# Chapter 10 Chemical Quantities

Editor: Erin Cropanese

Coeditors:
Nick Romero
Kevin McAllister
Tess Murphy

Here is a youtube video that demonstrates the value of a mole with a song to help introduce this chapter!...(in the video they say the value of the mole is 6x10^23 when in fact, we learn a more precise value of 6.02x10^23)

# Introduction

##### Chapter 10 begins with the mole and applying it to chemistry. In section one the students learn about converting the mole to particles, methods of measuring amounts of substances, Avogadro's number, the relationship between atomic mass and molar mass an an element, and how to calculate the mass of a mole of a compound. In section two the students learn about the mole-mass relationship and how to convert each, the mole-volume relationship and Avogadro's hypothesis, calculating volume at standard temperature and pressure, and calculating molar mass from density. The chapter concludes with section three, which teaches the students to calculate the percent by mass of an element in a compound, to calculate the percent composition from mass data, to calculate the percent composition from a formula, about empirical formulas, and about molecular formulas.

Group 1
Tess Murphy- Coeditor
Henry Dodge
Cassie Naimie
Gabe Hannawi
Alex Trombetta
Andrew Ware

## The Mole: A Measurement of Matter

### Tess Murphy

• Our world is quanititive. It’s all about numbers!
• Always answering questions- “How many?” “How much?”
• There are three ways to measure matter.
• Count the items
• Determine its mass
• Find out its volume
Here’s what specific units use for measuring mean-
Pair= 2
Dozen= 12
Apples can be measured in three different ways-
• At fruit stand, by count (3 for \$2.40)
• In a grocery store, by weight (\$1.29/pound) or by mass (\$2.79/kg)
• At orchard, by volume (\$12.00/bushel)
• By count- 1 dozen apples= 12 apples
• By mass- 1 dozen apples= 2.0 kg apples
• By volume- 1 dozen apples= 0.20 bushel apples
• All equal a dozen apples!
• Knowing the relationship between the count, mass, and volume of something allows you to convert among the units!

### Henry Dodge

• Chemists use a unit that is a specified number of particles, called a mole.
• A mole of a substance is 6.02 x 1023 representative particles of that substance. It is the SI unit for measuring the amount of a substance.
• The number of a representative particles in a mole, 6.02 x 1023 is called…..AVOGADRO’S NUMBER!!!!!
• What is a representative particle? It is the smallest unit into which a substance can be broken down without a change in composition. Most representative elements are atoms, molecules, or ions.

In summary:
• A mole of any substance contains Avogadro’s Number of representative particles, or 6.02 x 10^23 representative particles.

Here is the formula for converting number of representative particles to moles:
• Moles = representative particles x 1 mole
6.02 x 1023 representative particles

### Cassie Naimie (Pg. 291-292)

Converting Number of Particles to Moles
• The relationship of 1 mol = 6.02 x 1023 is the basic conversion factor used to convert numbers of representative particles to moles.
• Moles= representative particles x 1 mol/6.02 x 1023 representative particles
• *Sample Problem:

• Magnesium is a metal used in building of cars, tools, outdoor furniture, etc. How many moles of Magnesium is 1.25 x 1023 atoms of Mg?
1. List what is known and unknown
Known
• number of atoms = 1.25 x 1023 atoms Mg
• 1 mol Mg = 6.02 x 1023 atoms Mg
• the conversion you want is atoms moles

Unknown
• moles = ? mol Mg

2. Solve for the unknown
• -The conversion factor is: 1 mol Mg
6.02 x 1023 atoms Mg
• Just multiply to find the answer:
moles = 1.25 x 1023 atoms Mg x 1 mol Mg
6.02 x 1023 atoms Mg
moles = 2.08x 10-1

