Measurements and Calculations Laboratory Activity

Objectives - Each student is expected to:

1.       Apply safety precautions from previous laboratory period.

2.       Measure each physical quantity to the maximum accuracy allowed by the appropriate instrument.

3.       Record measurements and calculations with the appropriate units from the international system of units (SI.)

4.       Calculate volumes and densities to the appropriate number of significant digits.

5.       Demonstrate the factor-label method for converting units

6.       Demonstrate the use of scientific notation.

7.       Demonstrate the use of the 5-step method for solving density and percent error problems.

 Introduction

Measurements

     It would be hard to overstate the importance of taking proper measurements in the Chemistry lab.  The goal of most of the experiments that you perform this year will be to compare the results of calculations to some known standard, and to determine your source of error.  Obviously, these calculations can only be as accurate as the measurements that they are based on.  For this reason, you must take each measurement to the maximum accuracy allowed by the instrument you use.   The accuracy of each measurement is limited by two things; the limitations of the instrument, and the care of the experimenter.   You must also make sure that you don't accidentally claim that a measurement or calculation is more accurate than it actually is.   For example, let us look at the picture below.

Image borrowed from: http://antoine.fsu.umd.edu/cgi-bin/senese/tutorials/sigfig/IA.cgi

     You should see that a small section of a rod has been place in between two different rulers.  Before we go over the example, let us remember that when taking a measurement in Science, it is assumed that a measurement is made up of a number of digits that are certain, and one additional digit which represents an estimation.  For example, if you read that an object had a mass of 27.865 g.  The last digit, the 5, would be an estimated digit.  Units must also be included with each measurement.

     The ruler on the left has line markings for each inch.  We can accurately say that the rod is in between 1 and 2 inches.  Each measurement that we report must contain one estimation digit.  We might estimate that the rod is about 30%-50% beyond the 1-inch mark.  Our final recorded measurement might be 1.4 inches, with our estimation digit in the tenth place.

     The ruler on the right has line markings for each tenth of an inch.   Because there are more markings on this ruler, we can report our measurement with higher accuracy.  We can accurately say that the rod is in between 1.4 and 1.5 inches.  Again, each measurement that we report must contain one estimation digit.  Our final measurement recorded from the ruler on the right might be 1.49 inches, with our estimation digit in the hundredth place.

     What would we have done if the rod were a little longer and seemed to land right on the 1.5 inches mark?  We would have used our estimation digit to say that we estimate it to be right on, by reporting the measurement as 1.50 inches.  If we leave off the zero on the end, people will assume that the tenth place is our estimation digit.

Calculations and Significant Digits

     What about the calculations based on these measurements?  Let's say we wanted to find the area of a wooden block (LxWxH) and we were using the ruler on the left of figure 1.  We might end up with the following data:

     When we calculate the area with the formula L x W x H we get:

1.1 in x 1.3 in x 4.7 in = 9.776 in³

     Can you see why this cannot be our final answer?  Surely we cannot have an area that is more accurate then the measured values that were used to derive it!  How can our area be accurate to the thousandth place when our length, width and height are only accurate to (including the estimation digit) the tenth place?  Based on our rules for rounding for multiplication, we would have to round our area to the same number of significant digits as the measurement with the least number of significant digits.  Our width only had one significant digit, so we must round the area to 9.8 in³

Conversions Made Simple - The Factor-Label Method

     The measurements above are in the English system, and we know that we should make our measurements using the international system of measurements.  In our lab, we would use the metric side of our meter sticks.   If we received data in inches we could still convert to SI units by using the factor-label method, as demonstrated below:

If we knew that there are 2.54 centimeters in one inch, we could use this as a conversion factor.

1 in = 2.54 cm

We could then slip these conversion factors into our original calculation for the area of the wood block.

1.1 in x 1.3 in x 4.7 in = 9.776 in³

becomes

1.1 in   x    2.54 cm  x  1.3 in  x 2.54 cm  x   4.7 in  x 2.54 cm
            -----------                      ----------                    ----------
             1 in                          1 in                           1 in

 We know our conversion factors are set up correctly if the unwanted units cancel out, leaving the desired units, as below:

1.1 in   x    2.54 cm  x  1.3 in  x 2.54 cm  x  4.7 in  x 2.54 cm
             -----------                     ----------                       ----------
              1 in                             1 in                              1 in

The result of this calculation is 110.1374571 cm³, but we would still need to round based on the original measurements, giving us 110 cm³.   The "1 in" in our conversion factor does not affect our rounding, because it is not a measurement. 

Pre-Lab Assignments

1.       Read the above introduction.

2.       Review Science Help Online (S.H.O.) lessons 2-1 through 2-6

3.       Complete the pre-lab questions from the report sheet.

4.       Print out the international system of measurements reference tables from S.H.O.

5.       Print out the rules for significant digits from S.H.O.

6.       Print out the rules for calculating with significant digits from S.H.O.

7.       Select a partner or have one assigned to you.

 Materials

Meter stick, thermometer, balance, 10ml graduated cylinder, 250ml graduated cylinder, 250ml beaker, wood block, screw. 

Procedures

I - Determining the limitations of common laboratory instruments.

1)       Observe the smallest place value represented by the lines on your meter stick (on the metric side).  Record this value, with the appropriate unit (i.e. hundredth of a cm, or 0.01cm), as the "smallest certain place value" for the meter stick in Table A of the data section for this lab.

2)       Add one decimal place value (i.e. tenth becomes hundredth, or hundredth becomes thousandth) to the value from the previous step.  This is your estimation digit for this instrument.  Record this value, with the appropriate units, in Table A of the data section for this lab. 

3)       Repeat steps 1 and 2 for each of the following intruments; thermometer, balance, 10ml graduated cylinder, 250ml graduated cylinder, 250ml beaker.  Record these values, with the appropriate units, in Table A of the data section.

II - Measuring Length

4)       Using the metric side of the meter stick, measure the length, width and height of your wood block.  Make sure that you include an estimation digit, for each measurement, that matches the place value determined in part I of this lab activity.  Record your values, with units, in Table B of the data section.

III - Measuring Mass

5)       Zero out your balance before each of the following steps.

6)       Determine the mass of a clean, dry 10ml graduated cylinder.  Record this value in Table C of the data section.  Be sure to include an estimation digit, and unit with your answer.

7)       Add 10.0 ml of water to the graduated cylinder.  Dry the outside of the cylinder to avoid massing extra water.

8)       Mass the graduated cylinder with the water inside.  Record this value in Table C of the data section.

9)       Determine and record the mass of your wood block.

10)   Determine and record the mass of your screw.

IV - Measuring Volumes of Water

11)   Measure out any appropriately-sized sample of water in the 10ml graduated cylinder.  Record the volume and units, to the highest possible degree of certainty, in Table D in the data section.

12)   Repeat step 11 with the 250ml graduated cylinder and the 250ml beaker.

V - Measuring the Volume of an Irregularly-shaped Object

13)   Place some water in the 10ml graduated cylinder and record the value in Table E of the data section.

14)   Carefully place the screw in the 10ml graduated cylinder.  It must be completely submerged, and the volume must be no greater than 10ml.  Record the new water level in Table E.

VI - Measuring Temperature

15)   Take the temperature of the lab room and record in Table F.