Unit 1 Measurement & Lab Equipment Abstract

Unit 1
Measurement & Lab Equipment
Abstract
This lab reviews the concept of scientific measurement, which you will employ weekly
throughout this course. Specifically, we will review the metric system so that you will be
able to measure length, mass, volume and temperature in metric units, and convert
between the English and metric systems. You will also familiarize yourself with common
laboratory equipment. You will review and practice scientific notation so that you will
understand its use in scientific measurement. Finally, you will utilize basic statistical
methods to evaluate data that you gather and graph.
The sections entitled “Put what you have read into Practice” will be due as homework
next week. Whatever you do not complete during the lab period should be completed at
home.
1.1 Conversions within the Metric System
Introduction
Length, Mass, Volume
To convert within the metric system, you must remember the following:
k
h
da
Base
Units
d
c
m
µ
n
p
kilo
hecto
deka
meters,
liters,
grams
deci
centi
milli
micro
nano
pico
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
To convert between metric units, you will need to move the decimal to the right or to the
left, relative to where you begin, as shown by this chart. This means that you will need to
add a decimal to the end of any whole number! For instance “35” is the same as “35.”
Example 1: Convert 5 mg to g. To get from mg to g requires you to move to the left on
the chart 3 units, thereby moving the decimal to the left 3 units. Therefore the value will
be 0.005 g.
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Example 2: Convert 80 hectoliters to centiliters. To get from hecto to centi requires you
to move to the right 4 units. Therefore the number will become 800000 hl.
Example 3: Convert 400 ml to nl. To get from milli to nano requires you to move 6 units
to the right. Notice that we are referring to the exponent associated with 10 when we
count places to move the decimal- we are not counting actual words listed on the chart.
Therefore 400ml becomes 400,000,000 nl.
Tip
Make sure you look at your answer to see if it makes sense! Does it make sense that
1 liter is the same as 0.001 ml?! No, because milliliters are smaller units than liters!
Therefore you would know that you had moved the decimal the wrong way. One liter
is equal to 1000 ml.
Important conversions to know about water under standard conditions!
1 cc = 1ml
1dm3 = 1 liter
1 ml = 1 g
1 liter = 1 kg
This means that 50 ml of water weighs 50 g.
Also, 3 liters of water equals 3 kg.
Check your understanding
If you weigh 142 ml water, how many mg would it equal? ___________________
Temperature
Temperature can be measured in Fahrenheit or in Celsius. Here in the US we are used to
thinking of temperature in terms of °F. In science we evaluate temperature using the
Celsius scale. It is called the centigrade thermometer because there are 100 (centi)
degrees between the freezing (0°C) and boiling point (100°C) of water. To convert
between the two, use the following conversions:
Equations
From Fahrenheit to Celsius:
1. Subtract 32 from degrees Fahrenheit
2. Multiply by 5
3. Divide by 9
From Celsius to Fahrenheit:
1. Multiply degrees Celsius by 9
2. Divide by 5
3. Add 32
4
From °F to °C
5
℃ = (℉ − 32)
9
From °C to °F
9
℉ = ℃ + 32
5
To get you thinking in terms of Celsius, know the following common knowledge points.
This will help you evaluate your answer in terms of “does this make sense”?
Freezing: 0°C = 32 °F
Room Temperature: 21.1°C = 70 °F
Body Temperature: 37°C = 98.6 °F
Boiling: 100°C = 212 °F
Example 1:
What is the temperature in °C if the outside air temperature is 43°F?
1. 43-32 = 11
2. 11 x 5 = 55
3. 55 divided by 9 = 6.11
Therefore the answer is 6.11 °C.
Practice
Convert the following numbers to the units indicated. Indicate what each
are measuring- are they units of mass, volume, or length?
1. 5.5 mg =
_______ hg
Unit of: ___________________
2. 61 pl =
_______ ml
Unit of: ___________________
3. 110 m =
_______ km
Unit of: ___________________
4. 7.89 dg =
_______ µg
Unit of: ___________________
5. 0.003 km =
_______ mm
Unit of: ___________________
Convert the following temperatures as indicted. You must show your
work. Do not use a calculator!
