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Chemistry 310

Laboratory Exercise #1 Measurements

Your Name:

Date:

Purpose: The purpose of this experiment is to familiarize you with some of the commonly used equipment in the chemistry lab as well as the proper methods for measuring masses, volumes and temperatures.

Chem 310

Lab Exercise #1 – Measurements

1.3

Introduction

When in a laboratory it’s important to distinguish between measured and exact values to ensure the maximum accuracy of our observations. So what’s the difference? An exact value is a counted value, where we can exactly determine the number of objects or have a defined relationship. Counting people is an exact value, we don’t get partial people. Conversions with defined relationships (e.g. 12 eggs in a dozen or exactly 10 mm per cm) also are considered exact numbers. Who or how we observe exact values doesn’t change the number and there is no error associated with an exact value. Exact values have infinite significant figures. A measured value is measured by an observer using a measuring device, and is open to interpretation and error. There are exactly 10 mm per cm, but how many mm long is an object?

Is there a fraction, a blurring of the edge, difficulty distinguishing between marks on a ruler? Is the object flexible or moving? Is the ruler accurate? Who is looking at the ruler, from what angle? These are places where error and uncertainty can come in. All measured values have an uncertainty associated with them. The magnitude of the uncertainty varies from measuring device to measuring device, but is usually associated as one half of the smallest measurable unit on the measuring device. Or in the case of digital devices +/- 1 to the last measured digit. So a ruler that is marked in cm and mm will be accurate to the mm mark and have an uncertainty of +/- .5 mm. If we read something as 14.0 mm, we’re sure it’s not 13.5 mm or 14.6 mm, but it might be a bit higher or lower than perfectly 14.0 mm (e.g. 14.1 mm) and our eyes might not be sure. A digital scale that measures to 0.1 g could measure 10.4 g and we know the value is somewhere between 10.3 g and 10.5 g. So when we take a measurement in lab it’s

important to also note the uncertainty so we can also calculate the range of the answer determine the accuracy and precision.

Accuracy and precision are ways of determining the correctness of a measured value. Accuracy is how close the value is to the correct number. Precision is how close the value is to other measurements of the same object. We may not always be able to know the accuracy (we don’t always know the correct number), but we can use multiple measurements of the same object to determine precision. If we account for all sources of systematic error and reach the same value with a variety of measurement techniques we can be fairly certain that a value that precise value is also accurate.

Measuring Liquids using graduate cylinder

Liquids flow to fill their container and can interact with the sides of the flask. So the surface of a liquid isn’t perfectly flat when in a container. We measure water and aqueous solutions (mixes made from water) by using the meniscus, see

Figure 1
next page.

Liquids and glass can change volumes with temperature so most precise glassware (that which measures 0.00 ml or more significant figures) tends to be calibrated to a particular temperature and purpose. Most chemical glassware holds its labelled volume at 20.oC. Some glassware is designed TO CONTAIN (TC) a particular amount of liquid, volumetric flasks and pipettes may be used to contain a particular volume of liquid. Some glassware is designed TO DELIVER (TD) a particular amount of liquid, burets and certain pipettes will deliver a particular amount of liquid. Other glassware is less precise and can be used for either number but generally with less significant figures (e.g. 0.0 ml or 1. ml precision), such as beakers and graduated cylinders. Often precision glassware is expensive so scientists use a variety of different types of glassware in lab depending on their purpose and the level of precision needed. If we’re testing for trace pollutants we’ll need as much precision as possible (e.g. 00.00 mL) , if we’re just trying to make a salt water bath for cooling +/- 5% is fine.

Figure 1: Measuring liquid

Read from the bottom of the meniscus. This measurement is between 46 and 47 mL… from the bottom of the meniscus, it may be estimated to be 46.5 mL. When reading the level of the liquid, estimate the volume to the nearest 0.1 mL, as shown.
The last digit you record is uncertain (it is your best guess) and indicates the precision of the measuring instrument (in this case, the graduated cylinder).

Graduate cylinder

Measuring mass of an object using balance

A digital balance is a more convenient.

Measuring temperature using thermometer

Measuring length using ruler

The diameter of a watch glass is the distance through the center and across the watch glass.

Measuring volume of unknown object

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Experimental procedure:

1) Look at the given pictures and determine the volume of liquid in each graduated

cylinder.

a. Report the volume and the uncertainty in mL on the report sheet.

b.

Don’t forget to include units and sig. figs.

2) Using displacement to measure the volume of pennies.

a. Solid objects take up space and liquids will move around these objects to show the volume of the solid. Since the change in volume of the liquid equals the volume of the solid we can find the exact volume of an irregular object.

b. Each of the following images starts at a different volume of liquid (initial volume, V0) and adds 10 pennies to give a new volume (final volume, Vf).

c. Find the difference between the volumes to find the total volume of 10 pennies.

