# MASS AND VOLUME RELATIONSHIPS

Revision 4.0.1 01 December 2016

LC CHE 167 Exp. #2

MASS AND VOLUME RELATIONSHIPS

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1. Introduction.

Not all properties can be determined by a single measurement. In many cases, several properties must be determined by direct measurement, and then, the value of the property desired must be calculated using the measured properties. When combining the value of several properties in this way, it is especially important that the measuring devices used are capable of producing meaningful results as any errors can be magnified by the calculation process. Therefore, it is important that one has a knowledge of how to estimate the reliability of the measurements and the calculated results.

This experiment will involve the determination of the density of a solution of sodium chloride in water and of a rubber stopper. The density, D, is defined as the ratio of the mass, m, of a sample of a substance to the volume, V, occupied by that mass of sample, or

D = mV .

The determination of this important physical property then, requires the measurement of two quantities — the mass and the volume of a given quantity of the substance — which are then used to calculate the density.

The mass will be measured using an electronic balance, which can measure to the nearest 0.001 g (or 1 mg). Directions for the operation of the balances will be given to you by your instructor.

The volume will again be measured using a graduated cylinder, and will be expressed in units of milliliters (symbol: mL). In this experiment, a 50-mL cylinder, which is capable of measuring the volume of a liquid or solution to the nearest 0.1 mL, will be used. Remember that you should be reading the bottom of the meniscus and be sure to avoid parallax errors when reading the scale on the cylinder.

Duplicate measurements will be made for both the density measurement of the solution and the rubber stopper. This is done so that a measure of precision can be obtained. In most cases, replicate measurements should be reasonably close to each other. This situation is indicated by a small average deviation. If a series of measurements (two or more) do not agree, a large average deviation will be calculated. In these cases, one or more additional determinations may be required.

For example: Assume a student has determined the density of the sodium chloride solution in Part I in two separate measurements to be (1) 1.20 g/mL and (2) 1.26 g/mL. The average density is 1.23 g/mL. To get the average deviation of these measurements, first, take the difference between each measured value and the average value:

diff1 = 1.20 − 1.23 = −0.03 g/mL

diff2 = 1.26 − 1.23 = 0.03 g/mL

2 Note that the sum of these values is zero! (This may not always happen because of round-off errors,

but it should be very close to zero.) Next, take the sum of the absolute values of the differences and divide that value by the total number of measurements made:

g/mL 0.03= 2 06.0

= 2

)0.03++0.03-(

As indicated, the units will be the same as the quantity being determined and, in this case, the average value of the density would be reported as 1.23 ± 0.03 g/mL. This means that the actual value of the density, as measured in this experiment, will be found in the range between 1.20 g/mL and 1.26 g/mL. This result would be generally acceptable. If, however, the average deviation would have been in the 0.3 g/mL range, it would be wise to make one or two additional measurements in an attempt to determine which of the original measurements was in error.

If the quantity being measured has been previously determined and published*, accuracy is the term used to indicate how close one’s determination is to the accepted or true value. The accuracy can be expressed in terms of either the actual error or the percent error. The actual error is the difference between one’s experimentally determined value and the accepted value; the percent error is the ratio of the actual error to the accepted value multiplied by 100, or, in equation form

Actual error = Experimental value − Accepted value

% Error = Actual error

Accepted value x100

% Error = Experimental value – Accepted value

Accepted value x100

If in the above example, the accepted value of the density of the solution is 1.25 g/mL, the actual error and the percent error would be

Actual error = 1.23 g/mL − 1.25 g/mL = −0.02 g/mL

% Error = (−0.02 g/mL/1.25 g/mL) x 100 = −2%

The negative value for the percent error indicates that the experimental value is smaller than the accepted value. Also note that the calculated percent error [−1.60…] has been rounded off to one significant figure. This is done because the number in the numerator has only one significant figure. This follows the rule for dividing two measured values. An error of this magnitude would be very good for this experiment.

