## Methodology

Problem One
Calculate the mass of 6 x 1020 atoms of silicon.

Step #1. Determine the number of moles of silicon.
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One mole of silicon is 6 x 1023 atoms. Therefore, 6 x 1020 atoms is:
(6 x 1020 atoms/ 6 x 1023 atoms per mole) = 1 x 10-3 mole

Step #2. Determine the mass of one mole of silicon.
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One mole of silicon has a mass equal to the atomic weight in grams; that is, 28g.

Step #3. If we know the mass of one mole and the number of moles, how do we calculate the mass of this number of moles?
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The mass is calculated by multiplying the number of moles by the mass of a mole.
1 x 10-3 mole x 28 g/mole = 0.028 g
This process is analogous to the procedure that we use if we know the cost of meat per pound and want to know how much a quarter of a pound will cost.

Problem Two
Calculate the mass in grams of one 12C atom.

Step #1. What do we know that would allow us to calculate the mass of any amount of 12C atoms?
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We know that the atomic weight in grams of any element contains 6 x 1023 atoms of that element.

Step #2. What is the mass of a mole of 12C?
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12.00 g

Step #3. What is the number of atoms in a mole of 12C?
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6 x 1023

Step #4. If 100 pencils weigh 100 g, what is the weight of one pencil?
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One gram, (100 g/ 100 pencils) = 1 g per pencil

Step #5. If 6 x 1023 atoms weigh 12.0 g what is the weight of one atom?
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12.0 g/ 6 x 1023 atoms = 2 x 10-23 g per atom

Problem Three
What is the mass of 0.2 moles of oxygen atoms?

Step #1. Determine the mass of one mole of oxygen atoms.
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16 g
Remember that the atomic weight in grams is the mass of one mole.

Step #2. If the mass of one mole of oxygen is 16 g, what is the mass of 0.2 mole?
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(16 g/ 1 mole) x 0.2 mole = 3.2 g

Step #3. Solve the problem again using proportions.
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1 mole/ 16 g = 0.2 mole/ x
x = 3.2 g

Problem Four
How many atoms are there in 50 g of phosphorus?

Step #1. What is the mass of one mole of phosphorus?
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Its molar mass in grams; that is, 31 g.

Step #2. How many moles are there in 50 g of phosphorus?
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50 g/ 31 g per mole = 1.6 mole

Step #3. How many atoms are there in one mole?
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6 x 1023

Step #4. How many atoms are there are 1.6 moles?
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1.6 moles x 6 x 1023 atoms/mole = 9.6 x 1023 atoms

Problem Five
How many moles of hydrogen are there in 32 g of methane (CH4)?

Step #1. What should we do first?
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Determine the number of moles of methane.

Step #2. What information do we need in order to determine the number of moles of methane?
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The molar mass of methane, which is 16 g per mole.

Step #3. How many moles of methane are there in 32 g of methane?
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32 g/16 g per mole = 2.0 mole

Step #4. How many moles of hydrogen are there in each mole of methane?
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The formula CH4 reveals that there are 4 moles of hydrogen for each mole of CH4.

Step #5. How many moles of hydrogen are there in 2 moles of methane?
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2 moles CH4 x (4 moles H/ 1 mole CH4) = 8 moles H

Problem Six
How much gold contains the same number of atoms as 20 g of iron?

Step #1. Outline a procedure for solving the problem.
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1. Determine the number of moles of iron.
2. Recognize that the number of moles of gold will equal the number of moles of iron.
3. Determine the mass of gold.

Step #2. Determine the number of moles of iron.
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20 g/ 55.8 g per mole = 0.36 moles

Step #3. Determine the masss of 0.36 moles of Au.
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197 g/mole x 0.36 moles = 71 g Au

Problem Seven
How many molecules of Br2 are present in 0.15 g of Br2?

Step #1. Determine the molar mass of Br2.
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158.8 g per mole

Step #2. Determine the number of moles of Br2.
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0.15 g/ 158.8 g per mole = 9.4 x 10-4 mole

Step #3. Determine the number of molecules of Br2 in one mole of Br2.
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6 x 1023 molecules

Step #4. Calculate the number of molecules of Br2.
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(6 x 1023/1 mole) x 9.4 x 10-4 = 6 x 1020

Problem Eight
How many moles of HCl are present in 100 mL of 12 M HCl?

Step #1. Determine a strategy for solving the problem.
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1. Find the number of moles of HCl in one liter of 12 M solution.
2. Determine the number of moles in 100 mL.

Step #2. What is the definition of molarity?
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The number of moles of solute per liter of solution.

Step #3. How many moles of HCl are present in one liter of 12 M HCl?
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12 moles

Step #4. How many moles of HCl are present in 100 mL (0.1 L) of 12 M HCl?
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0.1 L x (12 moles/ 1 L) = 1.2 mole

Problem Nine
How many mL of 12 M HCl are required to prepare 500 mL of 0.1 M HCl?

Step #1. Clearly state the definition of molarity.
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Molarity is the number of moles of solute (in this case HCl) per liter of solution.

Step #2. How many moles of HCl will be contained in 500 mL of 0.1 M HCl?
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There are 0.1 mole of HCl in one liter of 0.1 M HCl. In 500 mL (0.5 L) there are 0.5 L x 0.1 mole/1 L = 0.05 mole HCl

Step #3. How many mL of 12 M HCl contain 0.05 mole HCl?
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0.05 mole HCl/ 12 moles HCl/L = 4.2 x 10-3 L = 4.2 mL

Problem Ten
How many moles of CO2 are obtained in the complete reaction of CH4 with O2 (in addition to CO2, water is formed in the reaction)?

Step #1. Outline the procedure that you will use in solving the problem.
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1. Determine what the reactants and products of the reaction are.
2. Write an equation for the reaction.
3. Determine the mole-mole relationship between CH4 and CO2.
4. Apply the mole-mole relationship to the number of moles of CH4.

Step #2. Follow the procedure above.
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1. CH4, O2 = reactants, CO2, H2O = products
2. Write an equation for the reaction:
CH4 + 2 O2 → CO2 + 2 H2O
3. According to the equation, one mole of CH4 produces one mole of CO2.
4. 0.1 mole CH4 x (1 mole CO2/1 mole CH4 ) = 0.1 mole CO2

Problem Eleven
How many moles of Cl2 are required to form 0.2 mole of SiCl4 in the reaction of elemental silicon (Si) with Cl2?

Step #1. Write an equation for the reaction.
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Si + 2 Cl2 → SiCl4

Step #2. How many moles of Cl2 are required to form one mole of SiCl4?
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The coefficients of 2 for Cl2 and 1 for SiCl4 tell us that 2 moles of Cl2 are required.

Step #3. How many moles of Cl2 are required to form 0.2 mole SiCl4?
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0.2 mole SiCl4 x (2 mole Cl2/1 mole SiCl4) = 0.4 mole Cl2