#### Answer: mol Mg = 0.208 mol Mg

Converting Moles to Number of Particles
• To determine how many atoms are in the mole of a compound you must know how many atoms are in the representative particle of the compound. This number comes from the chemical formula. For carbon dioxide, CO2, the subscripts show 3 molecules-Two carbon atoms and one oxygen atom. A mole of carbon contains Avogadro’s number of CO2 molecules. Yet, each molecule of carbon dioxide has the 3 atoms. A single mole of carbon dioxide contains 3 times Avogadro’s number of atoms.
• To find the number of atoms in a mole of a compound, you have to determine the number of representative particles first.
• Equation: representative particles = moles x 6.02 x 1023 representative particles1 mole
• Then, you multiply the number of representative particles by the number of atoms in each formula unit.
*Example
1. How many molecules of carbon dioxide are found in 2.50 moles of carbon dioxide?
Solution: We use the formula: Total number of particles = number of moles x 6.02 x 1023
Given: Number of moles = 2.50 mol
Total number of molecules of CO2 = 2.50 mol x 6.02 x 1023 molecules/mol

Answer = 1.51 x 1024 molecules of CO2

Molar Mass (Page 294)
Gabriel Hannawi
• In labs, it is easier to use grams than to use moles
• Scientists have converted the scale of the masses of elements from atomic mass units to grams

• The atomic mass of an element expressed in grams is the mass of a mole of the element
• The mass of a mole of an element is its molar mass
• ex. 12.0g of carbon= 1 molar mass of carbon or 1 gram of hydrogen= 1 molar mass of hydrogen

The Mass of a Mole of a Compound (Page 295)

### Alex Trombetta

Key Concept: To calculate the molar mass of a compound find the number of grams of each element in one mole of the compound then add the masses of the elements in the compound.
In order to determine the mass of a mole of a compound, you first need to know the formula of a particular compound. To find the mass of this compound you add the atomic masses of that compound. This can be found in the periodic table. If there is more then one of the same elements then you must multiply the elements atomic mass by the number of atoms of that element. You then remove the grams unit and replace it with the atomic mass unit (amu) The molar mass is the mass of 1 mole of a substance. This is measured in grams. This formula can be used for molecular or ionic compounds.

• Examples:
1.) H20:
2 x molar mass of H + 1 x molar mass of O
2(1.008) + 16.00= 18.016 amu

2.) PO3
1 x molar mass of Phosphorous + 3 x molar mass of O
30.97 + 3(16.00)= 78.97 amu

• Practice Problems
Write the molar mass of the following compounds
1.) CaSO4
2.) NH4Cl
3.)K2CO3
4.) NaCl
5.) CH3COO

### Andrew Ware

What is the Molar Mass of Hydrogen Peroxide?
1. List the knowns and unknowns
Knowns
• Molecular formula = H2O2
• 1 Molar mass H = 1 mol H = 1.0 g H
• 1 Molar mass O = 1 mol O = 16.0 g O
Unknowns
• Molar mass =? g
2. Solve for the unknown.
• Convert moles of hydrogen to grams of hydrogen and oxygen to grams of hydrogen and oxygen then add the results.
2 mol H x 1.0g H/1 mol H = 2.0g H
2 mol O x 16.0g O/1 mol O = 32.0g O
• Molar mass of H2O2 = 34.0g
3. Does the result make sense?
• The answer is the sum of two times the molar mass of hydrogen oxygen. The answer is expressed to the tenth’s place because the numbers being added are expressed to the tenth’s place.

Group 2
Kevin McAllister (Coeditor)
Lauren Sachs
Jess Mahoney
Joe Hatch
Caity Vogt

## 10.2: Mole-Mass and Mole-Volume Relationships

### By Lauren Sachs

• Molar mass=mass in grams of one mole of a substance
• Used for elements, molecular compounds and onic compounds
• May be unclear
• Ex. molar mass of oxgen could be refering to O﻿2 (32.0 g) or an oxygen atom (16.0 g)
• Use the molar mass of an element or compound to convert between the mass of a substance and the moles of a substance
mass(in grams)= number of moles x (mass (in grams)/1 mole)

• Ex. mass of NaCl=3.00 mol x (58.5 g/1 mole)
• This equals 176 g, so if you have 176 g of NaCl, you have 3.00 moles
• Sample Problems:
• A. What is the mass of 9.45 mol of Al2O3?
• Analyze: Number of moles= 9.45 mol Al2O3; Mass= ?g Al2O3
• Calculate: mass= 9.45 mol Al2O3 x (102.0g Al2O3/1 mol Al2O3)=964g Al2O3
• 102.0g is the combined molar mass of 2 Al and 3 O
• Evaluate: Does the result make sense?