6. 83 °F =
_______ °C
9.
98 °C =
_______ °F
7. 22 °C =
_______ °F
10. 62 °F =
_______ °C
8.
_______ °F
4 °C =
5
1.2 Converting from English to Metric Units
Converting from English to metric units:
The basic metric unit of length is the meter. To compare English and metric values of
length, it is handy to know that 1 inch = 2.54 cm.
Mass is expressed in grams. To compare English and metric values of mass, it is handy to
know that 1 kilogram = 2.21 pounds.
Volume is measured in liters. To compare English and metric values of volume, it is
handy to know that 1 ounce = 30 milliliters and 1 gallon = 3.8 liters.
1.3 Becoming familiar with Laboratory Equipment
In this lab course, you will work with equipment and glassware that is common in the
laboratory setting. Locate the following items.
Graduated cylinder
Beaker
Erlenmeyer flask
Triple Beam Balance
Digital Balance
Graduated Pipette
Weigh boat
Hot/Stir Plate
Stir Bar
***Use the space below to make a sketch of each of them so that you will recognize it in
the future.
Measuring Volume:
Fill your graduated cylinder with 45 ml of water. When measuring the volume of a liquid
in a graduated cylinder, you will observe a “meniscus.” Locate the meniscus (and include
it in your drawing.) Do you think that you should measure the volume from the top or
bottom of the meniscus? Check with your instructor to make sure you are correct!
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Now transfer the water to your beaker. Is this as accurate at measuring volume as the
graduated cylinder?
Using a Balance:
For the digital and triple beam balance, practice using each by finding the mass of a coin.
To do this, you will need to use a weigh boat since you typically do not want to place the
material you are weighing directly on the balance.
1. Locate and place the weigh boat on the digital balance, on the triple beam
balance, you may set the coin on the metal pan without the weigh boat.
2. “Tare” the digital balance in order to reset the balance to “0” grams. This will
ensure that you do not add the weight of the weigh boat to what you are weighing.
Make sure that your triple beam balance set to zero as well by using the adjustment
knob underneath the pan.
3. Add the coin. Record the weight of the coin for each.
Triple beam:
___________ grams
Digital balance: ___________ grams
4. Which balance is more accurate, and why?
Practice
Now you will apply the knowledge you have gained. In this section
of the lab, you will learn about the different pieces of laboratory
equipment, as well as how to measure the different properties
of matter with them.
Using a Balance:
During a practical, Sally Student and Sid Student were asked to
find the weight of a penny on a digital balance. Sally found that the
weight was 0.001 grams whereas Sid found that the weight was 4.3
grams. The correct answer was 2.5 grams.
a. What do you think Sally might have done incorrectly?
b. What might Sid have done incorrectly?
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Understanding Meters:
1. Meters are the base unit of the metric system used to measure length. Please state what
measuring device or devices you would use to measure an object in the following units:
3 mm:
20 cm:
1.5 m:
2. Find two items: one measured in centimeters (cm) and, if possible, one measured in
millimeters (mm). Use the instruments that you listed in #1 to measure these objects.
Write down the name of the item and how many centimeters or millimeters it measures.
Please include the units (cm or mm) with your measurement.
3. Is a centimeter larger or smaller than a millimeter?
4. What property of these items do cm or mm measure: length, volume, mass or
temperature?
5. The height of the average person is a little over 1.5 meters. Knowing this, is one
centimeter larger or smaller than one meter?
6. Is one millimeter larger or smaller than one meter?
7. Runners often run a 5K, which is five kilometers (km). Is a kilometer larger or smaller
than a meter?
8
Understanding grams:
8. Grams are the base unit of the metric system used to measure the amount of matter in
an object. There are two instruments that you could use to measure something in grams.
Please list those two instruments here (note: you will draw these instruments later).
9. Find one item that is measured in grams (g). Write down the name of the item and how
many grams it weighs. Please include the units (g) with your measurement.
