Learning Goals

1. Use bomb calorimetry to measure heat of reaction;
2. Use a thermometer and analyze the limitations of thermometry;
3. Observe changes in phases of matter and consider the challenges associated with volatile substances;
4. Apply the ideal gas law and analyze the limitations of using the ideal gas law in an experiment;
5. Synthesize a simple procedure and a data table to collect experimental data;
6. Choose a follow-up experiment based on initial results;
7. Write a conclusion based on a specific prompt and tabulate results to support the conclusion.

Ideas for portions of this lab were drawn from the University of Pennsylvania Laboratory Program for Chem 53, accessed at this webpage: http://www.sas.upenn.edu/~kennethp/chemlab1.pdf, and the University of Calgary Laboratory Program for Organic Chemistry, accessed at this webpage: http://www.chem.ucalgary.ca/courses/351/laboratory/boilingpoint.pdf.

Introduction

In many ways, chemistry can be a puzzle: since you cannot see atoms directly, you must instead collect as many pieces of data as you can and put them together to get the best possible answer. In this lab, you are tasked with identifying an unknown volatile liquid.

First, you will measure the molar mass of the liquid using the ideal gas law, but is the molar mass enough information to identify an unknown? How much uncertainty is associated with the molar mass measurement, anyway? If you were publishing a paper and wanted to convince the scientific community that you have identified a liquid, measuring the molar mass would surely not be enough information!

As additional pieces of evidence, you will measure the density in the liquid state, the boiling point, and the heat of combustion. These four pieces of evidence should pinpoint the exact identity of the liquid with enough certainty to convince even the most skeptical audience, who is hopefully yourself.

When you think you know the identity of the unknown, you can run a confirmatory test.

Background

What is a volatile liquid?

A volatile liquid is a liquid that vaporizes readily under normal conditions. Many volatile liquids have a noticeable smell because they vaporize into your nose! Throughout this lab, you will be working with a volatile liquid. When it is warm, it is mostly a gas, and when it is cool it is mostly a liquid. Note that you will be measuring the density of the substance in both the liquid and the gaseous state, but you will find that the tendency of the volatile liquid to vaporize and condense introduces uncertainty in both of these measurements.

Measuring molar mass from density of the gaseous state

The ideal gas law provides a way to relate the number of moles of a gas to the volume of the gas: n/V = P/RT

If you are also able to relate the number of grams of the gas to the volume of the gas (g/L, in other words, density), then these two formulas together allow you to then relate the number of grams of the gas and the moles of the gas, which is the molar mass: molar mass = (density)RT / P.

Your textbook shows a more detailed derivation in Section 8.3.

In this lab, you will measure the density of a volatile liquid in its gaseous state, the pressure, and the temperature, and this will allow you to calculate the molar mass. To measure the density, you will need to measure the mass and volume of a gas. The procedure will guide you through forming the gas and measuring the mass, but you must design your own method of measuring the volume of the gas. Be creative! Try to get as many significant figures as possible.

Heat of combustion

This is a topic you have not yet covered, but you will soon! Here is a simple explanation of what you need to know for this lab:

The heat of combustion is the amount of energy released when a given amount of a substance is burned in the presence of excess oxygen. Normally this value is reported in terms of energy per mole of the substance, but because we do not yet know the molar mass of the liquid, we will measure it in terms of energy per gram of the substance and compare it to the list of possible sample identities at the bottom of this page, also in those units, in order to identify the liquid.

Density of the liquid state

You should be very comfortable measuring the density of a liquid. You just need the mass and the volume: density = mass/volume. You will be comparing the density of your liquid to the list of possible sample identities at the bottom of this page to help you identify the liquid.

Refer back to Lab 1 for a refresher on density measurements.

Boiling point

Boiling point is the temperature at which a substance changes from a liquid state to a gaseous state. Boiling point is actually a function of pressure, but because most people measure it under atmospheric pressure, it is typically reported at 1.000 atm (1013 mbar). If you notice that the atmospheric pressure on the day of your measurement is greater than or less than 1013 mbar, know that this will contribute to a discrepancy between your results and the literature boiling point values.

