S C I E N T I F I C N O T A T I O N : M O L E S & A V O G A D R O ‘ S N U M B E R
Part I: Introduction to a Mole
Do you like to eat eggs for breakfast? Have you ever eaten a dozen? Probably not, that’s a lot of eggs (unless you’re Rocky.) A dozen eggs is an example where a unit, in this case a dozen, is used to represent a specific number. So, no matter what you have for breakfast, a dozen cups of coffee, a dozen
donuts, a dozen eggs, we know that we are talking about having twelve of that object. A dozen is
equivalent to having 12 of something.
A mole is similar to a dozen as it represents a specific number. Instead of twelve though, it represents 6.02 × 1023 (called Avogadro’s’ Number). That’s a really, really large number! Moles are most commonly used in chemistry to talk about how many particles are found in an atom or molecule. If you have 1 mole of a water molecule that means you have 6.02 × 1023 water molecules. If you have 1 mole of
Carbon atoms that means you have 6.02 × 1023 Carbon atoms.
>Try this: If you have 1 mole of a water (H20) molecule, how many water molecules do you have?
(Answer: 6.02 × 1023 water molecules)
Example of Problems
Example 1: Find the number of Boron atoms in 2 moles. Make sure the answer is in Scientific Notation.
Solution:
We are going from moles to atoms so we will multiply:
2 moles × = 12.04 × 1023 atoms
Did you notice how the mole units cancel each other out?
But 12.04 is larger than 10, so this isn’t in Scientific Notation. So we convert it to Scientific Notation:
12.04 × 1023 = 1.204 × 1023 + 1 = 1.204 × 1024 atoms Final Answer
Example 2: Find the number of moles in 3.01 × 1025 atoms of Helium.
Solution:
This time we are going from atoms to moles which means division:
3.01 × 1026 atoms ÷ OR
3.01 × 1026 atoms × 0.5 × 103 moles
Did you see how the atoms canceled each other out?
This isn’t in Scientific Notation (note 0.5 is smaller than 1), so we convert it: 0.5 × 103 = 5 × 103 - 1 = 5 × 102 molesFinal Answer
Tip of the Day: Sliding the decimal to the right corresponds to subtracting from the exponent.
Part II: Mole Exercises
1. Find the number of sugar molecules (C12H22O11) in 4 moles.
2. Find the number of atoms in 8.5 moles of I (Iodine).
4. Find the number of moles in 3.1 × 103 moles of Ca (Calcium).
5. Find the number of moles in 1.806 × 1027 atoms of He (Helium).
6. Find the number of moles in 1.806 × 1019 atoms of He (Helium).
7. Find the number of moles in 3.612 × 1010 molecules of Carbon Dioxide (CO
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S C I E N T I F I C N O T A T I O N – C O N T I N U E D , N A S A D A T A
1. The sun produces 3.9 × 1033 ergs per second of radiant energy. How much energy does it produce in
one year (3.1 × 107 seconds)? (Hint: Multiply.)
2. The mass of the sun is 1.98 × 1033 grams. If a single proton has a mass of 1.6 × 10-24 grams, how
many protons are in the sun? (Hint: Divide.)
3. The approximate volume of the visible universe (a sphere with a radius of about 14 billion light years) is 1.1 × 1031 cubic light-years. If a light-year equals 9.2 × 1017 centimeters, how many cubic
centimeters does the visible universe occupy?
4. Pluto is located at a distance of 5.9 × 1014 centimeters from Earth. At the speed of light (2.99 × 1010
cm/sec) how long does it take a light signal (or radio message) to travel to Pluto and return?
5. The planet HD209458b, now known as Osiris, was discovered by astronomers in 1999 and is at a distance of 150 light-years (1 light-year = 9.2 × 1012 kilometers). If an interstellar probe were sent to
Name_________________________________________________________ U N I T (DIMENSIONAL) A N A L Y S I S : G R A M S & M O L E S Part I: Grams and Moles – How are they related?
How much do a dozen eggs weigh? How much do a dozen donuts weigh? Just because we have 12 eggs or 12 donuts, we know that eggs and donuts don’t weigh the same thing. It’s the same thing in chemistry, just because we have 1 mole of Helium or 1 mole of Calcium, it doesn’t mean they have the same mass. In this section you will learn how to figure out how much 1 mole of an atom or compound weighs.
The atomic mass (measured in atomic mass unit – amu) of an atom or compound can be found by using the periodic table.
