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An overview of the course Mathematics of Chemistry.

In order to successfully delve into the mathematics of chemistry, you need to be familiar with some basic chemical concepts. These include:

- Atomic structure
- Bonding
- The Periodic Table, and
- Chemical properties

Terms such as *atom*, *element*, valence* electrons*, *metal*, and *nonmetal* will be referred to during the course of writing chemical formulas and chemical equations. The formulas and equations will be a major part of the mathematical analysis you will learn in this course. This lesson reviews these concepts so you can move smoothly through the mathematics in the later lessons.

Lesson summary and worksheet review.

In measurement, numbers by themselves often lack real meaning. For example, 4 grams (g) and 4 liters (L) both have the number 4, but they are not the same quantity. The "unit" or "label" provides a context for the number. We can compare 4 grams and 5 grams. We can't compare 4 grams and 5 liters.

Sometimes, there are relationships between different units. The density of water is 1,000 grams per liter. That means, for water, 1,000g = 1 L. That type of equality between different units is called a definition. Definitions such as these can be used to do unit conversions. In this lesson, you will learn to:

- Create conversion factors from definitions
- Select the correct conversion factor to make units factor or cancel, and
- Do conversions by factor label

You will also become familiar with metric units and prefixes. Factor label will enable you to convert a metric unit with one prefix to an equivalent unit with a different prefix.

Lesson summary and worksheet review.

Scientific notation is a convenient way to express very large or very small numbers. This lesson will explain how to convert from standard notation to scientific notation and from scientific notation to standard notation. It will also explain how to do calculations using scientific notation. You will learn:

- The proper format for scientific notation
- How to move the decimal and adjust the exponent to convert notations
- How to multiply, divide, add, and subtract numbers with exponents

These skills will be useful for other quantitative work in chemistry.

Lesson summary and worksheet review

Observation is a key process in science, but our senses can be misleading. Scientist use measurement to improve observation, but measurements have limitations too. Observations must be evaluated for accuracy and precision. This lesson will teach you:

- The definition of accuracy
- The definition of precision
- How to evaluate a measurement for accuracy and precision

For now, this is a qualitative concept. In later lessons, errors will be evaluated quantitatively.

Lesson summary and worksheet review

A measurement such as 35.1 m has two measured values and one estimated value. A measurement can only have one estimated value. It is always the last digit. In 35.1 mm, the 3 and the 5 are measured values, and the 1 is estimated. If 35.1 mm is converted into millimeters, 35,100 mmthe 3 and the 5 are still the measured values, and the 1 is still estimated. The zeros are place holders, and are not significant figures.

When students do calculations with measurements, estimated values are frequently multiplied, divided, added, or subtracted by and from other estimated values. How many decimal places should be in the answer so that there is still only one estimated digit? Your calculator does not know. It gives you lots of decimal places in your computations. It is your job to round the result to something sensible. Significant figures help you do just that. In this lesson, you will learn:

- How to distinguish significant figures from place holders
- How to count the number of significant figures in a measurement
- How to round the results of calculations to the correct number of significant figures

This skill will ultimately help you to arrive at sensible answers from your calculations.

Lesson summary and worksheet review

Errors of measurement are unavoidable. This is because measuring devices have their limitations. But how bad are the errors they cause? It's not just the size of the error that matters. It's the size of the error compared to the size of what is measured. In this lesson, you will learn to:

- Calculate the absolute error, and
- Calculate the percentage error

The percentage error makes the comparison between the absolute error (the size of the error) and the size of what is being measured.

Lesson summary and worksheet review.

Atomic mass is measured by a mass spectrometer. The data from a mass spectrometer comes in the form of masses and percentages. This makes it possible to calculate a weighted average. In this lesson, you will learn to:

- Understand the similarity between the standard way of calculating an average and a weighted average
- Understand why average atomic masses are weighted averages, and
- Calculate average atomic mass from masses and their respective percentages

Lesson summary and worksheet review.

Chemical formulas are the shorthand on which all chemistry is based. The formula tells you the number and type of each atom in a compound. All the mathematics of chemistry starts with the chemical formula. In this lesson, you will learn:

- The rules used to derive the chemical symbols for the elements
- The meaning of the components of a chemical formula, and
- How to count the atoms shown in a chemical formula

The chemical formula is the foundation for all quantitative work in chemistry.

Lesson summary and worksheet review.

The chemical formula shows the ratio of elements in a compound. The crossover rule is a simple technique for determining the ratio of elements in a compound. In this lesson you will learn:

- The meaning of the oxidation state
- The relationship between the oxidation state and the chemical formula, and
- How to achieve the same result easier by applying the crossover rule with oxidation states

Once you learn how to write chemical formulas, you're on your way to serious quantitative analysis.