Procedure

Note: do this lab with a partner. There are five parts to this lab, which will be done over two weeks. I suggest doing part 1 on the first week and parts 2-5 on the second week, although you may chose to do parts 2 and 3 whenever it is convenient. Be sure to use the same thermometer throughout the experiment.

1. Measuring molar mass from density

Thermometer calibration

At some point, you probably had this thought but were afraid to say it out loud: “are these thermometers right? I always thought water boiled at 100 °C, but it looks like this water is boiling at 105 °C. I don’t know, maybe I’m reading it wrong?” If you have had this thought, then pat yourself on the back for being observant. The alcohol thermometers are not perfect, and to get a reasonably accurate temperature measurement with them, you will need to calibrate them. Since we are making most of our temperature measurements in this experiment near 100 °C, we will calibrate at 100 °C.

Bring a beaker of tap water to a rolling boil over a bunsen burner. It doesn’t matter what size beaker and exactly how much water, but a 600 mL beaker about 3/4 filled with tap water would be a great choice. Once boiling, place your thermometer into the water. Hold it or clamp it so it doesn’t touch the bottom or sides. When the temperature is stable, record the “thermometer calibration temperature” to the nearest 0.2 °C in Table 1.

You can now calculate the offset for your individual thermometer.

100.0°C – “thermometer calibration temperature”(°C) = thermometer offset (°C)

This number may be positive or negative. Use a piece of label tape to label your thermometer with its thermometer offset. From now on, factor that offset into your temperature measurements before recording them in your data table. Keep that calculator handy!

As an example, let’s say your thermometer calibration temperature is 105.0 °C.

100.0°C – 105.0 °C = -5.0 °C

Now you know to subtract 5.0 °C from every temperature you measure throughout the experiment. If your thermometer reads 92.2 °C, then record 92.2 °C – 5.0 °C = 87.2 °C.

Pressure

Record the barometric pressure of the atmosphere in Table 1. If you have reason to believe the pressure is changing throughout the experiment (maybe there is a hurricane outside?), check it before beginning every trial, but normally checking at the beginning of the experiment is sufficient.

Mass and temperature

Use the same 125-mL Erlenmeyer flask throughout this section. Dry the Erlenmeyer flask thoroughly. Measure the mass of the 125-mL Erlenmeyer flask with an Aluminum foil cover secured with a rubber band. Trim the Aluminum foil cover to right below the rubber band. Record the mass of the covered flask in Table 1. Make a tiny hole in the foil cover with a thumbtack.

Set up a hot water bath with a 600 mL beaker about 3/4 filled with tap water, similar to the one shown:

Bring the water to a boil over a blue bunsen flame.

While the water begins to heat, remove the foil cover and rubber band, place about 2 mL of the volatile liquid from the small bottle into the Erlenmeyer flask, then replace the foil cover and rubber band.

Turn off the flame. Submerge the covered Erlenmeyer flask up to its neck in the hot water, and use a clamp to attach it to the ring stand. Add more water if you need it to cover the flask up to the neck, but try not to get the aluminum foil wet.

Also, submerge a thermometer in the water, and use a clamp to attach it to the ring stand.

Monitor the temperature of the water to ensure it stays around 90 °C (don’t forget to factor in your calibration offset). Turn on the flame if the temperature drops below 80 °C. Maintaining this temperature, watch the vapor escape through the pinhole. Watch for the vapor to stop escaping through the pinhole and for visible condensation in the flask to disappear (tendrils dripping down the sides of the inside of the flask). This should take no more than 10 minutes. If you continue seeing condensation after the first 10 minutes, turn up the heat because your thermometer may be reading low. You can verify that the vapor has stopped escaping by holding a small watch glass over the pinhole and seeing that no condensation develops right above the pinhole. As soon as the vapor stops, record the temperature of the hot water bath to the nearest 0.2 °C in Table 1. Be sure to factor in the calibration offset!

Remove the Erlenmeyer flask from the hot water bath, but keep the cover on. Be sure all of the liquid has vaporized. If there is visible liquid, put it back into the hot water bath for a few minutes. Dry the outside of the flask completely. Then, measure the mass of the covered flask with the vapor inside (it may condense back to a liquid). If the mass is not stable, let it cool longer. Record the mass in Table 1. Expect a mass around 0.2 g. Consider re-doing the trial if your mass is much lower or higher.

