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This is a Sequential Activity

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This is a Sequential Activity

and the Mole

This group activity is intended to introduce you to two very important parts of the study of chemistry. First, you will learn the basics of using scientific notation. This is a way of writing very large and very small numbers with a minimum of fuss and without having to count a lot of zeros. Second, you will learn about the scientific unit for ‘amount of substance’. You may have encountered this unit before and in this activity it will be made clear exactly what is meant by it.

Scientific notation is exceptionally useful for dealing
with numbers like 137,760,000,000 or 0.000 000 000 679.
The first number is a whole number and can be rewritten
as 1.3776 x 10^{11}. The second number is a
fraction and can be rewritten as 6.79 x
10^{–10}. The first way that I wrote both
of these numbers is ungainly and requires you to count
out zeros every time you write the number. And if you
miscount your zeros you get a much different number.

**Numbers in scientific notation have two parts.
The first part is a number between 1 and 10. The second
part is the number 10 raised to some whole-number
exponent or power.** You can see how this works by
looking at this **general model for a number in
scientific notation: N x 10 ^{x}**. To
express a number in scientific notation is really as
simple as counting the number of digits. For example,
look at the number given above: 137,760,000,000. Write
this number down but put a decimal point between the 1
and the 3. Now, starting with the three, count digits to
the right until you get to the last zero before the
original location of the decimal point. You will find
these are 11 digits. So 11 is the x in the expression N x
10

smaller bigger Fraction 1/100 1/10 Decimal notation 0.01 0.1 1 10 100 1,000 ________________________________________________________ Scientific notation 10^{-2}10^{-1}10^{0}10^{1}10^{2}10^{3}

Here are some problems to make scientific notation more clear:

Write the number indicated as shown in the example.Examples10^{1}= 10 10^{5}= 100,000 10^{–3}= 0.001 10^{–7}= 0.0000001

- 10
^{4}= _____________ - 10
^{–4}= _____________ - 10
^{–5}= _____________

- 10
^{7}= _____________ - 10
^{14}= _____________ - 10
^{–12}= _____________

Put a box around the larger number in each pair.Examples10^{4}—— 10^{9}10^{–4}—— 10^{–9}

- 10
^{4}—— 10^{5} - 10
^{23}—— 10^{7} - 10
^{–4}—— 10^{0} - 10
^{–9}—— 10^{–12}

- 10
^{14}—— 10^{41} - 10
^{8}—— 10^{–9} - 10
^{–4}—— 10^{2} - 10
^{3}—— 10^{–1}

Write the following numbers in decimal form.Examples2 x 10^{3}= 2,000 4.1 x 10^{–5}= 0.000041 2.9 x 10^{14}= 290,000,000,000,000

- 2.3 x 10
^{4}= _____________ - 4.71 x 10
^{9}= _____________ - 3.14 x 10
^{–3}= _____________ - 1.2 x 10
^{–1}= _____________

- 1.805 x 10
^{0}= _____________ - 6.02 x 10
^{23}= _____________ - 1.602 x 10
^{–19}= _____________ - 8.21 x 10
^{–2}= _____________

Write the following numbers in scientific notation.Examples602,200,000,000,000,000,000,000 = 6.022 x 10^{23}0.00132 = 1.32 x 10^{–3}0.0193 = 1.93 x 10^{–2}

- 0.068 0 = _____________
- 0.005 9 = _____________
- 502,000 = _____________
- 137,000,000,000 = _____________
- 0.000 789 = _____________

- 14,258 = _____________
- 1,580 = _____________
- 1,002,010 = _____________
- 0.000 002 5 = _____________
- 0.005 809 = _____________

Now you should know how to write numbers using scientific notation. If you do not yet understand any of the exercises on the previous page, please ask for help before going on.

Numbers written in scientific notation are easy to multiply and divide but a bit harder to add and subtract. So we’ll start with addition and subtraction.

The first thing to note when adding and subtracting numbers
in scientific notation is what order of magnitude the
numbers are in. **Order of magnitude refers to the
difference between two exponents of 10.** The number
1.2 x 10^{2} is one order of magnitude smaller than
the number 2.4 x 10^{3}. Likewise, 6.02 x
10^{23} is 20 orders of magnitude larger than 6.0 x
10^{3}. Numbers should only be added together (or
subtracted from one another) when they are within 2 or at
most 3 orders of magnitude. If you need to add two numbers
that differ by more than 3 orders of magnitude (like
10^{4} and 10^{9}) just write down the
larger number. It is so much larger that the smaller number
adds too small an amount to matter. If you must subtract a
smaller number from a larger one (say 10^{2}
– 10^{–3}) just write the larger number
as the answer: the number you are subtracting is too small
to matter.

Note that you must make the exponents the same in order of magnitude to add or subtract. To make a number have a larger exponent, you must write the number smaller. To make a number have a smaller exponent, you must write the number larger. That just means moving the decimal point:

These numbers all mean the same thing! (1.25 if not using scientific notation) 0.0125 x 10^{2}0.125 x 10^{1}1.25 x 10^{0}12.5 x 10^{–1}125 x 10^{–2}1,250 x 10^{–3}Write the following numbers so that they have the exponent of 10 shown.

