## Lab: Density

This lab has several objectives. The scientific purpose of the lab is to measure the density of salt water and the density of aluminum. The other objectives of the lab are concerned with learning laboratory skills and data analysis. You will learn how to use a measurement tool to its maximum precision by estimating the last digit of every measurement. You will learn how to watch for physical sources of experimental variation. You will learn to react to data you collect and adjust your techniques as needed. You will learn how to use a spreadsheet to analyze your data in two ways. First, you will make a data table and use the calculation functions of the spreadsheet to calculate the average, range, and percent error. Second, you will create a graph of volume vs. mass (x vs. y) and use the software to draw a trendline and calculate the equation of the line of best fit. The slope of such a graph is equal to the density of the material.

### Materials

• 10 mL, 50 mL, and 100 mL graduated cylinders
• lab balance
• pen
• lab notebook or paper
• water
• aluminum shot
• salt water

### Background

Density is a familiar property of matter. It is the mass per unit volume, calculated using D = m/V. For solids this is given as g/cm3 and for liquids as g/mL. These units are actually equivalent because a milliliter is defined as exactly one cubic centimeter.

How can density be measured? Since density is the mass per unit volume, two measurements (at least) must be made. Every measurement is subject to ways in which it may be higher or lower than a true measurement. Since for a solid the measurement of volume requires two measurements (before placing it in water and after) this increases the chances for experimental variation to affect the outcome. Other things to watch for are bubbles, splashing water, wet materials, and a badly calibrated lab balance. Another problem that may affect data collection is when a sample is too small. If a sample is too small then the change in volume in a graudated cylinder may be too small to measure accurately. By taking steps to guard against these problems, and any others you may discover, you can reduce the effect of experimental variation on your results.

The most important way to ensure good results is by using good measurement technique. Make sure you estimate properly between the marks on every tool to 1/10 of the smallest division.

1. Two data tables. One for aluminum and one for salt water following the guide in the sample spreadsheet.
2. Two graphs. The graphs must have a title, labeled axes, a line of best fit, and the equation of the line. Follow the formatting of the graphs in the sample spreadsheet.
3. Answer the following questions in separate cells. Format the cells to wrap text and size them for easy reading.
1. The true density of aluminum is 2.70 g/cm3. Subtract your result from this value (or vice versa to get a positive answer). How far off were you? (Use either the slope of the line on your graph or the result from your average and range).
2. The true density of salt water is 1.10 g/mL. Subtract your result from this value (or vice versa to get a positive answer). How far off were you? (Use either the slope of the line on your graph or the result from your average and range).
3. Give two reasons why your result value (average or slope) for the density might be higher than the true value. (Consider how measurements of mass or volume could be inaccurate).
4. Give two reasons why your result value (average or slope) for the density might be lower than the true value. (Consider how measurements of mass or volume could be inaccurate).
5. Think back to your data collection process in the lab. What, specifically, do you think led to your value being different from the standard accepted value for each density measurment you made? Consider that your measurements for mass or volume could either be higher or lower than an accurate measurement.

### Procedure

We are measuring density by measuring the mass and volume of five samples of the same material. Each sample will be different from the others in size. By making a graph of volume (x-axis) vs. mass (y-axis) and finding the slope of the line of best fit you will determine the density. The slope of the line in such a graph is the mass divided by the volume, which is the density. This procedure may produce a more accurate result than simply finding an average.

Precise measurement is absolutely critical to making a successful and accurate measurement. Measure between the lines on all measurement tools to estimate one tenth of the smallest division on the tool. On three-beam balances this means you must measure to the nearest 0.01 g. On a 10-mL graduated cylinder measure to the nearest 0.01 mL. On a 50-mL or 100-mL graduated cylinder measure to the nearest 0.1 mL.

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#### Measuring Density for a Liquid

Measuring the volume of a liquid is easy. Place a random sample of tap water or salt water (or some other liquid provided by your teacher) into a graduated cylinder and then read the volume. Measuring the mass requires a bit of care but is not too hard.

1. Using a three-beam balance measure the mass of a dry graduated cylinder to the nearest 0.01 g. Write this number down!
2. Put a small sample of liquid into the cylinder. The amount does not matter very much because density is the same regardless of the size of the sample. Still, fill it only about one fifth full.
3. Read the volume precisely, estimating to one tenth of the smallest division marked on the cylinder. Write this volume down in your data table (see the next page).
4. Look for ways to avoid measurement error. For example, make sure that the outside of the cylinder is not wet and that the balance pan is also not wet. Make sure that no liquid is clinging to the top part of the cylinder where it will add to the mass you measure but not the volume.
5. Measure the mass of the cylinder now that it contains your sample. Subtract the mass of the dry, empty cylinder from the mass you find. Write down this number in your data table.
6. Do not dump out any of the liquid in your cylinder. Instead, just add a little more. Read the new volume and write it down in your data table.
7. Measure the mass again and subtract the mass of the dry, empty cylinder. Write down this mass in your data table.
8. Repeat these steps until you have five measurements of volume and mass.
9. Calculate the density of each of your samples. All five results should be nearly the same if you have made careful measurements.
10. Find the average density and write it in your data table. Take a look at your data and evaluate it. Does it appear that you have a consistent set of data? If there are densities that you’ve calculated that are very different from the others then you must make further measurements. Careful measurement will result in consistent results and you can recognize a poor data point and replace it with a good one. Do so.

#### Measuring Density for a Solid

Measuring the mass of a solid is easy. Place a random sample of aluminum (or some other solid provided by your teacher) onto a balance and measure the mass. Measuring the volume requires a bit of care but is not too hard. You will use the method of Archimedes and submerge your solid samples in water to find the volume by difference.

1. Your first sample of aluminum must have a minimum sample size between 8 and 12 grams. Do not let your sample get wet before you weigh it.
2. Measure the mass of your first sample to the nearest 0.01 g and record it in your data table.
3. Obtain a graduated cylinder and fill it partway with tap water. Make sure no water is clinging to the inside of the cylinder where it could later drop into the liquid below. Measure the volume of the water as precisely as possible, estimating to one tenth of the smallest division marked on the cylinder. Write this down.
4. Add your solid to the cylinder containing your measured amount of tap water. Be careful not to splash any of the water out. Be careful about bubbles. If there are bubbles hidden in among the pieces of aluminum then they will make your measured volume bigger than the volume of the actual material. Gently tap the cylinder to dislodge bubbles.
5. Measure the volume in your cylinder now that the solid is submerged in the water. Subtract the original volume of water. Write the result in your data table as the volume of the material.
6. Do not dump out your cylinder and start over. Instead, measure the mass of an additional amount of dry solid that is about as large as your first sample. Add this mass to the mass of your first sample and record this total mass as the mass of your second sample.