Repeat this procedure two more times for a total of 3 trials. You may reuse your hot water bath. You must use the same 125-mL Erlenmeyer flask every time, but make sure you dump out the gas and any condensation before weighing the flask empty. If your aluminum foil gets wet, then you should use a new piece.

Volume

Measure the volume of your Erlenmeyer flask using your method, your partner’s method, or a combination of the two. If you need to measure the mass of the water in the flask, be sure to use a high capacity balance such as the CPA324s, which measures up to 320 g. Try not to spill water on the balances. Be sure to clean it up if you do. Record your data in Table 2.

2. Heat of combustion

When it is your turn to use the bomb calorimeter, begin by preparing your sample for analysis:

The experimental sample – this is a clean sample cup with 1.00 g of the volatile liquid inside. Record the exact mass of the volatile liquid in a tared sample cup in Table 3. Cover the sample cup with a piece of parafilm immediately after recording the mass of the sample to ensure none of the sample evaporates.

Your instructor or TA will walk you through measuring the heat of combustion for the sample. You will need the mass of the liquid in order to operate the bomb calorimeter. Record your results in Table 3.

3. Density of liquid state

Use a clean, dry 100 mL volumetric flask with a ground glass stopper for this experiment. How many significant figures do you get? Ask if you are not sure.

Measure the mass of the empty volumetric flask and stopper. Record the data in Table 4.

Fill the volumetric flask exactly to the point where the bottom of the meniscus is on the ground line with the volatile liquid from the bottle labeled “use for density of liquid experiment.” Cover the flask immediately to ensure none of the liquid escapes.

Measure the mass of the filled volumetric flask and stopper. Record the data in Table 4.

4. Boiling point

I will provide a demonstration apparatus for this rather complex set-up, but this is a description of how to build it:

Use the same thermometer that you previously calibrated. If you aren’t sure it is the same one, repeat the calibration procedure and record the offset. Gently push a thermometer through a split rubber stopper. Push the stopper up past the 100 °C mark so you can read temperatures below this mark.

Secure a 5 or 10 mm glass test tube to a thermometer with a rubber band. Be sure not to cover the temperature marks too much; temperatures below 30 °C are probably fine to cover. Make sure the bottom of the thermometer and bottom of the test tube are lined up together.

Use a bunsen clap attached to the rubber stopper to secure the thermometer/test tube apparatus to a ring stand.

Pour about 1 mL of the volatile liquid into the test tube. Drop a boiling chip in the test tube. Then, drop a capillary tube open end down into the test tube, as shown in the illustration. CAUTION! These volatile liquids are all flammable. Keep it away from open flames.

Below this apparatus, you will need to make a hot water bath. Attach an iron ring to the ring stand about an inch above a bunsen burner, which is connected to the gas with amber tubing. Place a wire gauze on it. Place a 250 mL beaker filled 3/4 of the way with water on the gauze.

Lower the thermometer/test tube apparatus into the water bath, making sure to submerge the volatile liquid completely but allowing sufficient space above the water to ensure no water splashes into the test tube.

Turn on the gas and ignite the bunsen burner. Heat up the water nearly to boiling. Watch the test tube carefully. At first a few bubbles will come out of the capillary tube, but eventually you will see a steady stream of bubbles coming out of the capillary tube. When you see a slow, steady stream of bubbles, turn off the bunsen burner and allow it to cool. Your thermometer should read at least 85 °C before you turn off the flame (that temperature is above all of the possible boiling points). While it is cooling, watch the capillary tube. When you see it start to draw the volatile liquid up into the capillary tube, record the temperature as the boiling point. Be sure to record the temperature to the nearest 0.2 °C. You might miss it if you aren’t watching carefully the whole time it is cooling because it gets slurped up like a straw very quickly. IMPORTANT: be sure to factor in the offset that you found in Part 1 when recording the boiling point temperature. Record data in Table 5.

