Measurement

An Introduction to Scientific Measurement:

Density Measurements

Introduction

A large part of the purpose of this first lab of the semester is to introduce you to some basic equipment and to allow you to find out for yourselves how to take accurate and precise measurements with it. You will use an electronic balance, beakers, graduated cylinders, burets, and pipets to measure the density of water, and then calculate the percent error and average deviation in your answers. As a result of these measurements you will be able to compare the degree of accuracy in the various measuring devices that you typically use in a chemistry laboratory.

Taking measurements of the physical world is a way to make that world more intelligible and less uncertain. Our ancestors have been measuring since the dawn of civilization, and sometimes with surprising accuracy, given the lack of suitable tools. One of the greatest feats of measurement was that of the Greek geographer Eratosthenes (276? - 195? B.C.). He measured the shadow cast at noon on June 21 at Alexandria and was able to calculate that the sun was 7° 14' away from being directly overhead. However he knew that at exactly the same time the sun cast no shadow at Syene (modern Aswan) and hence was directly overhead. Knowing that Syene was due south of Alexandria and calculating the distance between these two towns Eratosthenes was able to come up with an answer for the circumference of the earth of 28,700 miles. This was only 15% higher than the currently accepted value.

Density is a physical property. The formula for density is

Density = Mass

Volume

Density is constant for a given substance at a given temperature for solids and liquids.

Averages are calculated when several trials are performed. This average value can then be compared to an accepted value to determine the accuracy of the measurement. These comparisons will be performed by calculating a quantity called % error. The formula for determining % error is given below.

% error = l difference between accepted and measured values l _{x
100}

accepted value

Two other concepts that will be investigated in this laboratory are precision and accuracy. The accuracy of a measurement refers to how close it comes to the accepted value. The precision of a measurement refers to the reproducibility of a measurement. If the same mistake is made repeatedly in a measurement, the precision can be very high but the accuracy can be very poor. If a large number of readings are taken and averaged, a very accurate result might be obtained even though the individual readings are scattered rather widely. The drawings below using targets should illustrate the difference between accuracy and precision.

When dealing with experimental data, accuracy is determined by the % error between the accepted value and the average measured value. The lower the % error, the more accurate the result.

Precision can be determined by the average deviation, that is, the average difference between each of the readings and the average value. The formula for calculating average deviation is shown below.

total of all the |differences between

Average deviation = individual readings and the average|

number of readings

For example, if readings of 15.1, 18.2, 17.4 and 16.8 were obtained, the average would be:

15.1 + 18.2 + 17.4 + 16.8 = 16.9

The differences between the indiviudal readings and the average would be:

|15.1 – 16.9| = 1.8; |18.2 – 16.9| = 1.3; |17.4 – 16.9| = 0.5; |16.8 – 16.9| = 0.1

The average deviation would be:

1.8 + 1.3 + 0.5 + 0.1 = 0.9

In general, the smaller the average deviation, the more reproducible the measurement was and, hence, the higher the precision.

Procedure

Part A: Using a beaker to measure the volume

1. Weigh a small dry beaker and record its mass.

2. Add distilled water to the 10 mL mark on the beaker and reweigh the beaker plus contents. Record the mass and volume you measured in the report.

3. Empty and dry the beaker, then repeat Steps 1 & 2 for Trial 2.

4. Empty and dry the beaker, then repeat Steps 1 & 2 for Trial 3.

Part B: Using a graduated cylinder to measure the volume

1. Weigh a dry beaker and record the mass.

2. Obtain a dry 10-mL graduated cylinder and add distilled water to the 10-mL mark on the cylinder.

3. Pour the water from the cylinder into the beaker; reweigh the beaker plus contents. Record the mass and volume you measured.

4. Empty and dry the beaker. Also dry the cylinder, and then repeat Steps 1-3 for Trial 2.

5. Empty and dry the beaker. Also dry the cylinder, and then repeat Steps 1-3 for Trial 3.

Part C: Using a pipet to measure the volume

Note: NEVER ATTEMPT TO PIPET BY MOUTH.

1. Practice using a 10-mL pipet and bulb. Ask for help if you have trouble.

2. Weigh a dry beaker and record the mass.

3. Pipet 10 mL of distilled water into the beaker; reweigh the beaker plus contents. Record the mass and volume you measured.

4. Empty and dry the beaker, then repeat Steps 2 & 3 to obtain a second set of data.

5. Empty and dry the beaker, then repeat Steps 2 & 3 to obtain a third set of data.

Part D: Using a buret to measure the volume

A buret is used when a variety of accurately known volumes of solution are needed. The volume dispensed is determined by reading (using the bottom of the meniscus) the initial solution volume in the buret (estimating one decimal place past the graduations), dispensing solution, and then taking a final volume reading. The difference between the initial and final readings will be the volume of solution dispensed. The burets used in lab are calibrated to milliliters, allowing the volumes to be recorded to the nearest 0.01 mL.

1. Clean a buret with soap and water.

2. Clamp the buret in a buret holder.

3. Rinse the buret with deionized water and discard the water.

4. Fill the buret with deionized water, making sure that there are no air bubbles in the tip of the buret or the stopcock.

5. Record the initial volume of water in the buret (eye level with the meniscus).

6. Weigh a dry beaker and record its mass.

7. Add 10 mL of water to your beaker and record the final volume (the difference between the initial volume and the final volume is the volume of water collected).