* The act of publishing an experimental result in a reputable publication (a journal, book, manuscript, etc.) is frequently taken as an indication of a value that is reliable within the stated precision. This usually means that the experiment and its results have been carefully scrutinized by knowledgeable professionals for obvious errors and/or omissions. These values are then assumed to be the “true” value for that measurement.

3

2. Procedure.

Note: All work in these laboratory sessions will be done on an individual basis unless the instructor gives specific instructions or permission to work in a group of two or more.

PART I. Density of a solution of NaCl in water.

1. Weigh a clean and dry 50-mL graduate cylinder on an electronic balance; read and record the mass in grams to the nearest 0.001 g.

2. Add 45 to 50 mL of the NaCl solution to the cylinder. Measure and record the volume in milliliters to the nearest 0.1 mL.

3. Reweigh the cylinder with the solution recording the mass in grams to the nearest 0.001 g.

4. Calculate the density of the solution.

5. Repeat the procedure a second time with a new sample.

6. Average the two values of the density and calculate the average deviation and the percent error for your determination.

PART II. Density of a rubber stopper.

1. Select a rubber stopper that will fit easily into your 50-mL graduated cylinder.

2. Weigh the dry stopper on the electronic balance and record its mass in grams to the nearest 1 mg.

3. Add about 25 mL of tap water to the cylinder; read and record the volume in milliliters to the nearest 0.1 mL.

4. Carefully place the stopper in the cylinder without splashing; also, be certain that the stopper is completely covered with water.

5. Read and record the volume to the nearest 0.1 mL.

6. Calculate the density of the stopper.

7. Select* a different stopper, and repeat the procedure.

8. Average the two values obtained and calculate the average deviation and the percent error for your determination.

* This time take one that has a different number of holes than the one you used for the first determination. This may help you answer question #2 at the end of the experiment.

4 Revision 4.0.1 01 December 2016

LC CHE 167 Exp. # 2

MASS AND VOLUME RELATIONSHIPS

LABORATORY REPORT Name ________________________

Section ______ Desk No. _____

Date ____________________

PART I. DENSITY OF A SOLUTION OF NaCl IN WATER. Note: RECORD ALL DATA IN INK using the correct number of significant figures and correct units.

SHOW COMPLETE “SET-UPS” (and the rounding off) for all calculations on the back of this page or on a separate sheet.

A B Mass of cylinder and solution Mass of empty cylinder Mass of solution used Volume of solution used Density of solution

Average density of solution Average deviation Accepted value 1.18 g/mL Percent Error

PART II. DENSITY OF A RUBBER STOPPER. A B Mass of rubber stopper Volume of water and rubber stopper Volume of water Volume of rubber stopper Density of rubber stopper

Average density of rubber stopper Average deviation Accepted value 1.12 g/mL Percent Error

5 QUESTIONS AND PROBLEMS Note: Always show all work and use correct units and the proper number of significant figures in answering

these questions. Answer all essay questions with proper English sentences.

1. What is the density of a brass sample if 50.051 g of coarse turnings, when placed in a graduated cylinder containing 11.0 mL of water, raises the level of the meniscus to a reading of 17.0 mL?

2. Some stoppers used in Part II may have one or more large holes bored through them. How will these holes influence the density of the stopper?

3. Explain why the procedure in Part II could not be used as written to measure the density of a piece of elm wood (density = 0.57 g/mL). How could the procedure be modified to make it useable? (Assume the wood is not absorbent.)

4. The average density of soft rubber has been given as 1.12 g/mL. Showing the work, express this value in terms of the following units: a. kg/L:

b. kg/m3:

c. mg/L:

d. mg/m3:

e. kg/dL:

5. A student obtained the values of 1.14 g/mL and 1.20 g/mL for two determinations of the density of a solution of NaCl in water. (Assume the NaCl solution has the same concentration as the one in this experiment.) Calcualte the average of these measurements, the average deviation and the percent error.