Repeat for 3 trials total. If three trials do not agree within 3 °C, consult your instructor or TA about performing additional trials. If necessary, refill the test tube and/or hot water bath between trials. Extinguish the flame before refilling or otherwise handling the volatile liquid.

5. Confirmatory test

Once you have completed your calculations and think you know the identity of the unknown, present your answer to the instructor or TA. She will provide a confirmatory test that you can use to validate your answer (or not!). Instructions for your test will be available at that time. Record the name of the test you used and the result. If the first test is negative, you may try a second test.

Calculations

You can now calculate the molar mass of the unknown from the density of the gas. Then, compare the molar mass, the heat of combustion, the boiling point, and the density of the liquid state of the unknown to corresponding data from known substances. Use these results to select the identity of your unknown from this list of possible unknown liquids:

1. 1. Benzene – carcinogen found in gasoline
      • Molar mass = 78.11 g/mol
      • Heat of combustion = 9.992 kcal/g
      • Density of liquid = 0.876 g/mL
      • Boiling point = 80 °C
   2. Hexane – common organic solvent derived from crude oil
      • Molar mass = 86.18 g/mol
      • Heat of combustion = 0.452 kcal/g
      • Density of liquid = 0.659 g/mL
      • Boiling point = 68 °C
   3. Methanol – wood alcohol, causes blindness when consumed in moonshine
      • Molar mass = 32.04 g/mol
      • Heat of combustion = 5.410 kcal/g
      • Density of liquid = 0.792 g/mL
      • Boiling point = 65 °C
   4. Ethanol – grain alcohol, white lightning
      • Molar mass = 46.07 g/mol
      • Heat of combustion = 7.086 kcal/g
      • Density of liquid = 0.789 g/mL
      • Boiling point = 78 °C
   5. Acetone – nail polish remover
      • Molar mass = 58.08 g/mol
      • Heat of combustion = 7.360 kcal/g
      • Density of liquid = 0.791 g/mL
      • Boiling point = 56 °C

   Report

   Fill out the worksheet for the report.

Learning Goals

1. Employ several common separation techniques and analyze limitations of those techniques;
2. Practice decantation and gravity filtration;
3. Use a graduated pipette and an erlenmeyer flask;
4. Observe a precipitation reaction and the formation of a crystalline solid;
5. Use notions of stoichiometry to calculate reaction yield;
6. Use a drying oven and analyze limitations of the drying oven.

Introduction

James Andrew Harris was an American nuclear chemist who lived 1932 – 2000. While working at Lawrence Berkley National Laboratory (at the time, called Lawrence Radiation Laboratory), he helped discover synthetic elements 104 and 105, Rutherfordium and Dubnium. How are synthetic elements made? Often by smashing together very pure samples of lighter elements. Harris carefully produced these pure samples using separation chemistry.

These are a few more examples of the applications of separation chemistry today and in history:

1. Isolating the fissionable Uranium and Plutonium isotopes that were used to make the atomic bombs dropped on Japan in World War II;
2. Extracting metal from ore to make metal tools (ever heard of the “Iron Age” or “Bronze Age”?);
3. Purifying drinking water;
4. Purifying pharmaceuticals from natural sources;
5. Distilling spirits;
6. Treating sewage;
7. Dialysis for patients suffering from kidney failure;
8. Refining crude oil.

In this lab, you will be separating a mixture of substances using physical and chemical separation techniques and deducing the original masses of each substance in the mixture.

Background

The heterogeneous mixture you will begin with contains elemental iron filings, silicon dioxide (sand), sodium chloride, and sodium nitrate. You will be separating each of these substances using several common separation techniques that depend on the physical and chemical properties of the substances: magnetic separation, filtration, chemical coagulation, and finally evaporation.

1. Magnetic separation uses a magnet to pull out magnetic particles (such as iron filings);
2. Filtration removes insoluble particles (such as sand);
3. Chemical coagulation is the introduction of a chemical that causes part of a mixture to precipitate out of a solution so it can be removed physically such as with filtration;
4. Evaporation isolates soluble substances by evaporating water.

Procedure

Note: perform this lab with a partner.