Lesson summary and worksheet review.

Chemical compounds are referred to by their chemical formulas or by their chemical names. There are two major naming systems for inorganic compounds: The Stock system and the binary covalent system. In this lesson you will learn;

- When to use the Stock system, and when to use the binary covalent system
- The rules for naming compound according to the Stock system
- The rules for naming compounds according to the binary covalent system, and
- How to write chemical formulas based on compounds' chemical names

It is necessary to recognize compounds by their chemical names and to be able to write their formulas in order to interpret typical quantitative questions in chemistry.

Lesson summary and worksheet review.

Formula mass is based on individual atomic masses and the formula. Now that you can interpret formulas and count atoms, formula mass is the next step. You will learn how to determine the formula mass by adding the products of the individual atomic masses and their respective subscripts.

Lesson summary and worksheet review.

Empirical formulas are formulas expressed in lowest terms. You will learn to:

- Recognize empirical formulas
- Derive empirical formulas from molecular formulas
- Understand the importance of empirical formulas, and
- Determine the molecular formula from an empirical formula and molecular mass

Empirical formulas are extremely useful for chemical analysis by combustion, a skill you will learn later.

Lesson summary and worksheet review.

Percent composition is the percentage by mass of each element in a compound. In this lesson, you will learn to:

- Calculate percent composition of each element in a compound based on the formula mass
- Calculate the percentage of a component by organizing the data, and
- Calculate the mass of a component based on the sample size and the percentage

This skill is important in the real world in determining the amount of an active ingredient delivered in a medication.

Lesson summary and worksheet review.

It will be easier to do quantitative work with chemical reactions when you recognize reaction types. In this lesson, you will learn to recognize four basic reaction types:

- Synthesis
- Decomposition
- Single replacement, and
- Double replacement

Lesson summary and worksheet review.

onservation of mass during a chemical reaction is a fundemental concept in chemistry. No atoms are created or destroyed during a chemical reaction. A properly written chemical equation should show conservation of mass. In order to show conservation of mass, an equation must be balanced. In this lesson ,you will learn to:

- Check for conservation of mass by counting atoms
- Balance unbalanced equations using coefficients.

Lesson summary and worksheet review.

A mole is a quantity just as a dozen is a quantity but it is much bigger than a dozen. The mole concept in chemistry is extremely useful for interpreting chemical equations because it makes it possible to scale up chemical reactions to quantities that are measurable in the lab. In this lesson, you will learn:

- How to define moles
- How to determine the mass of a mole of a substance
- How to calculate the mass of several moles of a substance
- How to calculate the number of moles of a substance contained in a sample from its mass

Lesson summary and worksheet review.

It is possible to determine the empirical formula of a substance just by knowing its percent composition. In this lesson, you will learn to:

- Convert percentages into masses
- Calculate moles from these masses
- Calculate mole ratios from the moles, and
- Determine the empirical formula from the mole ratios

Lesson summary and worksheet review.

Stoichiometry means calculations based on quantitative relationships in a balanced chemical equation. The simplest relationship in the balanced equation is a mole-mole relationship. In this lesson you will learn:

- The relationship between the coefficients of a balanced equation and mole ratios
- How to identify the known and the unknown in a mole-mole problem
- How to solve mole-mole relationships by factor label, and
- How to solve mole-mole relationships by setting up a proportion

Mole-mole relationships are a part of more complex stoichiometry

Lesson summary and worksheet review.

Mass-mass problems are the next step after mole-mole problems. Technically mass-mass problems are mass-mole-mole-mass problems. in this lesson you will learn:

- How to derive definitions for mole-mass and mole-mole relationships, and
- How to set up a factor label equation from these defititions to convert from mass of known to moles of known, from moles of known to moles of unknown, and from moles of unknown to mass of unknown.

Lesson summary and worksheet review.

In mass-mass problems you know the mass of one substance and assume it all reacts. If you know the mass of two reactants, one may get used up first. The reactant that gets used up first is the limiting reactant. In this lesson, you will learn:

- How to determine which is the limiting reactant
- How to complete the stoichiometry based on the amount of the limiting reactant, and
- How to calculate the amount of excess of the other reactant

Lesson summary and worksheet review.

Stochiometry based on the limiting reactant tells us how much product we can expect. We don't always get all that we expect, however. In this lesson, you will learn:

- How to calculate the theoretical yield based on limiting reactant stoichiometry, and
- How to calculate the percent yield as a ratio of the actual yield to the theoretical yield

Lesson summary and worksheet review.

When hydrocarbon fuels burn, they produce carbon dioxide and water. In this lesson you will learn to:

- Determine the mass of the carbon and hydrogen in the fuel from the mass of the carbon dioxide and water formed
- Calculate the number of moles of carbon and hydrogen burned from their masses
- Determine the mole ratios of the carbon and hydrogen in the fuel, and
- Determine the empirical formula of the hydrocarbon

Lesson summary and worksheet review.