3) Another way to find volume of a regular object is by using geometry. We can assume a penny is a regular cylinder with the volume = μr2h.

a. Look at the given photos of a penny with a ruler and measure the diameter and height in mm.

b. Remember that radius = ½ diameter.

c. Using a ruler at home and a penny measure make two additional measurements of height and radius in mm.

3) Using a metric ruler of your own, measure

a. diameter of your favorite drinking cup.

b. length of your favorite drinking cup.

4) Assuming your cellphone is a perfect rectangular, measure

a. the length of your phone

b. the width of your phone

c. the height of your phone

d. calculate the volume of your phone using this equation: V = L x W x h

Chemistry 310
Measurements
Report Sheet

Your Name:

Date:

Concept Questions

1) Which glassware would you use to do each of the following tasks:
beaker,

Erlenmeyer flask, graduated cylinder, pipette, or
volumetric flask?

a. Make exactly 100.00 mL of salt solution ____________________________

b. Deliver 25.00 mL of water into a reaction. ____________________________

d. Measure approximately 75.0 ml of water. ____________________________

e. To contain a solution for a reaction. ____________________________

2) Which graduated cylinder would you choose to most accurately measure 5.0 mL? (circle

one). Explain why below:

5.0 mL 10.0 mL 25.0 mL 50.0 mL 100.0 mL

Experimental Data and Calculations

1) Measuring liquid in graduate cylinders:

Don’t forget to include units and sig. figs.

Sample

Volume (uncertainty and unit)

A

B

C

2) Measuring volume of pennies using displacement

Don’t forget to include units and sig. figs.

a) Report volumes

Sample

Initial Volume

Final Volume

Volume Change

A

B

C

b) Average Volume of 10 pennies between three samples A, B, C in mL: ________________________

(Show calculation below)

c) What’s the average V if we’re at the maximum of the uncertainty range? ____________

d) What’s the average V if we’re at the minimum of the uncertainty range? ____________

e) Is 10 pennies an exact or measured value? (circle one)
Exact or Measured

f) Average Volume of 1 penny in mL: __________________________

(Show calculation below)

3) Measuring volume of pennies using a ruler

Don’t forget to include units and sig. figs.
a) Report volumes

Sample

Height

Diameter

Radius

Volume

A

B

b) Average Volume of 1 penny between sample A and B in cm3: ________________________

(Show calculation below)

c) Given that 1 cm3 = 1 mL. Which volume do you think is more accurate the volume from

displacement or with a ruler? (circle one) Why?

4) Using a metric ruler of your own, measure

Don’t forget to include units and sig. figs.

Sample

Measurement and metric unit

diameter

Length

5) Measuring the volume of your cellphone

Assuming your cellphone is a perfect rectangular, determine the volume

Don’t forget to include units and sig. figs.

Sample

Measurement and metric unit

Width

Length

Height

Volume of your cellphone in cm3: __________________________

(Show calculation below)

6) What did you learn from this experiment?

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Chem 310 – Chapter 2

Measurement and Significant Figure

Tools Needed to Deal with Numbers

Types of numbers

Accuracy and precision

Uncertainty

Scientific notation

Making measurements

Rounding numbers

Significant figures

Significant figures with calculations

Three Types of Numbers
Counted numbers:
I have 11 fingers
there are 12 dogs

Defined numbers:
1 foot =
1 kilometer =

Have NO uncertainty
Will NEVER affect “significant figures”
Measured numbers:
I live 6 and a half miles away
I drink 1.5 liters of water a day
This bench is…

ALWAYS have some uncertainty to them
Will ALWAYS affect “significant figures”
Can be discussed in terms of accuracy and precision

Accuracy and Precision
Accuracy of measurements
How close a measurement is to the “actual” measurement
Determined from a single measurement or from the average of more than one measurement versus a “known” or “accepted” value.
Gaged by percent error
Measured mass: 9.9 grams
“Known” mass: 10.0 grams
Percent error: –1 %
Pretty accurate!

Accuracy and Precision
Accuracy of measurements
How close a measurement is to the “actual” measurement
Determined from a single measurement or from the average of more than one measurement versus a “known” or “accepted” value.
Gaged by percent error
Average of measured volumes: 49.031 liters
“Known” volume: 27.241 liters
Percent error: 79.990 %
Not very accurate!

Accuracy and Precision
Accuracy of measurements
How close a measurement is to the “actual” measurement
Determined from a single measurement or from the average of more than one measurement versus a “known” or “accepted” value.
Gaged by percent error
Average of measured lengths: 202.796 meters
“Known” volume: 197.850 meters
Percent error: 2.500 %
Pretty accurate!