I. Sample the mixture

1. Weigh an 800 mL beaker. Record the mass in Table 2. The balance near the south entrance to the lab has the highest capacity. Use it if you have a heavy beaker.
2. Pour in the contents of your jar. Tap or scrape out every little bit.
3. Record the information written on the jar in Table 5 in the column labeled “original mass.” Table 5 is near the end of your lab worksheet.

II. Isolate the iron filings

1. Record the mass of a 250 mL beaker in Table 1.
2. Put a plastic bag over a bar magnet. Move the plastic-covered magnet around near the mixture. Observe the iron collecting on the magnet. Gently shake the magnet to keep sand and salt from collecting on the magnet: you only want iron filings to stick to the magnet.
3. To remove the iron, put the magnet into the 250 mL beaker. Open the plastic bag and remove the magnet. The iron filings should drop off the bag into the beaker. If you find that salt and sand were also collected, then try again. Try performing this step a few times until you perfect your technique.
4. Repeat the iron collection process three or four more times until no more iron accumulates on the magnet.
5. Record the mass of the iron filings in the beaker in Table 1.
6. After you have recorded the mass, put your recovered iron filings in the iron filings waste container.

III. Isolate the silicon dioxide

1. Add about 100 mL of DI H2O into the 800 mL beaker that contains the mixture, now depleted of iron. Swirl rigorously for a few minutes, but take care not to splash any out of the beaker.
2. Let the sand settle at the bottom of the beaker, then carefully pour the aqueous solution into a funnel in a 250 or 300 mL Erlenmeyer flask. Try not to lose any sand in the solution, but also try to pour off as much of the solution as possible. Imperfect separation in this step is a major source of error in this experiment. Record in your observations in Table 2, particularly note whether or not you lost sand in the solution and how wet your sand appeared after pouring off the aqueous solution (eg. “sand appeared soupy” or “sand had no visible liquid”).
3. Label your beaker containing the sand with a sharpie directly on the glass. Put the beaker with the wet sand inside in the drying oven for 20-30 minutes. You should continue with the next part of the lab while this dries. Your instructor or TA will help you decide when to take the beaker out. When the sand flows freely, take it out and let the beaker cool completely before weighing the beaker with the sand inside and recording the mass in Table 2.
4. Put the recovered sand into the trash.

IV. Precipitate chloride salt

1. Weigh a piece of filter paper on a watch glass. Record the mass in Table 3.
2. Use a graduated pipette to add 7 mL (notice the significant figures here?) of 3 M nitric acid [CAUTION!] to the solution. Swirl to mix.
3. Use a graduated pipette to add 5.00 mL (notice the significant figures here?) of the prepared 0.500 M (and here?) silver nitrate solution to your solution in the Erlenmeyer flask. Observe a white precipitate forming upon mixing these two clear solutions. Swirl to mix. Pro-tip: Erlenmeyer flasks are a great choice when you want to swirl a solution to mix rather than using a stir rod, which may inadvertently remove product.
4. Let the mixture settle in a dark cabinet for 5 minutes. Make sure to set up  your filtration apparatus while you let it settle.
5. Set up a filtration apparatus with the weighed piece of filter paper and small funnel, similar to the one in the illustration. Place the funnel into a 250 or 300 mL Erlenmeyer flask. Wet the filter paper with a little water to help it stick to the glass. 
   
   

   Filter apparatus  https://alfa-img.com/show/filter-paper-and-funnel.html

6. Once the mixture has settled for 5 minutes, pour the solution through the filter apparatus. If any solids stick to the flask, rinse the flask once or twice with a small amount of cool DI water. Note that any water you add will have to be boiled off, adding time to the end of the experiment! Scrape with the rubber policeman if necessary.
7. After all of the solution has passed through, carefully move the filter paper to the watch glass without losing any of the solids. Unfold the paper. Label the watch glass. Put this into the drying oven for about 20 minutes until completely dry. Use this time wisely. You can clean up other parts of the experiment and/or continue the experiment. You don’t need to watch it dry. If it isn’t dry before you are ready to leave for the day, then take it out of the oven, put it in your cabinet, and come back another day to weigh it.
8. Once dry, let the watch glass cool completely, then weigh it and record the mass on Table 3. Subtract the mass of the watch glass and filter paper to deduce the mass of the pure chloride salt. Dispose of the solids and filter paper in the trash.