The Celsius scale is not a ratio scale. It does NOT have a meaningful zero. It has an arbitrary zero based on the freezing point of water, and, as a result it has negative temperatures. On the Kelvin scale, zero is as cold as it gets. This lesson will explain the Kelvin scale. When you complete this lesson you will be able to:

- Distinguish between an arbitrary and meaningful zero
- Explain why the Celsius scale is not a ratio scale
- Define absolute zero
- Convert Celsius temperatures to Kelvin and vice versa

Lesson summary and worksheet review.

You blow up two identical balloons. After inflating, one is twice as big as the other. The difference is obviously due to the amount of gas - the number of moles. This lesson will explain Avogadro's law which deals with the relationship between the volume of a gas and the number of moles. When you complete this lesson, you will be able to:

- State Avogadro's Law
- State the gram molecular volume (GMV)
- Convert from volume to moles, to mass of a gas and back at STP using the GMV

Lesson summary and worksheet review.

The volume of a sample of gas is dependent on the temperature and pressure. In this lesson, you will learn how to calculate the change in volume of a gas as temperature and/or pressure changes using the combined gas law. When you complete this lesson, you will be able to:

- Explain what happens to the volume of a gas as pressure changes at constant temperature
- Explain what happens to the volume of a gas as temperature changes at constant pressure
- Apply the combined gas law to solve for volume, temperature, or pressure as one or more of the variables changes on a sample of gas

Lesson summary and worksheet review.

The volume of a sample of gas is dependent on the temperature and pressure. In this lesson, you will learn how to calculate the change in volume of a gas as temperature and/or pressure changes using the combined gas law. You will also learn how to use the ideal gas law where moles is also a variable, and initial and final conditions need not be specified. When you complete this lesson, you will be able to:

- Explain what happens to the volume of a gas as pressure changes at constant temperature
- Explain what happens to the volume of a gas as temperature changes at constant pressure
- Apply the combined gas law to solve for volume, temperature, or pressure as one or more of the variables changes on a sample of gas
- Apply the ideal gas law to solve for any of its variables.

Lesson summary and worksheet review.

The ideal gas law has moles and volume as two of its variables. Moles has a relationship to mass. Mass per unit volume is density. Thus the ideal gas law makes it possible to calculate gas density, or, given the density, the molar mass. When you complete this lesson, you will be able to:

- Calculate the density of a gas at any temperature and pressure based on its molar mass
- Calculate the molar mass of a gas at any temperature and pressure based on its density

Lesson summary and worksheet review.

Mass or volume of a gaseous reactant or product can be determined from the ideal gas law and a balanced equation. Stoichiometry uses mole relationships. The ideal gas law provides moles as one of its variables. You will learn how to use the gas law for stoichiometry. When you complete this lesson you will be able to:

- Complete a standard stoichiometry problem when one or more reactants or products is a gas by using the ideal gas law to determine the number of moles
- Do volume volume calculations based on Avogadro's law
- Do stoichiometry involving gases at STP using the GMV

Lesson summary and worksheet review.

As substances heat up, the molecules move faster. The speed of a moving molecule is not the only factor that influences energy. So does mass. For molecules at the same temperature, more massive molecules move slower. This is the basis for Graham's Law which you will learn about. When you complete this lesson, you will be able to:

- State Graham's law
- Calculate the relative effusion rate of two gases based on their molar masses
- Calculate the molar mass of an unknown gas based on its relative effusion rate with a known gas

Lesson summary and worksheet review.

Concentration is the amount of solute compared to solvent or solution. You will learn how to calculate several types of concentration. When you complete this lesson you will be able to:

- Define concentration
- Calculate concentration in:
- mass per unit volume
- percentage by mass
- percentage by volume, and
- parts per million

Lesson summary and worksheet review.

As you learned earlier, concentration is the amount of solute compared to solvent or solution. When the amount of solute is in moles, the concentration is in either molarity or molality. You will learn some calculations using molarity and molality. When you complete this lesson, you will be able to:

- Define molarity and molality
- Calculate molarity
- Calculate the mass of solute based on volume and molarity
- Calculate molality

Lesson summary and worksheet review.

Molarity can be used in stoichiometric calculations. Molarity and volume can be used to determine moles. This makes it possible to determine limiting reactants, standard and gas stoichiometry, and molarity calculations for soluble products or excess dissolved reactants. When you complete this lesson, you will be able to:

- Use molarity and volume to find moles and:
- identify limiting reactants
- do standard or gas stoichiometry

- Use moles of soluble product or remaining dissolved reactant to find molarity

Lesson summary and worksheet review.