10. Find one item that is most likely measured in kilograms (kg). Are you able to measure
this with the instruments that you listed in question 8? Why or why not?
11. Which item felt heavier, the item measured in grams or the item measured in
kilograms?
12. Based off of your answer to number 8, is a gram larger or smaller than a kilogram?
13. What characteristic of these items do grams and kilograms measure: length, volume,
mass, or temperature?
14. The other units that can be used to measure these items are either pounds or ounces.
These are commonly used to measure the weight of objects. What property of the item(s)
does weight measure? Is this property the same thing as your answer in number 13?
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Understanding Liters:
15. Liters are the base unit of the metric system used to measure volume. Please list all of
the pieces of glassware that could be used to measure volume.
16. If you were to pick two of these pieces of glassware to measure the volume of a liquid
as accurately as possible, which two would you pick? Why?
17. Find one item that is used to measure liters (l). Find one item that is used to measure
milliliters (ml). Write down the name of the item and how many liters or milliliters it
measures. Please include the units (l or ml) with your measurement.
18. Which item was larger, the one used to measure liters or the one used to measure
milliliters?
19. Based off of your answer in number 17, would you be able to place all of the contents
of a 2 liter container into a 1000 ml container?
20. Would you be able to place the contents of a 1 liter container into a 600 mililiter
container?
21. What characteristic of the contents of the container do liters measure: length,
volume, grams or temperature?
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1.4 Scientific Notation
Introduction:
Scientific Notation is a way of expression very large or very small numbers such that it is
easy to write, easy to determine the value and easy to make comparisons to other
numbers.
For instance:
• the number 342000033994 is a long number to write and difficult to say exactly
what that number’s value is without some thought. Adding commas helps:
342,000,033,994, while easier to read is still large and long!
•
how does 342000033994 compare to 45645612825? How about 342,000,033,994
to 45,645,612,825- how much bigger or smaller is it? This is very hard to do at a
glance!
Putting the numbers in scientific notation makes it easy to quickly determine the value
and to compare numbers.
Try 3.42 x 1011 vs. 4.56 x 1010? It is much easier to compare these values!
Scientific Notation is NOT difficult, but does require that you follow some simple steps,
and that you use your common sense. Follow these steps each time:
1. Rewrite your number and put a decimal point after the *first* non zero digit.
For instance,
a. 1234567 becomes 1.234567
and
b. 0.001234567 becomes 1.234567
2. Add “x 10” to the end of the digits
a. 1234567 becomes 1.234567 x 10
and
b. 0.001234567 becomes 1.234567 x 10
3. Count how many place values the decimal has moved from the original
placement to the current placement. Write that number as your exponent.
a. If the number became smaller when you moved the decimal, you will
need the exponent to be positive: 1234567 becomes 1.234567 x 106
b. If the number became bigger when you moved the decimal, you will
need the exponent to be negative: 0.001234567 becomes 1.234567 x
10-3
4. Always check your answers! Do they make sense? For instance:
Does 1.234567 x 106 equal a larger number by 6 tens, 1234567? Yes!
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What do the exponents mean, at a glance? Remember these values and you will be able
to read the value of very large numbers very quickly.
103: thousands
10-3: thousandths
106: millions
10-6: millionths
109: billions
10-9: billionths
Practice
Convert the following numbers from full expression to scientific notation.
1,345,635,000
____________________________________
457.430
____________________________________
0.000554433
____________________________________
47777.0055
____________________________________
0.0044551111
____________________________________
Convert the following numbers from scientific notation to full expression.
4.56 x 108
____________________________________
6.785544 x 10 -8
____________________________________
8.992233 x 106
____________________________________
9.11 x 10-2
____________________________________
6.789 x 105
____________________________________
1.5 Statistical Calculations
Introduction
To analyze data generated in the laboratory in order to determine its significance, you
must first be equipped to evaluate your data from a statistical perspective. A review of
basic statistical terms is included here for your review.
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I. Mean: This is an average of a group of measurements.