Error Calculations
absolute error: difference between a measurement (or average) and the “known” value
average of measured masses: 11.819 grams
“known” mass: 12.039 grams
absolute error =
absolute error = 11.819 g
absolute error = 11.819 g – 12.039 g
absolute error = 11.819 g – 12.039 g = – 0.220 g

percent error: What is the size of the absolute error relative to the “known” value?
Error Calculations
average of measured masses: 11.819 grams
“known” mass: 12.039 grams
percent error =

percent error = =
percent error = = = – 1.81 %

1.81 %
– 1.81 %

Calculate the percent error given the following data obtained by a student:
Error Calculations
actual: 450.0 oC
trial 1: 545.6 oC
trial 2: 197.2 oC
trial 3: 207.5 oC
trial 4: 476.1 oC
1) Calculate the average:

2) Calculate the percent error:

Accuracy and Precision
Precision of measurements
How close measurements are to each other
Must have two or more measurements
Do NOT need “known” value
Gaged by standard deviation or relative standard deviation
Measurements: 107.5 meters
106.9 meters
109.3 meters
107.1 meters
106.1 meters
Relative standard deviation: 1.1%
Pretty precise!

Accuracy and Precision
Precision
How close measurements are to each other
Must have two or more measurements
Do NOT need “known” value
Gaged by standard deviation or relative standard deviation
Measurements: 215.9367 grams
141.0352 grams
192.4929 grams
117.5333 grams
166.0023 grams
Relative standard deviation: 23.57%
Not very precise!

Standard Deviation Calculations
standard deviation is a way of measuring the “spread” of a set of data

x1, x2, x3, … , xn = individual measurements
= mean (average)

n = number of measurements

Standard Deviation Calculations
relative standard deviation (RSD) : standard deviation divided by the mean

= mean (average)

Calculate the standard deviation and RSD given the following data obtained by a student:
Standard Deviation Calculations
trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC
mean: 254.6 oC

trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC
mean: 254.6 oC
trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC
mean: 254.6 oC
trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC
mean: 254.6 oC

Calculate the standard deviation and RSD given the following data obtained by a student:
Standard Deviation Calculations
trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC
mean: 254.6 oC

s = 132.6

Accuracy versus Precision
accurate and precise
actual: 250.0 oC
trial 1: 250.2 oC
trial 2: 249.7 oC
trial 3: 249.2 oC
trial 4: 249.6 oC

mean: 249.7 oC
% error: – 0.130 %
RSD: 0.165 %
not accurate or precise

actual: 250.0 oC
trial 1: 545.6 oC
trial 2: 197.2 oC
trial 3: 207.5 oC
trial 4: 476.1 oC

mean: 356.6 oC
% error: 42.64 %
RSD: 50.59 %
precise not accurate

actual: 250.0 oC
trial 1: 362.5 oC
trial 2: 361.9 oC
trial 3: 362.0 oC
trial 4: 362.8 oC

mean: 362.3 oC
% error: 44.92 %
RSD: 0.117 %
accurate not precise

actual: 250.0 oC
trial 1: 167.8 oC
trial 2: 324.7 oC
trial 3: 121.3 oC
trial 4: 404.6 oC

mean: 254.6 oC
% error: 1.84 %
RSD: 52.07 %

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Accuracy versus Precision

accurate and precise
actual: 250.0 oC
trial 1: 250.2 oC
trial 2: 249.7 oC
trial 3: 249.2 oC
trial 4: 249.6 oC

mean: 249.675 oC
% error: – 0.130 %
RSD: 0.1647 %
accurate and precise
actual: 250.0 oC
trial 1: 250.17 oC
trial 2: 249.68 oC
trial 3: 249.19 oC
trial 4: 249.64 oC

mean: 249.670 oC
% error: – 0.132 %
RSD: 0.1604 %

accurate and precise
actual: 250.0 oC
trial 1: 250.169 oC
trial 2: 249.676 oC
trial 3: 249.194 oC
trial 4: 249.638 oC

mean: 249.669 oC
% error: – 0.132 %
RSD: 0.1596 %

17

around 12 cm
around 11.8 cm
All about uncertainty
ALL measured numbers have some uncertainty
Uncertainty
around 11.84 cm

around 11.834 cm

Uncertainty and Measurements
Three things to know when taking a measurement:
Units: What is the instrument measuring (mass, volume, time, length, etc.)
Graduations: What is the value of the lines on the instrument
Not always numbered

1 cm
0.2 cm
0.1 cm
0.01 cm

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Uncertainty and Measurements
Three things to know when taking a measurement:
Units: What is the instrument measuring (mass, volume, time, length, etc.)
Graduations: What is the value of the lines on the instrument
Not always numbered
Uncertainty: How precise is the instrument?
Is either given or assumed to be one graduation divided by 10

1 cm

0.2 cm

0.01 cm
± 0.1 cm
± 0.02 cm
± 0.001 cm

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Precision in Measurements

Read to the “ones” place, uncertainty in the tenths (±0.1)  11.8 cm

Read to the “tenths” place (0.1), uncertainty in the hundredths (±0.01)  11.82 cm

Read to the “hundredths” place (0.01), uncertainty in the thousandths (±0.001)  11.837 cm

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11.8 cm
Determine the size of the graduations and the degree of uncertainty

State the digits you can be sure of!