Colligative properties are the effect that the number but not the type of dissolved particles have on a solution. Among these is boiling point elevation and freezing point depression. You will learn how to do calculations based on boiling point elevation or freezing point depression and molality. When you complete this lesson, you will be able to:

- Define colligative properties
- Explain what causes boiling point elevation and freezing point depression
- Distinguish between an electrolyte and a nonelectrolyte
- Use molality to calculate boiling point elevation or freezing point depression
- Use boiling point elevation or freezing point depression to calculate molality or molar mass of a solute

Lesson summary and worksheet review.

**Course Description**

The ** Mathematics of Chemistry **video course is an advanced course for high school students with a basic chemistry background. The course does stand on its own, however, as it reviews all the basic concepts and vocabulary necessary to succeed in the course even without a prior chemistry course. The focus of the course is measurement, mathematical analysis of chemical formulas, chemical equations, gas laws, and solutions. The topics covered are at a level suitable for students who are planning to take the SAT II in chemistry.

**This course includes**

- 6 sections
- 43 worksheets
- 33 video lessons
- 33 video reviews that summarize the lessons and go over the worksheets
- 66 downloadable PDFs of all the lesson slides
- 1 complete set of reference tables for chemistry including the periodic table
- 33 online tests
- 33 online tests answer keys (for parents only)
- Resources for parents including outlines, practice questions and answers, and all answer keys
- Over 13 hours of videos consisting of 67 videos averaging about 11½ minutes each.

**Course Goals**

Upon completion of the course you will be able to

- understand the limitations of measurement and analyze errors of measurement
- use appropriate significant digits
- do unit conversions by factor label
- interpret chemical formulas including counting atoms, formula mass, and percentage composition
- Balance chemical equations and do stoichiometry with or without limiting reactants, including determining percentage yield
- Apply the gas laws and do gas stoichiometry
- Calculate solution concentrations including percentage by mass and/or volume, ppm, molarity, and molality
- Calculate boiling point elevation and freezing point depression.
- Do solution stoichiometry

**Target Audience**

This video course is primarily intended for honors level science students in highschool grades 10 through 12. It will be helpful to students planning to take the SAT II in chemistry.

**Course Requirements**

Students taking this course should have completed a basic high school chemistry course.

**COURSE TOPICS**

Section 1 - Introduction

**Lessons**

- Course Preview
- Introduction

Section 2 - Measurement

**Lessons**

- Unit Conversions
- Scientific Notation
- Accuracy and Precision
- Significant Figures
- Errors of Measurement
- Average Atomic Mass

Section 3 - Chemical Formulas

**Lessons**

- Interpreting Chemical Formulas
- The Crossover Rule
- Naming Chemical Compunds
- Formula Mass
- Empirical Formulas
- Percent Composition

Section 4 - Chemical Equations and Stoichiometry

**Lessons**

- Patterns of Chemical Reactions
- Balancing Equations
- Moles
- Formulas from Percent Composition
- Mole Ratios
- Mass-Mass Problems
- Limiting Reactants
- Percent Yield
- Analysis through Combustion

Section 5 - Gases

**Lessons**

- The Kelvin Scale
- Avogadro's Law
- The Combined Gas Law
- Gas Laws
- Density, Molar Mass and the Ideal Gas Law
- Gas Stoichiometry
- Graham's Law

Section 6 - Solutions

**Lessons**

- Concentration
- Molarity and Molality
- Solution Stoichiometry
- Colligative Properties

- Teacher: Evan
- Areas of expertise: Chemistry, Biology, Physics
- Education: B.S. Biology and Education SUNY at Stony Brook M.S. Biology and Education SUNY at New Paltz Post Graduate: Science Education Hebrew University, Jerusalem Psychology and Measurement N.Y.U
- Interests: Science, Exercise/Fitness, Music, Health, Animals, Diet, Vegan cooking
- Skills: Writing, Computer graphics, PowerPoint, Guitar, Vegan cooking
- Associations: American Federation of Teachers, National Education Association
- Issues I care about: Animals, Health and fitness, Education

I have been teaching since 1970. I started out as a biology teacher, but then discovered teaching chemistry was really fun. I particularly enjoy developing instructional materials including worksheets, PowerPoints, and, now, videos. Teaching and learning should be fun.

Outlines summarizing the topics with sample questions and answers and worksheet answer keys.

Outlines summarizing the topics with sample questions and answers and worksheet answer keys.

Outlines summarizing the topics with sample questions and answers and worksheet answer keys.

Outlines summarizing the topics with sample questions and answers and worksheet answer keys.

Outlines summarizing the topics with sample questions and answers and worksheet answer keys.

All the end of the lesson tests are provided with the correct answers for each question shown.