Chemistry, Canadian Edition Chapter 01: Student Study Guide

Chapter 1: Fundamental Concepts of Chemistry

Learning Objectives

Upon completion of this chapter you should be able to

• recognize elemental symbols and names of the elements and compounds from molecular pictures

• recognize the SI units commonly used in chemistry, and perform some common unit conversions

• analyze and solve problems in a consistent, organized fashion

• solve mass–number-molecular weight- type problems

• perform mole-mass-number conversions

• calculate concentrations of solutions and of diluted solutions

• balance chemical reactions

• calculate the amount of a product from the amounts of the reactants and a balanced chemical reaction

• solve limiting–reagent-type problems

Practical Aspects

This chapter provides a detailed overview of the terms used to describe matter and the ways in which chemists approach quantitative (numerical) problems. Chemistry is a subject that uses “vertical learning” – meaning that the material you learn today will be applied to later chapters. Learn the material now, so that you can use it as a tool for later chapters.

1.1 atoms, molecules, and compounds

Skills to Master:

·  Recognizing element symbols and names of the elements.

Matter can be viewed with varying levels of detail:

·  Macroscopic – water, for example, is clear and colorless and wet.

·  Microscopic – a sample of water might contain tiny organisms that one can’t see without a microscope.

·  Molecular/Atomic – water is “H2O”. Every molecule of water contains 2 H’s and 1 O. Water is a liquid at room temperature because of strong attractions that exist between water molecules.

Key Terms:

·  Physical Property – observable property of a substance (example: colour, texture, density).

·  Chemical Property – property that has to do with a substance’s potential to change its chemical make-up (example: chlorine combines with sodium in a 1:1 ratio to make table salt).

·  Atom – fundamental unit of a chemical substance (“atomos” means uncuttable in Greek).

·  Molecule – combination of two or more atoms held together by attractive forces.

·  Element – substance that contains only one type of atom (examples: C or H on the periodic table).

·  Compound – combination of two or more different atoms held together by attractive forces.

·  Chemical Formula – notation of the type and number of each element present in one unit of the substance (example: carbon dioxide’s formula is CO2, which designates 1 carbon and 2 oxygens per molecule).

Key Concepts:

·  Atoms are tiny.

·  Each element on the periodic table has a unique one- or two- letter symbol. The first letter is always capitalized and the second letter is lower case (example: H = hydrogen, He = helium).

·  Elements can be monoatomic (Ne, C), diatomic (H2, N2, O2), or polyatomic (S8).

·  Chemists colour-code commonly used atoms. See Figure 1-3 in the text for a list.

Exercise 1: Identify each as an element, atom, molecule, and/or compound. More than one definition might apply to each. a) H2O2; b) Cl2; c) CO; d) He; e) Na ; f) C6H12O6

Solution: a) molecule, compound; b) molecule, element; c) molecule, compound; d) atom, element; e) atom, element; f) molecule, compound

Exercise 2: Determine the chemical formula of each:

a)  a molecule that contains 7 atoms of hydrogen, 1 atom of nitrogen, and 4 atoms of carbon;

b)  a chemical that contains three atoms of oxygen

Strategy and Solution: Count up the number of each type of atom. (Don’t worry about the order of the atoms at this point.) a) C4H7N b) O3

1.2 Measurements in chemistry

Skills to Master:

·  Working with unit conversions.

·  Determining the correct number of significant figures in the result of a calculation.

All measurements in chemistry should convey three pieces of information:

·  Magnitude – the size of the measurement;

·  Unit – an indicator of scale; and

·  Precision – assessment of how carefully the number was measured.

Scientific Notation (“power of ten” notation)

What: Method of simplifying the writing of very large and very small quantities.

When: Any time you are working with potentially cumbersome numbers.

How: Find the number, which when multiplied by 10x, will give you the number written in the "normal" style.

Examples: / “Normal” / Scientific Notation
0.00000534 / 5.34 x 10-6
1,000,000,000 / 1 x 109
2,500,000 / 2.5 x 106
0.008767 / 8.767 x 10-3

Helpful Hint

·  Here’s a shortcut: Notice that the exponent in the scientific notation correlates to the direction and number of places the decimal had to move to get to the “normal” number. For the number “2.5x106,” the decimal must be moved 6 places to the right to get to 2,500,000 – similarly, 6 spaces to the right means 106 or 1,000,000. Practice this a few times to see the mathematical pattern.

Exercise 3: Convert these numbers to scientific notation: a) 4579; b) -0.05020; c) 3.8521. Convert these from scientific notation: d) 3.0033 x 104; e) 2.79 x 10-5; f) 3 x 1011.

Strategy and Solution:

Normal / Scientific Notation
a) / 4579 / 4.579x103
b) / -0.05020 / -5.020x10-2
c) / 3.8521 / 3.8521x100
d) / 30033 / 3.0033 x 104
e) / 0.0000279 / 2.79 x 10-5
f) / 300,000,000,000 / 3 x 1011

Exercise 4: Arrange these numbers from smallest to largest:

11.7 x 10-7 -1.48 x 10-4 -2.17 x 103 3.19 x 10-2

strategy: Mentally arrange the numbers on a number line.