• B. How many moles of Fe2O3 are contained in 92.2 g of pure Fe2O3?
• Analyze: Mass=92.2g Fe2O3; Number of moles= ?mol Fe2O3
• Calculate: moles=92.2g Fe2O3 x (1 mol Fe2O3/159.6g Fe2O3)= 0.578 mol Fe2O3
• 1 mol of Fe2O3=159.6 g
• Evaluate: Does the answer make sense?

• Find the mass in grams of 4.52 x 10﻿-3mol C20H42
• ﻿Hint: molar mass of C is 12.01g and the molar mass of H is 1.01g
• Begin by finding the molar mass of C20H42
• Calculate the mass in grams of 2.50 moles of iron (II) hydroxide
• Hint: the formula for iron(II) hydroxide is Fe(OH)2
• Find the number of moles in 3.70 x 10-1g of boron
• Calculate the number of moles in 75.0g of dinitrogen trioxide

## The Mole-Volume Relationship

### Jess Mahoney (pg 300)

• Volumes between different solid and liquid substances are more unpredictable than the volumes of moles between different gases (within the same physical conditions)
• Avogadro’s hypothesis- Amedeo Avogadro proposed in 1811 that the equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
• Gas particles aren’t the same size but they are so far apart that a group of big particles take up only a little more than small particles do
• Volume of a gas depends on the changes in temperature or pressure
• Ex: water bottle is more filled out when in a flying airplane than one on the ground because there is less pressure
• Standard Temperature and Pressure (STP)- a temperature of 0*C and a pressure of 101.3 kPa, or 1 atmosphere (atm) ---- typically how you measure the volume of a gas
• Main Idea- At STP, 1 mol or 6.02 times 1023 representative particles, of any gas occupies a volume of 22.4 L
• Molar volume- a quantity of a gas that equals 22.4 L

### Kevin McAllister (Co-Editor)

Understanding the Mole-Volume Relationship
• Moles and Volume play an integral role in Chemistry
• Volume can be defined as how much space a substance takes up (Like 3D area)
• Moles are 6.02*10^23
• Mole-Volume Relationship is how much space a Mole actually takes up
• Check out this link (a powerpoint) to help with the Mole Volume Relationship
• If the link doesn't work, its just the first one on Google search "Mole Volume Relationship"
• The Mole volume Relationship is basically that a Mole of a gas takes up 22.4 L of volume

### Joe Hatch

#### Calculating Molar Mass from Density

• Density of a gas is usually in grams per liter and at a specified temperature
• Molar mass of a gas can be found by using the density of the gas at STP and the molar volume at STP
• Molar mass = density at STP x molar volume at STP

Sample Problem

known
• density = 1.964 g/L
• 1 mol (gas at STP) = 22.4 L
unknown
• ? g/mol
Calculate: molar mass = (grams / L) x (22.4L / 1 mol)
molar mass = (1.964g / 1L) x (22.4 L / 1 mol) = 44.0 g/mol

• the mole connects mass, representative particles, and volume of a gas together

 http://miznerscience.org/First_semester_units/your_podcast_notebookPg2.html

### By: Caity Vogt

This is a Great Video about converting Mass to Moles

(second one is a website)

Enjoy and good Luck!

### Nick Romero (pgs 305-306)

﻿
• The percent composition of a compound is a measure of the mass of each different element in the compound.
• To find the percent composition of a compound you have to do the following

1. find the molecular mass (molecular weight, formula mass, formula weight), MM, of the compound
2. find the mass of each element in the formula of the compound
3. find the percent comositon : % by weight (mass) of element = (total mass of element present ÷ molecular mass) x 100

Examples
Calculate the percent by weight of sodium (Na) and chlorine (Cl) in sodium chloride (NaCl)

Calculate the molecular mass (MM):
MM = 22.99 + 35.45 = 58.44
Calculate the total mass of Na present:
1 Na is present in the formula, mass = 22.99
Calculate the percent by weight of Na in NaCl:
%Na = (mass Na ÷ MM) x 100 = (22.99 ÷ 58.44) x 100 = 39.34%
Calculate the total mass of Cl present:
1 Cl is present in the formula, mass = 35.45
Calculate the percent by weight of Cl in NaCl:
%Cl = (mass Cl ÷ MM) x 100 = (35.45 ÷ 58.44) x 100 = 60.66%

The answers above are probably correct if %Na + %Cl = 100, that is,
39.34 + 60.66 = 100.

