## Methodology

Problem One

Calculate the mass of 6 x 10^{20} atoms of silicon.

**Step #1. Determine the number of moles of silicon.**

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One mole of silicon is 6 x 10^{23} atoms. Therefore, 6 x 10^{20} atoms is:

(6 x 10^{20} atoms/ 6 x 10^{23} 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 ^{12}C atom.

**Step #1. What do we know that would allow us to calculate the mass of any amount of ^{12}C atoms?**

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We know that the atomic weight in grams of any element contains 6 x 10^{23} atoms of that element.

**Step #2. What is the mass of a mole of ^{12}C?**

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12.00 g

**Step #3. What is the number of atoms in a mole of ^{12}C?**

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6 x 10^{23}

**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 10 ^{23} atoms weigh 12.0 g what is the weight of one atom?**

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12.0 g/ 6 x 10^{23} 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 10^{23}

**Step #4. How many atoms are there are 1.6 moles?**

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1.6 moles x 6 x 10^{23} atoms/mole = 9.6 x 10^{23} atoms

Problem Five

How many moles of hydrogen are there in 32 g of methane (CH_{4})?

**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 CH_{4} reveals that there are 4 moles of hydrogen for each mole of CH_{4}.

**Step #5. How many moles of hydrogen are there in 2 moles of methane?**

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2 moles CH_{4} x (4 moles H/ 1 mole CH_{4}) = 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 Br_{2} are present in 0.15 g of Br_{2}?

**Step #1. Determine the molar mass of Br _{2}.**

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158.8 g per mole

**Step #2. Determine the number of moles of Br _{2}.**

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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 Br _{2} in one mole of Br_{2}.**

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6 x 10^{23} molecules

**Step #4. Calculate the number of molecules of Br _{2}.**

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(6 x 10^{23}/1 mole) x 9.4 x 10^{-4} = 6 x 10^{20}

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 CO_{2} are obtained in the complete reaction of CH_{4} with O_{2} (in addition to CO_{2}, 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 CH_{4} and CO_{2}.

4. Apply the mole-mole relationship to the number of moles of CH_{4}.

**Step #2. Follow the procedure above.**

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1. CH_{4}, O_{2} = reactants, CO_{2}, H_{2}O = products

2. Write an equation for the reaction:

CH_{4} + 2 O_{2} → CO_{2} + 2 H_{2}O

3. According to the equation, one mole of CH_{4} produces one mole of CO_{2}.

4. 0.1 mole CH_{4} x (1 mole CO_{2}/1 mole CH_{4} ) = 0.1 mole CO_{2}

Problem Eleven

How many moles of Cl_{2} are required to form 0.2 mole of SiCl_{4} in the reaction of elemental silicon (Si) with Cl_{2}?

**Step #1. Write an equation for the reaction.**

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Si + 2 Cl_{2} → SiCl_{4}

**Step #2. How many moles of Cl _{2} are required to form one mole of SiCl_{4}?**

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The coefficients of 2 for Cl_{2} and 1 for SiCl_{4} tell us that 2 moles of Cl_{2} are required.

**Step #3. How many moles of Cl _{2} are required to form 0.2 mole SiCl_{4}?**

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0.2 mole SiCl_{4} x (2 mole Cl_{2}/1 mole SiCl_{4}) = 0.4 mole Cl_{2}