For example, for Helium the atomic mass is 4.00 amu.
If we know the atomic mass, we can ascertain how much one mole weighs for that element or compound. An amu is related to moles and grams as:
1 mole = # amu which is equivalent to the # grams
So, 1 Helium mole = 4.00 amu which is equivalent to 4.00 grams (g). Or, in other words, 6.02 × 1023 He atoms = 1 mole = 4.00 amu = 4.00 grams.
>Try this: What does 1 mole of Hydrogen weigh? (Use your periodic table) (Answer: 1.008 g)
Example of Problems
Example 1: Find the weight of 2 Calcium moles. Solution:
The amu of Ca is 40.08:
2 moles × = 80.16 g Final Answer
See you later mole!
Example 2: Find the weight of 3 H20 moles.
Solution:
Using the periodic table, the amu of H is 1.008 and for O its 16.00. So, a water molecule has a total amu of:
2 × 1.008 = 2.016 amu (2 Hydrogen)
1 × 16.00 = 16.000 amu (1 Oxygen)
18.016 amu
3 moles × = 54.048 g Final Answer
Tip of the Day: If given a compound, the first step is to figure out the compound’s total amu.
Example 3: Find the number of moles in 88.625 g of Cl. Solution:
Using the periodic table, the amu of Cl is 35.45.
This time we are going from g to moles which means division:
88.625 g ÷ OR
88.625 g × = 2.5 moles Final Answer
Part II: Exercises on Moles Grams 1. Find the weight of 8 Copper moles.
4. Find the number of moles in 69.4 g of Lithium.
5. Find the number of moles in 115.475 g of Manganese.
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U N I T (DIMENSIONAL) A N A L Y S I S : M E A S U R E M E N T S Metric
Length 1 km = 1000 m Volume 1 kl = 1000 l Weight 1 kg = 1000 g
1 hm = 100 m 1 hl = 100 l 1 hg = 100 g
1 dkm = 10 m 1 dkl = 10 l 1 dkg = 10 g
1 m = 1 m 1 l = 1 l 1 g = 1 g
1 dm = 0.1 m 1 dl = 0.1 l 1 dg = 0.1 g
1 cm = 0.01 m 1 cl = 0.01 l 1 cg = 0.01 g
1 mm = 0 m 1 ml = 0.001 l 1 mg = 0.001 g
Note: 1 cc = 1 ml
Metric / American
Length 1 in = 2.54 cm Volume 1 cup = 0.237 l Weight 1 oz = 28.25 g
1 yd = 0.91 m 1 qt = 0.946 l 1 lb = 453.59 g
Temperature
Kelvin to Celsius (°C to K) Celsius to Fahrenheit (C to F) Fahrenheit to Celsius (F to C)
K = °C + 273 (°F - 32) × 5/9 = °C °C × 9/5 + 32 = °F
Tip of the Day: Make sure your units cancel so your finished product has the units you’re looking for.
1. 3.45 m = _________ dm
2. 5,023 cc = _________ dkl
3. 10 qt = _________ l
4. 5.5 yd = _________ cm
6. 3 K = _________ ° C
7. 45° F = _________ ° C
8. 0 K = _________ ° F
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U N I T (DIMENSIONAL) A N A L Y S I S: P R O J E C T
Choose 3 out of the 5 following questions. Research the question and type up 1 paragraph for each question you choose. This is worth 50 points and you have one week to complete.
1. What is the International System of Units? Provide an explanation and a brief history of when and why they are used.
2. In which fields are Kelvin, Celsius and Fahrenheit units most commonly used? Provide a brief history of when each was founded and by whom.
3. Compare and contrast the Metric and American (English) systems of measurement. Which do you prefer? Provide at least 2 thought out reasons to explain your preference. Do you think the U.S. should switch over to the Metric system? Why or why not?
4. Provide a brief history of the periodic table. When was the modern periodic table put together? Include a timeline to show at least 10 of the elements and when and by whom discovered them. 5. Provide a brief history of the mole and Avogadro’s Number. Who was Avogadro? How did you
discover this infamous number?
The following is the Rubric which will be used to grade your project:
Rubric: Unit Analysis Project
Weight 1 2 3 4 5
Question 1 Info 10 points
Question 2 Info 10 points
Question 2 Info 10 points
Grammar/Clarity 10 points
Typed 5 points
Sources Cited 5 points