*Percent Composition from Mass Data:

Percent Composition from the Chemical Formula
Sahana Nazeer(pgs 307-308)

• %mass = (mass of element in 1 mol compound) / (molar mass of compound) * 100%

1. The subscripts in the formula of the compound are used to calculate the mass of each element in a mole of that compound; g.

2. The sum of the masses is the molar mass; g/mol.

3. The mass of each element in 1 mol compound is then divided by the molar mass of the compound.

4. The result is then multiplied by 100%.

Example: Calculate the percent composition for Propane (C3H8).

1. mass of C in 1 mol C3H8 = 36.0g; mass of H in 1 mol C3H8 = 8.0g
2. molar mass of C3H8 = 36.0g + 8.0g, which is equal to 44.0g/mol
3. %C = (mass of C) / (mass of propane) à (36.0g) / (44.0g) = .818
%H = (mass of H) / (mass of propane) à (8.0g) / (44.0g) = .18

4. 0.818 * 100% = 81.8%, therefore the %C = 81.8%
0.18 * 100% = 18%, therefore the %H = 18%

*Here is a video that helps further explain the process, with examples.

Percent Composition as a Conversion Factor
• à Percent Composition can be used to calculate the number of grams of any element in a specific mass of a compound.
• Multiply the mass of the compound by a conversion factor based on the percent composition of the element in the compound.
Example:
Calculate the amount of carbon and hydrogen in 82.0g of propane.
• From the previous example, it is known that there is 81.8% carbon and 18% hydrogen in propane. Hence, in 100g of propane, there would be 81.8g of carbon and 18g of hydrogen. (Percents are out of 100).
• Use the ratios 81.8g C/100g C3H8 and 18g H/100g C3H8 in this problem.
• Mass of Carbon:
è 82.0g C3H8 * [(81.8g C) / (100g C3H8)] = 67.1g C.
• Mass of Hydrogen:
è 82.0g C3H8 * [(18g H) / (100g C3H8)] = 15g H.
• Hence, in 82.0g of propane, there would be 67.1g of carbon and 15g of hydrogen.

### Chris Hughes(pg 309)

• The word empirical means from observation and experience rather than theory.
• An empirical formula must be obtained from experimental data, and therefore relies on experience.
• For all compounds there is a basic ratio of the elements involved.
• This basic ratio is called the empirical formula.
• The empirical formula of a compound shows the smallest whole-number ratio of the atoms in the compound

For example, the empirical formula for hydrogen peroxide is HO, however the actual molecular formula is H2O2.

A simple analogy can be seen in the pictures below:

﻿
The following video uses examples and goes step by step on how to determine the empirical formula.

Molecular Formulas

### Zac Boulerice & Ian Travis (pgs 310-312)

• Though some compounds such as ethyne and benzene may have the same empirical formula (CH in this case), the two compounds in such a group may have different molar masses.
• The molar masses of these compounds would be simple, whole-numbered multiples of the molar masses of their empirical formulas.
• ##### Once an empirical formula is determined for a compound, it can be converted into the molecular formula, but to do this the molar mass must be known. This can be determined through use of a mass spectrometer.

Mass Spectrometer- An instrument designed to determined molar mass. Breaks a compound into ions that travel through a magnetic field. This field will deflect a certain amount of moving particles. Based on the rate of deflection, molar mass is calculated.

From the empirical formula you can calculate the
• Empirical Formula Mass (efm)- This is the molar mass represented by the empirical formula.
• Then you can divide the experimentally determined molar mass by the empirical formula mass.
• ### This gives the number of empirical formula units in a molecule of the compound and is the multiplier to convert the empirical formula into the molecular formula.

To Illustrate:

The empirical formula of hydrogen peroxide is HO. The molar mass of H2O2 is 34.0g/mol.Its empirical formula mass is 17.0g/mol.

34.0g/mol
------------------ = 2 From here, multiply the subscripts in the empirical formula by "2" to find the molecular formula for hydrogen peroxide. (HO)2= H2O2
17.0g/mol