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CHE 105 – Week 1
Formative Assessment.
Instructions:
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Each student will work on this assignment alone.
Assignments with identical answers will earn grades of zero.
If you have questions, you are to ask me, your instructor, not your peers.
This assignment is a fillable PDF. You can download it to your computer and completed
it, and upload it back to the assignment submission area.
You may also print this out, complete it, scan it back, or photograph it and uploaded to
the upload area.
Only Microsoft Word assignments uploaded to the class will be graded.
You must show ALL your calculations and your work.
Submissions with answers only will incur significant point deductions.
Note: if you cannot scan your work before submitting, you are welcomed and encouraged to do
the following:
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Take an image of each page of your work with your phone.
Copy/paste those images to a Word document.
Make sure the image size is the same as the page and the correct orientation. Submit one
image per page.
Save the file as a Word document or PDF.
Submitted files in the following formats will NOT be evaluated:
• Pages
• Lone Jpeg images
• Any other file formats
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The Week 1 Formative Assessment Assignment in three parts. In part 1, you will complete an
exercise designed to help you understand significant figures. Part 2 involves the factor-label
method, and part 3 puts the two together.
Completing this assignment is likely to take you several hours. Please work on it
throughout the week! Start early!
Part 1: Significant Figures
A key to ‘getting the right answer’ when solving science problems requires being accurate in
math. This requires an understanding of how to use the numbers that you are dealing with. A
huge part of that involves significant figures.
A significant figure (or significant digits) is the number of digits of a number that carry
meaning. Believe it or not, some numbers do not carry meaning! Why bother? Well – using
significant figures creates an answer which is as precise as it can be.
As an example, you need to know if the best answer is 15.02 or 15.0227786472. It matters.
When deciding how much rocket fuel is needed to get people to the moon, or enough fuel to get
your airplane from Boston to Hawaii, there’s no such thing as ‘close enough.’ An error (too little
calculated) would be catastrophic!
Math always requires that we use the same number of significant digits for all numbers. If
we only have a limited number of one number, then the others need to adapt to it (we
round down).
For example, if we are adding two numbers: 2.22 + 2.0000999, the answer would be: 4.22
because we do not know anything past the second decimal place on the first number.
Thus, for this calculation, the number 2.0000999 becomes 2.00.
Here are the rules:
a) All non-zero numbers are considered significant (unless it’s ruled out)! Example: the
number 333.3 has four significant figures.
b) All zeros between two significant figures are significant. Example: 303 has three
significant figures; however 033 or 330 each have only two significant figures. The
number “330.” has three significant figures because of the decimal – which tells you that
the zero is significant.
c) A final zero in a number is only significant if it’s part of a decimal. Example: 3.30 has
three significant figures.
d) When doing calculations, you must cut and round all numbers to the lowest number of
significant figures before you perform the math. For example:
4.01 x 3.01
In this case, the number of significant figures is the same so that you can do this
problem right away. Your answer will also have 3 significant figures.
5.79909383 x 3.01
In this case, the number of significant figures is not the same, so you have to
round:
5.80 x 3.01
to find the most accurate answer.
Let’s apply this.
Application #1:
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To complete this assignment, you will create a random number with at least four
digits to the left of the decimal and 4 to the right. At least two of the digits must be
zero. List the number here and explain how many significant figures you have.
Your number:________________
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Describe the number of significant figures there are, and why the zeros are or are not
significant:
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Round your number to 5 places and explain how many significant figures are in the
result.
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Create another random number with at least four digits to the left of the decimal and 4
to the right but make sure to include four zeros in this number. So – of the eight digits,
four of them will be zero. List it here and explain how many significant figures you
have.
Your number:________________
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Describe the number of significant figures there are, and why the zeros are or are not
significant:
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Round your number to 5 places and explain how many significant figures are in the
result.
Application # 2: Operations involving significant figures are only as reliable as the figure with
the smallest number of significant figures.
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Create two numbers randomly, one with two significant figures, and the second with
four significant figures. List them here ( ## & ####):______________
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Round the number with four significant figures to 2 significant figures and add them,
here:
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Describe why the numbers which were rounded away don’t matter?
Application number 3: When doing multiplication or division, the numbers must also be
rounded before the mathematical work is done.
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Create two more numbers randomly, one with three significant figures, and the second
with six significant figures. List them here( ### & ######):______________
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Round the number with six significant figures and multiply them, making sure that your
answer conforms to the correct number of significant figures:
Part 2: Factor-Label method
The factor-label method, also known as dimensional or unit analysis is a way of solving
numerical problems which are common in science. It relies on the fact that a number, that
number has two parts which tell you how much and of what:
Part 1… the number! For example, 9 is a number.
Part 2… the unit! For example, 3 pounds. A “pound” is a unit associated with the number 3.
Without both the number and the units, there is really no meaning, and it’s far more likely that
one using that number will lead to a mistake. If someone asks you how much your baby
weighed at birth, you would say 9 pounds (or whatever it was), but you would not say 9. Think
about math and science the same way.
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Exercise: Find a random object. Weigh it, and list the weight of that object, along with
the units here: ______________.
So, think of the number/unit combination as a fail-safe way to get that A in your chemistry class
because you are focused on the numbers and the units. Just like numbers, units can be
multiplied, divided, and squared.