Guess the next digit! (and only the next digit)
uncertainty: ± 0.1 cm
Making Measurements
I KNOW it is between 11 cm and 12 cm
measurement:
11
uncertainty:
uncertainty: divide graduations by 10 (unless it is given)
graduations (marks): 1 cm
graduations (marks):
11.8

22

11.84 cm
Determine the size of the graduations and the degree of uncertainty

State the digits you can be sure of!

Guess the next digit! (and only the next digit)
uncertainty: ± 0.01 cm
I KNOW it is between 11.8 cm and 11.9 cm
measurement:
11.8
uncertainty:
uncertainty: divide graduations by 10 (unless it is given)
graduations (marks): 0.1 cm
graduations (marks):
11.84

Making Measurements

23

520
520 cm
5
between 500 cm and 600 cm
measurement:
graduations (marks):
uncertainty:

52
graduations (marks): 100 cm
uncertainty: ± 10 cm

Determine the size of the graduations and the degree of uncertainty
State the digits you can be sure of!
Guess the next digit! (and only the next digit)
Making Measurements

24

The final digit in a measurement must ALWAYS be in the SAME PLACE AS, and be a MULTIPLE OF the uncertainty!
If your instrument has an uncertainty of ± 0.01 mL, your measurement will end with .00 .01 .02 .03 .04 .05 .06 .07 .08 or .09

If your instrument has an uncertainty of ± 0.2 g, your measurement will end with .0 .2 .4 .6, or .8

If your instrument has an uncertainty of ± 0.005 cm, your measurement will end with .000 or .005
Uncertainty and Measurements

Relationship between uncertainty of an instrument and its measurements:
The final digit in a measurement must ALWAYS be in the SAME PLACE AS (have the same precision as) the uncertainty!
If uncertainty is ± 0.1, then all measurements must have one decimal place (no more and no less)
If uncertainty is ± 0.0001, then all measurements must have four decimal places (no more and no less)
If uncertainty is ± 10, then all measurements must be to the tens place (no more and no less)
Uncertainty and Measurements
29.3 mL, 234.0 g, 0.2 s
0.5787 g, 8.0001 m, 17.3650 s
870 km, 20 m, 10 s

Relationship between uncertainty of an instrument and its measurements:
The final digit in a measurement must ALWAYS be a multiple of the uncertainty!

If uncertainty ends with a 2, (i.e. ± 0.0002, ± 0.02, etc.) then all measurements’ final digit must be a multiple of 2
If uncertainty ends with a 5, (i.e. ± 0.005, ± 0.5, etc.) then all measurements’ final digit must be a multiple of 5
If uncertainty ends with a 1, (i.e. ± 0.01, ± 1, etc.) then all measurements’ final digit must be a multiple of 1
Uncertainty and Measurements
1.04 mL, 234.0 g, 27.06 s
0.0235 g, 8.000 m, 17.5 s
89 kg, 2.4 m, 1.00 s

Which of the following would be correct if measured on this ruler?

Uncertainty and Measurements

too many decimals
(more precise than ruler)
too few decimals
(less precise than ruler)
too many decimals
(more precise than ruler)
assume ± 0.1 cm uncertainty
a) 7.0 cm
b) 2.50 cm
c) 12 cm
d) 0.6 cm
e) 4.00 cm

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Which of the following would be correct if measured on this ruler?

Uncertainty and Measurements
too many decimals
(more precise than ruler)
too few decimals
(less precise than ruler)
too few decimals
(less precise than ruler)
assume ± 0.02 cm uncertainty
a) 11.5 cm
b) 7.50 cm
c) 1.004 cm
d) 7.5 cm
e) 12.68 cm

29

For the graduated cylinder to the right, provide the following information (Given: the uncertainty is ± 0.5 mL)

What is the size of the graduations?
1 mL
What is the volume?
67.6 mL ± 0.5 mL

Uncertainty and Measurements

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Significant Figures
Significant figures tell you about the uncertainty in a measurement.
Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit
11.84 cm

4 significant figures

The guessed digit is always the last significant figure in a value

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Significant Figures
Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit
520 cm

2 significant figures

This is called a “place-holder” zero. These are NEVER significant (though they are important)

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60. mL

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