1s
Balancing Mass
OBJECTIVES
•
To accurately measure masses in the kitchen.
•
To recognize the graphical characteristics of proportional relationships.
•
To apply proportional relationships in problem solving.
INTRODUCTION
Webster's Dictionary defines the word measure as "to determine the extent, dimensions, etc. of, especially
by a standard." Science relies on measurements to help us better understand our universe. Scientists can
measure the length of a piece of wood or the mass of a small rock directly. Other measurements, such as
the mass of the moon or the length of a molecule, have to be determined indirectly. In chemistry most
experiments require some kind of measurement and often we make indirect measurements to help us learn
about things that we cannot measure directly. The measurements most commonly made in a chemistry
laboratory are mass and volume, and your kitchen "laboratory" will be no exception. Volume
measurements are familiar, especially in a kitchen. Most recipes call for quantities given in cups,
tablespoons and teaspoons, all measurements of volume. Measuring mass in the kitchen is a little trickier
because most people do not have a balance or scale that can measure small quantities of substances with
any degree of accuracy or precision. So as part of the first experiment in this program, you have the option
of making or purchasing a simple, inexpensive balance (Figure 1.1) that you will use for many of the
subsequent experiments
Figure 1.1
In this experiment, you will use the mass of a post-1983 penny (2.5 g) as your primary standard. A standard
is an established quantity or value that can be used as a basis of comparison. You will use the penny to
determine the masses of other things. If you find something that has a reliable and consistent mass relative
to the penny, you can use it as a secondary standard. This is useful for measuring the masses of things that
are lighter or heavier than the penny, and adds more precision to the mass measurement.
Aspirin tablets have consistent and reliable masses. The picture below (Figure 1.2) demonstrates the
relationship between the mass of our primary standard and a particular aspirin product:
Figure 1.2
1.
Based on Figure 1.2, what is the mass of four aspirin tablets? ___________
2.
What is the mass of one aspirin tablet?
___________
You may have determined that the mass of each aspirin tablet is 0.62 g without thinking about the
necessary mathematical steps. However, it is worth taking a closer look at the logic underlying this
calculation since it is used to solve many different types of problems. Figure 1.1 depicts an "equivalence"
between 4 aspirin tablets and 1 penny; one "balances" the other. In other words, the mass of 4 aspirin
tablets is the same as the mass of 1 penny. Each aspirin tablet must have ¼ of the penny's mass of 2.5 g or
0.62 g.
Knowing the number of aspirin that balance 1 penny, we can find the number of aspirin needed to balance
any number of pennies. Consider in the measurement shown in Figure 1.3
Figure 1.3
3.
How many aspirin are needed to balance two pennies?
________
4.
How many aspirin are needed to balance three pennies?
________
5.
How many aspirin are needed to balance three hundred eighty seven pennies?
________
Depicted below are the solutions to the questions you just answered. As long as you are dealing with
small whole numbers, it is easy to figure out in your head the number of aspirin needed to balance any
number of pennies; but it isn’t so easy when we involve large numbers. Notice, however, that the
calculations are exactly the same.
 4 aspirin 
 = 8 aspirin
 penny 
( 2 pennies ) 
 4 aspirin 
 = 12 aspirin
 penny 
( 2 pennies ) 
 4 aspirin 
 = 1548 aspirin
 penny 
( 387 pennies ) 
If we take advantage of the proportional relationship described above we can solve problems with
small or large numbers. And, we can state that "for any quantities that are proportionally related, the
ratio of the two quantities is constant." Using the aspirin/penny example, this can be stated
mathematically as:
8 aspirin 12 aspirin
1548
aspirin
=
=
=4
2 pennies 3 pennies
387 pennies
penny
Graphs of Proportional Relationships
Let’s look at one more property of proportional relationships. We''ve used the data shown below to plot
a graph showing the number of pennies along the x-axis and the number of aspirin required to balance
the pennies along the y-axis axis.
Pennies Aspirin
Plot of Pennies vs Aspirin
40
1
2
3
4
4
8
12
16
30
20
10
0
0
2
4
6
8
Pennies
Figure 1.3a
6.
What is the y-intercept? (i.e., where does the line cross the y-axis.) _____
7.
What is the slope of the line? _____
8.
What is the unit of the slope? ________
The reason we have taken time to graph the proportional relationship between number of pennies and
number of asprin required to maintain balance is that all proportional relationships produce this same kind
of graph, a straight line passing through the 0,0 point (origin). Furthermore, the slope of the line always
tells you the number of the quantity plotted along the y-axis that corresponds to one of the quantity plotted
along the x-axis. If you considered the Figure 1.3a, the slope of the line is "4 aspirin/1 penny" (usually read
"four aspirin per penny" or "four aspirin for every one penny"). If you considered the plot of the number of
pennies along the y-axis and the number of aspirin along the x-axis (Figure 1.3b), the slope of your line is
"0.25 pennies/1 aspirin" (usually read "one quarter penny per aspirin" or "0.25 pennies for every aspirin").