V. Dry the nitrate salt

1. Weigh your 800 mL beaker, and record the mass in Table 4 (yes, it might be different from the last time you weighed it. you might have mixed it up with someone else’s).
2. Pour the solution now containing just the nitrate salt into the weighed 800 mL beaker.
3. Set up a ring stand with wire gauze with a bunsen burner underneath, similar to the one in the illustration. Set this up in a fume hood. 
4. With the hood sash closed, boil the solution until the volume decreases to about 10 mL or less. When the volume gets very low, watch it carefully for crystal formation. As soon as you see a crystal form, turn the gas down and stay close. When it is dry, turn the gas off. If you keep heating after it is dry, the salt will spatter (lost product) and the beaker may shatter (yikes!). After the beaker is cool, weigh the beaker and the crystals. Record the mass in Table 4. Wash the crystals down the drain. (Look at how soluble this product is!) Subtract the mass of the beaker to deduce the mass of the impure nitrate salt.

Calculations

The masses of the recovered iron filings and sand are directly measurable, but the masses of the salts require advanced stoichiometry to deduce. Embrace the challenge!

Report

Fill out this worksheet. Turn in either a paper or digital copy.

Learning goals:  follow instructions to complete a chemistry experiment, collect and analyze experimental data, explain likely sources of experimental error, work collaboratively with a lab partner.

Introduction

Rules about significant figures may seem arbitrary from a theoretical standpoint, but in the laboratory you will see that they allow you to determine the precision of your measurements and calculations. When your measurement has a limited number of digits, your subsequent calculations will also have a limited number of digits.

In this lab, you will be measuring the density of water using a variety of tools. Although your results should be similar every time, the number of significant digits you get will vary depending on the uncertainty associated with the measurement techniques.

Background

Significant digits from common measurements

1. 1. Mass – analytical balances generally give many significant digits, particularly when weighing 0.1 g or more, you get 4, 5, 6, or 7 significant digits. For example, 0.5012 g of a substance has 4 significant digits. Higher masses give you more significant digits until you reach the capacity of the balance. 319.9999g is 7 significant digits. That is the maximum mass for one of our balances.
   2. Volume
      • Volumetric flasks are extremely precise tools for measuring volume and often give you 4 or more significant digits, depending on the size of the volumetric flask. For example, a precision 1 liter volumetric flask filled exactly to the line etched on the neck contains 1.0000 L, which is 5 significant digits. The precision is usually printed on the flask for reference.
      • Micropipettes are very precise tools for measuring extremely small volumes (less than one milliliter). The number of significant digits you get from a micropipette is printed on the pipette for your reference, but it is usually about 4 significant digits.
      • Burets are very precise tools for measuring volume. Our lab is equipped with burets that measure to the nearest 0.01 mL, so a volume greater than 1 mL will have 3 significant digits, and a volume greater than 10 mL will have 4 significant digits. You always estimate one more digit than you can read from the lines and estimate to 1/5th between lines.
        

        50 mL graduated cylinder https://images-na.ssl-images-amazon.com/images/I/318fpllZXkL.jpg

      • Graduated cylinders are the most flexible tool for measuring volume. Our lab is equipped with many different graduated cylinders, and the number of significant digits they give you depends on the exact graduated cylinder you are using and the volume you are measuring. The number of decimal places you can read is printed on the glass for your reference. Typically you will get 3 significant digits from a graduated cylinder. You always estimate one more digit than you can read from the lines. You will normally estimate to the nearest 1/5th between lines.
      • Repeat after me: “Erlenmeyer flasks and beakers are not designed to measure volumes,” although they can be used to get a rough estimate if the volume is not critical. For example, if you are making a hot water bath with approximately 400 mL of water (1 significant digit), then it is appropriate to use a beaker measure that volume.
   3. Temperature – our red and blue alcohol thermometers are read to the nearest 0.1 °C. This means that we can only read 3 significant digits for temperatures between 10 and 99.9 °C, and we only get 2 significant digits for temperatures between 0 and 9.9 °C. You always estimate one more digit than you can read from the lines. Mercury thermometers give more significant digits, but they have fallen out of favor due to safety concerns when they (inevitably) break.

