# 1 Exp. 1: Exploration of Matter Through Density Determination

Pre-Lab

Use BB to quiz on the following before the lab: Define the following:

1. Density:

1. Specific gravity:

1. Buoyancy:

1. RSD (Relative Standard Deviation):

1. The density of a cardboard box is 43 pounds/cubic foot (lb. /ft3).  What is the density in the metric units of g/cm3?

1. What volume of liquid, expressed in mL, would a 16lb bowling ball displace (diameter = 8.5 in)? The following information may be useful for you:

1 in = 2.54 cm, 16 oz. = 1 lb., 28.3 g = 1 oz., volume of a sphere = (4/3) Πr3

1. A cylinder of lead weighs 1095 grams.  If the density of lead is 11.4 g/cm3, what is the volume of the lead?

1. A cylinder of lead has a diameter of 0.635 cm and a length of 5.08 cm. What is the mass of the lead?

1. If a piece of aluminum foil weighs 4.08 grams, the length of the piece of foil is 10.0 cm, and the width of the piece of foil is 93.5 cm, what is the thickness of the foil in cm?

Al = 2.70 g/cm3

1. Explain the safety concerns of this lab and how to avoid being injured.

Introduction

Density, specific gravity, and buoyancy are related, but not identical. Steel, for example, has a density of between 7.75 g/mL and 8.05/mL while water has a density of very nearly 1 g/mL.

ρ = m/v     Equation 1

Steel sinks in water. A large steel ship, such as an aircraft carrier weighing several tons, floats on water, however. The mass of water displaced by the hull of the ship must be greater than the mass of the ship. The air-filled ship is buoyant. The Greek mathematician and physicist, Archimedes, discovered this principle, called the Archimedes principle, in present day Cicely. King Hiero II, a friend to Archimedes, commissioned a gold crown, and gave a precise mass of gold to a smith for the project. The finished crown was returned, weighing identically to the mass of the gold that was provided. King Hiero, however, suspected that silver had been alloyed with the gold, and that he had been cheated. Archimedes was tasked with verifying the composition of the crown without destroying it. Puzzling over his task, Archimedes climbed into his filled bath, displacing his exact volume in water. The solution was apparent to him; Archimedes had solved the king’s dilemma, and without pausing to put on a towel, ran through the streets crying, ‘Eureka,’ or I have found it! Archimedes then displaced and measured a certain volume of water with a mass of gold equal to that of the crown. When the process was repeated with the crown, it displaced more water. The smith had replaced some of the gold with silver or some other less valuable and less dense metal.

SPECIFIC GRAVITY – Specific gravity is related to both density and buoyancy. Specific gravity is the ratio of the density of a material at a specified temperature compared to that of water at the specified temperature. Specific gravity is a unitless term since it is a ratio of densities. Specific gravity is frequently given with temperatures added. One temperature will give the temperature at which the density of the material was measured (the top temperature) and the second temperature (the bottom temperature) will give the temperature at which the density of water was measured.

Objective

The objective of lab one is to use careful measurements to calculate the density of various liquids, to use ancillary measurements to calculate the thickness of aluminum foil, and to use density to discover the percent composition of an alloy.

Safety

• Wear goggles. Assume that any unknown liquid is caustic.
• Check for broken glassware.
• Read and understand the lab before attending and ask questions in lab. It is better to ask before than fix after.

Waste/Housekeeping

• Dispose of water and ‘sea water’ in the sink
• Place your alloy on a paper towel in the back of the room and leave to dry

Procedure

Day 1: Density Determination of a Liquid

1. Record the mass of your smallest clean, dry beaker in the data table below under Trial 1*.
2. Pipette 5 mL of distilled water into the beaker using a volumetric pipette.

-Note the error printed on the bulb end of the pipette; it will inform your significant figures.

1. Measure the temperature and mass of the water. Record your data under the Trial 1 heading.
2. Perform a second density mass and volume measurement as Trial 2.
3. Determine the average density of water based on your two trials.

 Data Table 1: Water Trial 1 Trial 2 Mass of beaker (g) Tared mass of water (g) Volume of water (mL) Density of water (g mL-1) Average density of water (g mL-1) Laboratory temperature (ºC)

$\frac{}{}$   % error = |(experimental value) – (accepted value)|/accepted value x 100            Equation 2

Percent error communicates how much your experimental results differ from an accepted literature value. *Statistical equations are provided for your first lab. In future labs, please refer to your appendix.

Using Table 1, calculate the percent error in your water density measurement. Be sure to show your work on all calculations for credit.

 Table 1: Density of water at Various Temperatures Temperature ºC Water Density (g mL-1) 18 0.998595 19 0.998405 20 0.998203 21 0.997992 22 0.997770 23 0.997538 24 0.997296 25 0.997044 26 0.996783 27 0.996512 28 0.996232

% error, density of water _________________________________

Repeat the density analysis for seawater.

 Data Table 2: Seawater Trial 1 Trial 2 Mass of beaker (g) Tared mass of water (g) Volume of water (mL) Density of water (g mL-1) Average density seawater (g mL-1)

The density and salinity of seawater varies with temperature. In this case, rather than using a percent error to analyze your results, you will calculate a percent difference between trials one and two. Percent difference communicates how precise two measurements are, or how they agree with each other when neither can be considered the true or correct value. The percent difference is the absolute value of the difference of the experimental values over the mean times 100. Calculate the percent difference between your seawater samples. Be sure to show your work for credit.