If you want to know the area of a square that has a side which is 2 feet long on one side and 2
feet long on the other, you figure it out by multiplying both the sides together: the numbers and
the units: 2 feet x 2 feet = (2×2) (feet x feet) = 4 feet2.
Why else do units matter? In chemistry you’ll encounter a lot of examples where you have to
convert units. It’s pretty basic to add up all the weights of the flasks, for example. Instead,
scientists are interested in what’s inside the flask – and that can change.
Let’s say we have 10.0 grams of ice. Ice is the solid form of water, as most people know. But,
let’s say we also have 10.0 grams of solid ethyl alcohol. No, we’re not having a party. Instead,
we’re going to melt both and see how much liquid of each substance there is.
This will allow us to calculate the density of each liquid.
The density is a measure of the number of grams per unit volume. That means: how much a
certain volume of a liquid weighs. In the old days, scientists would run around measuring things
like this. Thankfully we have all that data now!
The density is also something which is called identity or a conversion factor because it has units
which are in the form this/that. For example:
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Grams / mL is one of these.
Miles/gallon is another one.
Identities provide a way to equate two different things. We use them all the time.
You can use them right side up, for example, 10 grams/mL or upside down, 1/10 mL/gram.
They work both ways – and the way you use them has to do with what you want to figure out.
Generally you are eliminating one of the units.
For example, in our 10 grams of water ice, we want to know, using the density (in grams/mL),
how many mL that will be when it melts. It’s easy – just look at the units when setting up the
problem. We are starting with grams, and we want to find mL using the density.
The units of density are grams/mL, so we are going to want to set up an equation which gets rid
of the grams, but leaves mL in the numerator.
The density of ice is 0.917 grams/mL. Grams is in the numerator; mL are in the denominator.
To set up the proper equation, we have to ‘flip the fraction’ which puts mL in the numerator and
grams in the denominator.
10 grams of water ice
x mL_______
= 10.9 mL of liquid water.
0.917 grams of water ice
This allows the grams (units) to be canceled out, giving us mL.
10 grams of water ice x ______mL___________ = 10.9 mL of liquid water.
0.917 grams of water ice
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Apply and Solve: The density of ethyl alcohol is 0.798 grams/mL. Set up the equation
for how to solve the problem of how much volume (in mL) 10 grams of ethyl alcohol will
take up? Show your work.
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Apply and Solve: Another example of creating a unit is to figure out how many miles
you can go on 2.00 gallons of gasoline. Estimate what the fuel efficiency of your vehicle
is in miles/gallon, and calculate how far you could travel if you only 2.00 gallons of
gasoline?
a. Please list the approximate fuel efficiency of your vehicle (or one you know
about): ___________________
b. Determine how far you could go on 2.00 gallons of gasoline. Show your work.
c. Apply and Solve: Knowing the following information:
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Given: 1.609 km = 1.000 mile
How many Km is a marathon: 26.2 miles? Show your work. The answer
converts miles into km.
d. Apply and Solve: Knowing the following information:
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Given that a car is moving at 55 miles/hour, and
There is 1.61 Km/mile, determine:
How fast that car is moving in meters/second. Think about the units. Show
all work.
Part 3: Moles
One of the basic units of measurement in chemistry is the ‘mole.’ It’s a unit kind of like a dozen
is a unit, but for MUCH more things (dozen = 12 things).
A mole allows us to know about quantities of very small things: molecules and atoms.
1 mole = 6.02 x 1023 things. That’s a LOT of things, isn’t’ it! Atoms and molecules are really
small, and there are a lot of them, even in the tiniest spec of something. Thus, moles are a very
convenient way of dealing with atoms and molecules. The mole value is also known as
“Avogadro’s number” because he figured it out. 6.02 x 1023 is Avogadro’s number.
If we have 100 grams of Silver, we can calculate how many atoms of Silver we have by using
moles. Follow the units. We’re converting from grams to atoms.
From the periodic table, we find that the atomic weight of Silver is 107.86 grams/mole. This
means that if you have 6.02 x 1023 atoms (1 mole) of Silver, it will weight 107.86 grams.
Based on the above, if we have 100.0 grams of Silver, if we want to approximate, we know that
we should have something less than 1 mole of Silver by comparing 100 grams to 107.86
grams/mole. Let’s check it out:
100.0 grams Silver x moles Silver___
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107.86 grams Silver
100.0 grams Silver x moles Silver___
=
0.927 moles of Silver.
107.86 grams Silver
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Look up the atomic weight of any atom on the periodic table. Pick a random number
of grams and calculate how many moles you have using the method above. Describe
your process and show how you convert from grams to moles:
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Find the atomic weight of Gold (Au) on the periodic table. If you have 1 ounce of
Gold, calculate how many moles you have using the method above. First you’ll need to
figure out how many grams are in an ounce. Describe your process and show how you
find the number moles:
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Next, take that number of moles and use Avogadro’s number (6.02 x 1023 atoms/mole),
to find how many atoms of Gold are in that 1 ounce of Gold. Remember to focus on
units. Show all your work.
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Next, please describe any item you have in your world in terms of moles. For example, if
you ave 10 dollars in your pocket, you can find out how many ‘moles’ of dollars you
have. Hint: it’s a TINY number. Pick something and calculate how many moles of that
thing – there is.
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