Significant digits from common calculations

1. Adding/subtracting: Use the least number of decimal places involved in the calculation. For example, if you measure a temperature change from 25.0 °C to 28.1  °C, 28.1 – 25.0 = 3.1 °C. See how fast you can lose significant digits in the lab?
2. Multiplying/dividing: Use the least number of significant digits involved in the calculation. For example, if you dissolve 0.3829 moles of a substance in 1.0000 L of water, then the concentration is 0.3829 moles per liter. The volume had 5 significant digits, but the number of moles only had 4 significant digits, so you are left with just 4 significant digits in your answer.
3. Averaging: We have special rules for averaging multiple measurements. Ideally, if you measure the same thing 3 times, you should get exactly the same result three times, but you usually don’t. The spread of your answers affects the number of significant digits in your average; a bigger spread leads to a less precise average. The last significant digit of the average is the first decimal place in the standard deviation. For example, if your average is 3.025622 and your standard deviation is 0.01845, then this is the correct number of significant figures for the average: 3.03, because the first digit of the standard deviation is in the hundredths place, so the last significant digit of the average is in the hundredths place.

Rules for rounding

Numbers between 6 and 9 round up.

Numbers between 1 and 4 round down.

5s round up or down to an even number. For example, if your average in lab is 92.5, the 5 would round down to 92, so an A- letter grade. If your average is 89.5, the 5 would round up to 90, so an A- letter grade.

Procedure

1. Measure the density of 5 mL of water with a graduated cylinder

Use an analytical balance to measure the mass of an empty, dry 50 mL beaker or Erlenmeyer flask. Remember to zero the balance before you use it. Record the mass in Table 1.

Measure out 5 mL of DI water with a 50-mL graduated cylinder. Read the exact volume at the bottom of the meniscus and record it in Table 1. Be sure to record all significant figures. Estimate to the nearest 1/5th mL (1/5th between lines). You will estimate the last decimal place.

Transfer the contents of the graduated cylinder to the beaker or Erlenmeyer flask. Use an analytical balance to measure the mass of the beaker that now contains 5 mL of water. Remember to zero the balance before you use it. Record the mass in Table 1.

2. Measure the density of 50 mL of water with a graduated cylinder

Use an analytical balance to measure the mass of an empty, dry 50 mL beaker or Erlenmeyer flask. Remember to zero the balance before you use it. Record the mass in Table 1.

Measure out 50 mL of DI water with a 50-mL graduated cylinder. Read the exact volume at the bottom of the meniscus and record it in Table 1. Be sure to record all significant figures. Estimate to the nearest 1/5th mL (1/5th between lines). You will estimate the last decimal place.

Transfer the contents of the graduated cylinder to the beaker or Erlenmeyer flask. Use an analytical balance to measure the mass of the beaker that now contains 50 mL of water. Remember to zero the balance before you use it. Record the mass in Table 1.

3. Measure the density of water with a volumetric flask

Use an analytical balance to measure the mass of an empty, clean, dry 100 mL beaker or Erlenmeyer flask. Remember to zero the balance before you use it. Record the mass in Table 1.

Fill a 100 mL volumetric flask with DI water until the bottom of the meniscus is exactly at the etched line. You may need to use a dropper to reach the line exactly. Record the volume to the tenth place: 100.0 mL. Record that volume in Table 1.

Transfer the contents of the volumetric flask to the beaker or Erlenmeyer flask. Use an analytical balance to measure the mass of the beaker that now contains 100 mL of water. Note that not all of the balances in the lab may be able to measure this mass. Use a different balance if you get an error. Remember to zero the balance before you use it. Record the mass in Table 1.

Data analysis

Review the rules about significant figures, then calculate the mass of water, volume of water, and density of water for each method. Fill in Table 2. Note: density = mass ÷ volume.

Report

Fill out this worksheet. Turn in either a paper or digital copy. You may use this table to look up the correct density of water at a variety of temperatures.