- 1.2 x 10
^{–1}= _____________ x 10^{1} - 2.7 x 10
^{1}= _____________ x 10^{3} - 3.9 x 10
^{4}= _____________ x 10^{2} - 4.2 x 10
^{3}= _____________ x 10^{1}

- 12.7 x 10
^{6}= _____________ x 10^{4} - 11.1 x 10
^{1}= _____________ x 10^{3} - 13.3 x 10
^{–5}= _____________ x 10^{–7} - 4.97 x 10
^{–3}= _____________ x 10^{–2}

Addition and Subtraction Examples(3 x 10^{4}) + (2 x 10^{3}) = (3 x 10^{4}) + (0.2 x 10^{4}) = 3.2 x 10^{4}= 32,000 (3 x 10^{4}) - (2 x 10^{3}) = (30 x 10^{3}) - (2 x 10^{3}) = 28 x 10^{3}= 2.8 x 10^{4}Change numbers so that both in each problem have the same exponent, then add or subtract. If numbers differ by more than 2 orders of magnitude, then write down the larger number without performing any operation.

- 1.2 x 10
^{–1}+ 2.4 x 10^{1}= _____________ - 2.7 x 10
^{2}– 1.3 x 10^{1}= _____________ - 3.9 x 10
^{4}+ 4.7 x 10^{9}= _____________ - 4.2 x 10
^{3}+ 6.82 x 10^{4}= _____________

- 12.7 x 10
^{6}– 3.11 x 10^{5}= _____________ - 11.1 x 10
^{1}– 9.99 x 10^{–1}= _____________ - 13.3 x 10
^{–5}+ 14.9 x 10^{–4}= _____________ - 4.97 x 10
^{–3}– 3.2 x 10^{–7}= _____________

Now multiplication and division are actually quite easy. When multiplying, multiply the numbers and add the exponents. When dividing, divide the numbers and subtract the exponents. Finally, once you have an answer in scientific notation change the answer so that the number multiplied by a power of 10 is between 1 and 10:

Multiplication and Division Examples(2 x 10^{2}) × (6 x 10^{3}) = (6 x 10^{3}) ÷ (2 x 10^{2}) = 12 x 10^{5}= 1.2 x 10^{6}3 x 10^{1}(2.7 x 10^{9}) × (4.2 x 10^{3}) = (2.16 x 10^{2}) ÷ (1.2 x 10^{6}) = 11.34 x 10^{12}= 1.134 x 10^{13}1.8 x 10^{–4}(5.6 x 10^{–9}) × (2.3 x 10^{3}) = (4.5 x 10^{2}) ÷ (9.0 x 10^{–5}) = 12.88 x 10^{–6}= 1.288 x 10^{–5}0.50 x 10^{7}= 5.0 x 10^{6}Multiply or divide as indicated. Simplify all answers so that the number multiplied by a power of 10 is between 1 and 10.

- (2.5 x 10
^{–1}) × (5.0 x 10^{2}) = _____________ - (1.80 x 10
^{2}) ÷ (9.0 x 10^{–1}) = _____________ - (3.2 x 10
^{3}) × (4.0 x 10^{8}) = _____________ - (4.2 x 10
^{3}) ÷ (7.0 x 10^{1}) = _____________ - (9.0 x 10
^{3}) × (2.1 x 10^{–9}) = _____________ - (3.6 x 10
^{5}) ÷ (6.0 x 10^{4}) = _____________

- (5 x 10
^{-5}) × (11 x 10^{4}) = _____________ - (2.4 x 10
^{-4}) ÷ (4.0 x 10^{3}) = _____________ - (8 x 10
^{6}) × (4 x 10^{3}) = _____________ - (3.6 x 10
^{8}) ÷ (1.2 x 10^{4}) = _____________ - (4.8 x 10
^{3}) × (8.0 x 10^{5}) = _____________ - (9 x 10
^{21}) ÷ (3 x 10^{19}) = _____________

- A box contains 1.81 x
10
^{24}atoms. One third of them are carbon, the other two thirds are oxygen. How many carbon atoms are in the box? How many oxygen atoms?

Bonus: what chemical compound might this be?

Atoms are too small to weigh one at a time. Not only are
there no scales that could handle the extremely tiny mass
of one atom but it would take forever to get anything
done if you had to weigh 1.2 x 10^{23} atoms one
at a time. So chemists have a short-cut and it is called
the mole or Avogadro’s Number.

First, a word or two about the number.
**Avogadro’s Number is 6.02 x 10 ^{23}
and is also called ‘the mole’.** This
is such a large number that it is hard to visualize, but
here are a few tries: if you had a watermelon the size of
the moon, it might have a mole of seeds inside it. One
mole of chicken eggs would cover the entire surface of
the Earth…four miles deep. This is a seriously
large number.