How to calculate mean?
Add all values and divide by total number of values.
Example:
Values: 40, 38, 22, 20, 30
Mean = 40 + 38 + 22 + 40 + 30 divided by 5
Mean = 30
Equation
𝑥 = !
!
!!! !
!
II. Median: The value that is in the middle of a group of measurements.
How to calculate median with an odd number of values?
Using previous example:
Example
Values: 40, 38, 22, 20, 30
Rearrange from low to high: 20, 22, 30, 38, 40
Median = middle value = 30
How to calculate median with an even number of values?
Using previous example:
Example
Values: 40, 38, 22, 20, 30, 24
Rearrange from low to high: 20, 22, 24, 30, 38, 40
Median = add two middle values and divide by 2
Median = 24 + 30 / 2
Median = 27
III. Range: The difference between the smallest and the
largest measurements.
How to calculate range?
Using previous example:
Equation
Example
Values: 40, 38, 22, 20, 30
Subtract smallest value from largest value
Range = 40 – 20 = 20
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𝑅 = 𝑀𝑎𝑥 − 𝑀𝑖𝑛
IV. Deviation: Measures how the measurements vary from the mean (+ or -). In other
words, what is the difference between an actual measurement and the mean, or average,
of the sample?
How to calculate a deviation?
Using previous example:
Example:
Values: 40, 38, 22, 20, 30
We determined the mean to be 30.
We find the deviation for each number in the data set.
The deviation for the value “38” would be +8.
This value is 8 more than the mean.
Equation
𝑑 = 𝑥! − 𝑥
V. Variance: This measures how much difference, or variation, there is between the
values you have obtained. The smaller the variance, the closer the values will be to the
mean. Likewise, the larger the variance, the farther the values will be from the mean.
How do I calculate variance?
Calculate the sum of the squared deviations divided by the number of values
minus one. Using previous example:
Equation
Example:
Values: 40, 38, 22, 20, 30
Variance=
100+64+64+100+0
= 82
5-­‐1
(𝑥 − 𝑥)!
𝑠 = 𝑛−1
!
VI. Standard Deviation: Standard deviation gives you an idea of the widely spread your
values are about the mean. The smaller the standard deviation, the closer your values will
be to the average. If you were to graph data having a small standard deviation, you
would expect a tall, thin bell shaped curve. On the other hand, if the standard deviation
were large, your bell shaped curve would be wider.
How to calculate Standard Deviation?
Calculate the square root of the variance.
Using previous example:
Example: values- 40, 38, 22, 20, 30
The variance equaled 82.
Take the square root of the variance.
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 82 = 𝟗. 𝟎𝟔
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Equation
𝜎 = (𝑥 − 𝑥)!
𝑛−1
Tip
Standard deviation can be used to evaluate the percentage of a population that is
near “average”. One standard deviation to the left and right of the mean will cover
68% of the population; two standard deviations to the left and right of the mean
will cover 95% of the population.
Practice
Purpose: In this exercise you will record the gender and height of
everyone in the lab. You will determine the average height of males
and females in your lab section.
Materials and Methods
Meter Stick
Lab participants
Have each individual list their gender and height on the whiteboard. Record this
information in the data table provided. Where necessary, convert measurements recorded
in English units to metric centimeters. Use the space provided to record deviations
(required on next page).
Results:
Males (inches):
Males (cm):
Females (inches):
15
Females (cm):
Males (inches):
Males (cm):
Females (inches):
Females (cm):
Figure 1. Height measurements of Biology 1406 Laboratory population. Use the data from your table to calculate the following, using the information and
examples of each given previously (show your work!). Make sure that you use the data
expressed in cm, not inches!
________________________________________________________________________
Size of sample:
Males ___________
Females__________
Entire Class___________
________________________________________________________________________
Mean height:
Males ___________
Females__________
Entire Class___________
________________________________________________________________________
Median Height:
16
Males ___________
Females__________
Entire Class___________
________________________________________________________________________
Range of height:
Males ___________
Females__________
17
Entire Class___________