__Solution:__6.02 * 10 ^{23}*molecules of sugar = 342 grams of sugar*

602*billion trillion molecules of sugar = 342 grams of sugar*Students who are unfamiliar or uncomfortable using scientific notation can complete the calculation with the unit “billion trillion molecules”.__Hints:__Students can be guided to the answer if they were not able to solve the problem on their own.__Post Lab:__

*Problem 3: Metal Identification*__Clarification____:__Students are to identify an unknown metal and determine the length, in centimeters, of one side of a cube containing a 1,000 grams of that metal.

Students find the mass of the metal using a scale and the volume by water displacement. Students find the identity of the metal by calculating its density with the data they have collected, and comparing the experimental density to known densities in the reference table provided. Once students identify the metal, they can use the density of the metal to solve for the volume of a cube containing 1,000 grams of the metal. After solving for volume, students use the fact that all sides of a cube are equal in length. Therefore, the equation V = L x W x H can be re-written as V = L x L x L. The cubed root of the volume is the length of one side of the cube. Many middle school students will struggle to calculate a cubed root directly. Therefore, they are instructed to first find the two whole numbers that the side length falls between. Then using calculators and trial and error, they can determine a more precise length.__Solution:__

Students should have some experience using the water displacement method before this activity. Students may have varying backgrounds and strength in mathematics, and many students will need assistance using the volume of a cube calculation.__Hints:__

- When choosing the unknown metal, it should be in powder, rock, or pellet form. Although it can be done in sheet form, the method will change. Examples of metals to use could be: Al, Cu, galvanized steel.

- Mossy zinc does not work well for this experiment, because the pieces of zinc also contain air pockets, resulting in a lower overall density. Iron filings are difficult to transfer and clean afterwards.

- 25 or more standard, galvanized steel paper clips works well as the unknown metal.

- Make sure to give students large enough samples of the unknown metal so that they can detect a meaningful change in volume when the samples are placed in water. Since the students are determining the identity of the metal using density, the exact amount of the metal is not significant.

- Use small, well-marked graduated cylinders so the volume can be read as precisely as possible.

Teacher may need to assist students with the calculations.__Post Lab:__

*Problem 4: Densities of Different Versions of the U.S. Penny*Students experimentally determine the density of pre-1982 penny (95% copper, 5% zinc) and post-1982 pennies (97.5% zinc, 2.5% copper). They then compare their experimental values to the actual values and calculate the percent error.__Clarifications:__

Students should mass the pennies. One pre-1982 penny is 3.1 g and one post-1982 penny is 2.5 grams. Volume is found by measuring the diameter and the thickness, and using the formula:__Solution:__

- *
*The thickness is 0.15 cm, and both pennies have the same volume, 0.35**cm*^{3}.

To reduce error, students should measure the thickness and mass of a stack of five pennies, and then divide by 5. Students can use a caliper to measure the dimensions of the pennies, or a ruler if calipers are unavailable. In 1982 both compositions were minted, so do not use pennies from that year. Ask students to bring in old pennies the weeks leading up to the lab.__Hint:__

Discuss error analysis and the percent error equation.__Post Lab:__

### For the Student

Download all documents for this lab, including the teacher guide, from the "Downloads box" at the top of the page.