Second, an introduction to some things you need to know
to make use of this number. Think of the mole like you
think of the words ‘pair’,
‘dozen’, and ‘gross’. A pair has
2 objects in it. A dozen has 12. A gross is a dozen dozen
or 144 items. Well, a mole is just 6.02 x 10^{23}
items. Mostly, a mole is only useful for counting very
small and very numerous items. I feel a bit sorry for all
the chickens (and those who have to clean up after them)
that would be needed to lay a mole of eggs.

The value of Avogadro’s number was not randomly
chosen but instead was determined experimentally. You
know from previous lessons that a carbon-12 atom
(^{12}
_{6}C) weighs exactly 12 amu. Scientists
have experimentally determined the number of carbon atoms
in exactly 12 *grams* of carbon to be 6.022 137 x
10^{23}. This means that when you weigh out 12 g
of carbon on a scale you have a mole of carbon atoms. The
usefulness of this comes when you realize that you can
relate the mass of an atom or molecule in amus to the
mass of a mole of that atom or molecule in grams.
**The mass of a mole of atoms or molecules in grams
is the same number as the mass of those atoms or
molecules in atomic mass units. The mass of a mole of
atoms or molecules is called the molar mass and has units
of g/mol.**

Examples(using the Periodic Table) 1 Cu atom has a mass of 63.55 amu 1 mole of Cu atoms has a mass of 63.55 g: copper has a molar mass of 63.55 g/mol 1 S atom has a mass of 32.065 amu 1 mole of S atoms has a mass of 32.065 g: sulfur has a molar mass of 32.065 g/mol Find the formula mass of the following atoms using your periodic table. Express your answer using both amu and g/mol.

- Fe 55.845 amu (1 atom) 55.845 g/mol
- Na
- K

- N
- Cl
- Xe

In the same way that you find the molar mass of an atom,
you can find the molar mass of a chemical compound.
Compounds are most commonly written in a formula notation
that shows what kinds of atoms are in the molecule (or
formula unit) and how many of each. For example, in the
formula for sugar (glucose) you can see that there are 6
carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms:
C_{6}H_{12}O_{6}. The small number
down and to the right of each atomic symbol is called a
subscript and shows how many of that kind of atom can be
found in each molecule of the substance. **The molar
mass of a compound is the sum of the molar masses of each
atom in the compound multiplied by its subscript.**

ExamplesC_{6}H_{12}O_{6}6 × 12.011 g/mol + 12 × 1.0079 g/mol + 6 × 15.999 g/mol = 180.16 g/mol Write the formula for each of the following compounds and find the formula mass. Express the mass in amu and in g/mol.

- 2 iron atoms, 3 oxygen atoms
- 1 sodium atom, 1 chlorine atom

- 2 C atoms, 6 H atoms, 1 O atom
- 1 potassium atom, 1 bromine atom

- 1 cobalt atom, 2 chlorine atoms
- 1 silver atom, 1 iodine atom
- 1 potassium atom, 1 oxygen atom, 1 hydrogen atom

- 2 aluminum atoms, 3 oxygen atoms
- 1 silicon atom, 4 fluorine atoms
- 1 molybdenum atom, 5 chlorine atoms

Use the following types of conversion factors for these problems: 6.02 x 10^{23}atoms/mol 6.02 x 10^{23}molecules/mol 6.02 x 10^{23}things/mol 1 mol 6.02 x 10^{23}things or ——————————————————— or ——————————————————— 6.02 x 10^{23}things 1 mol Express your answers using scientific notation.

- How many atoms are in 2.56 moles of C?
- How many molecules are in 4.7
moles of C
_{2}H_{5}O? - How many chickens are there in 27 moles of chickens?

- How many moles is 1 million (1 x
10
^{6}) molecules? - How many moles are in 4.7 x
10
^{17}molecules of sugar? - How many moles of paper clips do
you have if you have 1.204 x 10
^{25}paper clips?

A chemist makes use of all this by being able to find the mass of a chemical and be able to tell how much, that is, how many moles, of the chemical she has. Given the molar mass of a chemical, she can use a mass in grams to figure out how many moles she has. Or if she needs a certain numbers of moles, she can calculate how many grams that would be.

ExamplesMoles from grams C_{6}H_{12}O_{6}has a molar mass of 180.16 g/mol 1 mol 360.0 g of C_{6}H_{12}O_{6}× —————— = 1.998 mol 180.16 g

Grams from moles NaCl_{ }has a molar mass of 58.44 g/mol 58.44 g 2.700 mol of NaCl × —————— = 157.8 g 1 mol

Find the molar mass of each compound (hint, see your own answers above), then follow the instructions given. Convert to moles

- 10.0 g NaCl
- 42.0 g
Fe
_{2}O_{3} - 1.170 x 10
^{2}g C_{ 2}H_{6}O - 3.24 x 10
^{2}g KBr - 2.73 x 10
^{3}g CoCl_{2}

Convert to grams

- 21 moles AgI
- 17.2 moles KOH
- 1.9 moles
Al
_{2}O_{3} - 5.7 moles MoCl
_{5} - 4.2 moles SiF
_{4}