% difference = |(E1) – (E2)|/1/2 (E1) + (E2) x 100        Equation 3

% difference seawater __________________________________

Now that you have densities for D.I. water and seawater, find the specific gravity of seawater and include it in your report. Use the tabulated data for the density of water at a given temperature listed in Table 1.

Specific gravity seawater __________________________________

Day 2:

Thickness of Aluminum Foil

Obtain a piece of aluminum foil. The size, or area is up to you, but both your mass and area error will increase as size decreases. A sheet approximately the size of a sheet of notebook paper may work well. Given that the density of aluminum is 2.73 g/cm3, determine the thickness of the aluminum foil. Develop your own procedure. The following example data table may be helpful.

 Data table 3: Aluminum Thickness Length (cm) Width (cm) Mass (g) Thickness (cm) Trial 1 Trial 2

Thickness of Aluminum Foil: ____________________________________

Include a percent error or a percent difference of your findings. Choose the most appropriate one. Please refer to your appendix for clarification on the use of statistical methods.

% error or % difference: _____________________________________________

Density of an Alloy:

Now that you are well versed in using density for simple measurements, you will determine the percent composition of an alloy. Your alloy is a custom brass alloy, composed of copper and zinc. Any trace metals occur at small ratios and can be ignored. Some hints to keep in mind as you perform your analysis:

• Smaller graduated cylinders usually have more graduations, reducing volume measurement error and increasing significant figures
• If you weigh your brass sample before you wet it, you will reduce mass error
• You will need to dry your sample between trials and re-weigh.
• Increasing your displacement of water or ΔV will decrease volume error

Come up with a sound strategy for finding the density of your custom brass sample. Points will be awarded for obtaining the correct percent composition. The following example data table may be helpful. Your brass sample may be a cylinder or pellets, and differing glassware may be appropriate.

 Data Table 4: Percent Composition of an Alloy Trial 1 Trial 2 Trial 3 Trial 4 (if needed) Total mass brass (g) Initial volume water (mL) Final volume water (mL) Volume brass (mL) Density brass (g/mL) Average density brass

The density measurements for trials one and two and three should agree within +/-0.5 g mL-1. If the trials differ by more than this value, repeat your calculations a fourth time. You may choose to throw out the offending density measurement at this point.

Relative standard deviation, RSD, can inform you of the precision of your measurements. In this case you will not be using standard deviation from excel, although you may check your work using the program. You will calculate it the long way, showing all parts of the calculation.

$(xixm)2n1">(xixm)2n1−−−−−−−−−−−−√$\sqrt[]{\frac{\sum _{}^{}\left(��-��\right){}^{2}}{�-1}}$$                   Equation 4

$%RSD = sxm � � � (100)$                                         Equation 5

Standard deviation = = s

xi =each individual measurement

xm = mean (average) of the measurements

n = the number of measurements

%RSD of your three or four measurements __________________________________

Now that you have measured and calculated a reliable density in your brass sample, you are prepared to calculate the percent composition between copper and zinc. The mathematical operation can be expressed as follows:

x (copper density) + (1-x) (zinc density) = average density of brass                            Equation 4

where

x = the fraction of the alloy composed of copper

1-x = the fraction composed of all other metals (zinc)

The densities of some coinage metals are found in table 3.

 Table 2: Density and Cost of Coinage Metals Metal Density (g mL-1) Cost (\$ g-1) Zinc 7.13 0.00201 Copper 8.96 0.00591 Nickel 8.92 0.0129 Silver 10.5 0.570 Gold 19.3 55.68

https://www.moneymetals.com/precious-metals-charts/gold-price accessed 06/18/20

Composition of alloy = ________________% copper __________________ % zinc

Post Lab:

1. What would happen to your density calculation if you measured the volume of seawater with your burette, but class ended, and you kept the sample uncovered in your drawer to measure the mass the following week in lab?

1. Assuming your brass samples are identical in composition, or percent copper and zinc, how would your density measurements compare if you used differently sized brass samples during different trials? Be specific in your descriptions of density and its constituents, mass and volume.

1. You have a chunk of material about the size of a marble that appears to be antique ivory.  Describe in detail how you would determine the mass and the volume so that you could calculate the density?

1. Considering the data in Table 3, would equal masses of gold and copper result in the same volume change if added to water? Please explain.

1. What are the respective purposes for using %RSD and percent error? Name an instance from any discipline or application where each is applicable.

1. Complete the pre-lab and take the pre-lab quiz in your Blackboard shell before attending lab.
2. Use a lab notebook to record observations and make calculations.
3. Create an informal lab document to turn in at the beginning of the next lab. Your lab report should include clearly labeled and tabulated or graphed raw data, any formulas or equations, unknown number, or letter (if applicable), conclusive data such as density, % error, etc. with clear example calculations or sample calculations*. Discuss results relevant to your findings. Think about the main point of the lab, or the results that you worked for and be sure to include it or them. Refer to How to Write an Informal Lab Report as you draft your report.
4. Include numbered responses to any post lab questions. You do not need to re-write the questions but will use complete sentences or a short paragraph as appropriate. Be specific. If you describe an error, for example, you must describe the direction the data would skew and why.
5. Submit your document before your next lab appointment under the assignment tab on your laboratory Blackboard shell.

References:

Davila, R. In Lab 3: Density College of Southern Idaho; College of Southern Idaho; 2020.

Dieckmann, G., Sibert, J. In An Atoms First Approach to the General Chemistry Laboratory; McGraw Hill: New York, NY, 2014; pp 3–12.

Ross, R. Eureka! The Archimedes Principle. https://www.livescience.com/58839-archimedes-principle.html (accessed Jun 29, 2020).