8. Weigh the beaker + contents and record the mass.

9. Empty and dry the beaker, then repeat Steps 6-8 to obtain a second set and third set of data.

Part E: Using a pipet to measure the density of an unknown liquid

1. Weigh a dry beaker and record the mass.

2. Obtain approximately 25 mL of the unknown liquid.

3. Pipet 5 mL of the "unknown liquid" to the beaker; reweigh the beaker plus contents. Record the mass and volume you measured.

4. Empty and dry the beaker, then repeat Steps 1 & 2 to obtain a second set of data.

5. Empty and dry the beaker, then repeat Steps 1 & 2 to obtain a third set of data.

Part F: Using a graduated cylinder to measure the density of an unknown solid

1. Weigh a piece of "unknown solid."

2. Add distilled water exactly to the 5 mL mark on a 10 mL graduated cylinder.

3. Add the piece of "unknown solid" to the cylinder and record the new volume. Be certain to read all significant figures and estimate the last place value.

How to Dispense a Known Volume of Liquid Using a Pipet.
Report: Introduction to Scientific Measurement: Density Measurements

Name_____________________

Date______________________

Part A: Density of water using a beaker

mass of empty mass of beaker mass volume

beaker + water of water of water density

Trial 1 _________ _________ _________ _________ _________

Trial 2 _________ _________ _________ _________ _________

Trial 3 _________ _________ _________ _________ _________

Average density:_________

Average Deviation:_________

Show sample calculations of density and average deviation here:

Part B: Density of water using a graduated cylinder

mass of mass of beaker mass volume

empty beaker + water of water of water density

Trial 1 _________ _________ _________ _________ _________

Trial 2 _________ _________ _________ _________ _________

Trial 3 _________ _________ _________ _________ _________

Average density:_________

Average Deviation:_________

Part C: Density of water using a pipet

mass of mass of beaker mass volume

empty beaker + water of water of water density

Trial 1 _________ _________ _________ _________ _________

Trial 2 _________ _________ _________ _________ _________

Trial 3 _________ _________ _________ _________ _________

Average density:_________

Average Deviation:_________

Part D: Density of water using a buret

mass of mass of beaker mass

empty beaker + water of water

Trial 1 _________ _________ _________

Trial 2 _________ _________ _________

Trial 3 _________ _________ _________

initial buret final buret volume of

reading reading water dispensed density

Trial 1 _________ _________ _________ _________

Trial 2 _________ _________ _________ _________

Trial 3 _________ _________ _________ _________

Average density:_________

Average Deviation:_________

Part E: Density of "unknown liquid"

mass of mass of beaker mass volume

empty beaker + liquid of liquid of liquid density

Trial 1 _________ _________ _________ _________ _________

Trial 2 _________ _________ _________ _________ _________

Trial 3 _________ _________ _________ _________ _________

Average density:_________

Part F: Density of "unknown solid"

Mass of unknown solid:

Initial volume of water in the cylinder:

Final volume of water in the cylinder:

Volume of unknown solid:

Density of unknown solid: _________

Questions:

1) Precision can be measured by average deviation. Rank the measuring devices you used (beaker, graduated cylinder, pipet, and buret) from highest precision to lowest precision. Explain your ranking.

Highest precision:

2nd highest:

2nd lowest:

Lowest precision:

Explanation:

2) When dealing with experimental data, accuracy is determined by the % error between the accepted value and the average measured value. According to the CRC Handbook of Chemistry and Physics, the accepted mass of 10.00 mL of water at room temperature is 9.975 g. Use the average density found for each measuring device to calculate its percent error. Show all work in the space provided below.

% error for beaker:

% error for graduated cylinder

% error for pipet:

% error for buret:

3) Rank the measuring devices you used (beaker, graduated cylinder, pipet, and buret) from highest accuracy to lowest accuracy. Explain your ranking.

Highest accuracy:

2nd highest:

2nd lowest:

Lowest accuracy:

Explanation:

4) Consult Table 1-8 on page 32 of your text book. What is the most probable identity of the unknown liquid?

5) Consult Table 1-8 on page 32 of your text book. What is the most probable identity of the unknown solid?

Calculations with significant figures – Perform the following calculations, expressing all answers with the correct number of significant figures. For questions 1-4, use scientific notation if needed. For questions 5-10, give all answers in scientific notation.

1. 11.3 ´ 1.8 = 2. Ö27.3 =

3. (7.25 + 6.888) ´ 20 = 4. 28 – 28.4 =

28.4

5. (7.2 ´ 10^-9) ´ (8.65 ´ 10¹⁷) = 6. (7.45 ´ 10¹²) ´ (2 ´ 10³) =

7. (3.444 ´ 10^-9) ¸ (8.222 ´ 10⁷) = 8. (2.227 ´ 10^-9) ´ (5.68 ´ 10^-7) =

9. Ö1.787 x 10⁹ = 10. (7.72 x 10⁵)² =

(8.2 x 10^-8)(5.38 x 10¹⁴)

Unit conversions – Perform the following calculations, expressing all answers with the correct number of significant figures. Use scientific notation if needed.

1. 350 km to cm 2. 0.75 inches to mm

3. 350 gallons to mL 4. 3.0 x 10³ pt to mL

5. 37 lb/gal to g/mL 6. 7.22 yd³ to mm³