Plot of Aspirin vs. Pennies
5
4
3
2
1
0
0
5
10
15
20
Aspirin
Figure 1.3b
We could weigh everything in penny masses and aspirin masses, but we will not. The gram has been used
as the standard mass unit in science and provides a common reference for all scientists. We know that 1
penny mass = 2.5 grams. (If we placed pennies on one side of the balance in Figure 1.1 and standard gram
masses on the other side, 2 pennies would exactly balance five of the gram masses. There are 2.5
grams/penny just as there are 4 aspirin/penny.) With this in mind:
9.
How many grams does one aspirin weigh?
________
10. How many aspirin are needed to provide a mass of one gram? ________
We can use aspirin tablets along with pennies to achieve a higher degree of precision in measuring mass in
the kitchen. Figure 1.4 shows the results found using our balance to measure the mass of 1/4 cup (60 ml) of
table salt
Figure 1.4
11. Based on this figure, we can be sure that the mass of the salt is larger than
_____ g
12. Based on this figure, we can be sure that the mass of the salt is smaller than
_____ g.
13. If 3 aspirin are added to the 29 pennies, the table salt balanced. The mass is
_____ g
EQUIPMENT/MATERIALS
•
Balance
•
~50 pennies, must be post-1983.
•
8 to 10 nickels.
•
box of toothpicks
PROCEDURE
You will use your balance to determine the mass of three different substances. This will be done by placing
whatever you want to weigh in one of the balance pansand adding standard masses to the other cup until
balance is achieved. You need to develop a series of reliable standards that you can use to do this. We will
be basing the standards on the mass of a post-1983 penny, which is 2.5 g.
1.
Determining the mass of a nickel: Hold one hand under the cup on one side of the balance.
Carefully place a nickel in the cup. Allow the balance to tip and rest on the counter. Gently begin
adding pennies into the other cup until the balance begins to equalize. In the spreadsheet provided,
record the number of pennies required to balance the 1, 2, 4 and 8 nickels. A graph will
automatically be generated.
2.
Repeat the procedure above, using toothpicks instead of a nickel. Graph the relationship between
your toothpicks and pennies in provided spreadsheet. {Hint: you may want to use small paper cups
on both balance pans. Be sure to adjust the tabs so the cups balance when they are empty}
RESULTS & DISCUSSION
Now that you have developed relationships between the masses of your four standards, let's use them to
illustrate the power of proportional reasoning. Let's begin with your slopes. Based on the graphs generated
in your spreadsheet, indicate the slopes of the best-fit lines representing the relationships between:
•
•
Best fit slope pennies vs. nickels:
Best fit slope of toothpicks vs pennies:
________ pennies/nickel
________ toothpicks/penny
These slopes represent proportional relationships between the masses of the materials. Use them to answer
the following questions:
• How many nickels are required to balance 14 pennies?
____
• How many toothpicks are required to balance 9 pennies?
____
• What is the mass of an object if 3 nickels, 7 pennies, and 9 toothpicks balance it? ____
As these exercises illustrate, proportional relationships provide bridges between the different ways we
represent physical quantities. When we balance an object against pennies, toothpicks, or any other uniform
set of particles, we can determine the object's mass by multiplying the proportional relationship mass per
particles by the number of particles required to balance the object. Conversely, the mass per particle
relationship can be used to determine the number of particles of a substance that are present in a given
mass. This type of relationship represents a central idea in chemistry, since discrete, submicroscopic
particles called atoms, each with a well-defined mass, combine in large numbers to create the substances
such as pennies and toothpicks that we encounter every day.
There are a number of other proportional relationships that are also of great importance in chemisty. Many,
such as density, molarity and heat capacity, will be the subject of future laboratories. Others, like the
relationships among the metric units (c.f. Table 2.1, p ), must be memorized. Using metric relationships and
the relationships listed below, convert some personal information from "English" to "metric" units.
2.54 cm = 1 in; 2.2 lb = 1 kg; 1 mile = 1609 m
•
•
•
What is your height?
_____ in.
What is the distance between home and school?
_____ mi.
How long (on average) does it take to get from home to school? _____ min.
Use this information and the conversions above to answer the following questions:
• What is your height in meters?
• What is your average speed going from home to school?
• What is your average speed going from home to school in meters per second?
_____ m.
_____ mi/hr.
_____m/s.
Conversions involving proportional relationships are very common in chemistry, it is important to be able
to recognize their properties. In the coming lessons, we will reinforce the properties and techniques
associated with proportional relationships. As you become more familiar with them, you will find new
material less intimidating, since the relationships that are developed follow the same pattern we are now
exploring.
DATA SHEET—EXPERIMENT 1
Name_____________________________
Nickles
Pennies
Pennies vs. Nickels
10
0
8
Pennies
0
1
2
6
4
2
4
0
0
2
4
8
Pennies
6
8
Nickles
Toothpics
Toothpics vs Pennies
0
1
2
3
Toothpics
100
80
60
40
20
0
0
1
2
Pennies
3