Solution: -2.17 x 103, -1.48 x 10-4, 11.7 x 10-7, 3.19 x 10-2

Try It #1: Convert to scientific notation: a) 213,500,000 b) 0.0000000000450

Try It #2: Convert from scientific notation: a) 6.700 x 10-2 b) -1.20 x 107

Units

SI (Systeme International) Base Units:

Dimension / Unit / Symbol
Length / Meter / m
Mass / Kilogram / kg
Time / Second / s or sec
Temperature / Kelvin / K
Chemical Amount / Mole / mol
Electrical Current / Ampere / A
Luminous Intensity / Candela / cd

Key Term:

·  Derived Units – units which are derived from combinations of base units.

Examples: The dimension “volume” (length x width x height) has units of: m3 or cm3

The dimension “rate” has units of: m/sec

The dimension “density” has units of: g/mL

The dimension “molar mass” has units of: g/mol

Units and Conversions:

·  1 cm3 = 1 cc = 1 mL

Prefixes in SI

Table 1-1 in the text lists several SI prefixes. Here are the most frequently encountered ones:

Power: / 103 / 10-2 / 10-3 / 10-6 / 10-9
Prefix: / kilo- / centi- / milli- / micro- / nano-
Symbol: / k / c / m / m / n

Helpful Hint

·  The magnitude of a number can be simplified by using scientific notation or a prefix before the unit. For example, 756,000 g can be rewritten: 7.56x105 g or 756 kg.

Precision and Accuracy

Key Terms:

·  Precision - 1) how carefully a measurement is made; or 2) how close the values within a set of measurements are to one another.

·  Accuracy - how close a measurement is to the “true” value.

Exercise 5: Given that: “The true value is 5.74 m,” write a data set containing 3 numbers that:

a) is accurate and precise; and b) is precise but not accurate

Strategy and Solution: Use the definitions of accuracy and precision to come up with an appropriate data set:

a)  accurate and precise: 5.73 m, 5.74 m, 5.75 m (numbers are close to the true value and close to each other)

b)  precise but not accurate: 6.55 m, 6.56 m, 6.55 m (numbers are close to each other but not to the true value)

Try It #3: Given that the “true” value is 5.74 m, create a data set of three numbers that are neither accurate nor precise.

Significant Figures (“sig figs” for short)

“Significant figures” is the term used to describe how many digits should be recorded in a numerical answer. The number of significant figures is dictated by how precisely (carefully) a given measurement is made. An everyday example illustrates the concept of significant figures:

If someone is asked, “what is the distance between your home and your workplace?”, the person might respond, “Oh, around 30 miles.” If pressed, the person may say, “I think it is 27 miles.” Or the distance could be measured from the car’s odometer to be 27.3 miles. In each case:

the measurement: / has this many sig figs: / and indicates:
30 / 1 / an approximation
27 / 2 / a more precise measurement
27.3 / 3 / an even more precise measurement

Helpful Hint

·  To determine how many sig figs are in a number, read the numerals from left to right and start counting sig figs with the first non-zero number. Zeros at the end of a number are significant only if it is obvious they were measured.

Exercise 6: Determine the number of sig figs in each number: a) 2060; b) 2060.; c) 3.30x10-5;

d) 890,000,000,000; e) 0.003040

Solution:

The number / has this many sig figs: / Special note:
2060
(2.06x103) / 3 / The last zero only indicates decimal place (i.e. that the number is 2060 rather than 206).
2060.
(2.060x103) / 4 / A decimal point indicates that the number was measured to the one’s place.
3.30x10-5
(0.0000330) / 3 / The zero is significant; it didn’t have to be written, so it must’ve been recorded to emphasize that the measurement was taken that carefully.
890,000,000,000
(8.9x1011) / 2 / All of the zeros indicate decimal place only.
0.003040
(3.040x10-3) / 4 / The last zero is significant.

Notice that scientific notation eliminates sig fig ambiguity.

Try It #4: How many sig figs are in these numbers: a) 420,600; b) 0.0002; c) 0.00020; d) 7.0x106 ?

When performing calculations, the final answer for the calculation should reflect how carefully the data used within the calculation was measured.

Operations with Significant Figures

·  Multiplication/Division: Answer can have no more sig figs than the fewest number of sig figs in the original numbers.

·  Addition/Subtraction: Answer can have no more decimal places than the fewest places in the original numbers.

Helpful Hints

·  Watch out for “exact” numbers, which are infinitely significant (Example: 1 dozen=12).

·  Round off the final result to the correct number of significant figures.

·  Rounding: if the number to round is ³5, round up, if <5 then round down.

Exercise 7: Do the following mathematical operations and report each answer to the correct number of sig figs: a) 23.652 + 7.71; b) 55000 ¸ 5.00; c) (6.7 x 10-2)(3 x 10-5); d) (6.7 x 10-2)(3.0 x 10-5);

e) (6.7 x 10-2)(3.00 x 10-5); f) (6.7 x 10-2)+(3.00 x 10-5)

Solution:

Question / Numerical answer / To assign sig figs: / Answer reported to correct sig figs
a) / 23.652 + 7.71 / 31.362 / 7.71: hundredth’s place / 31.36
b) / 55000 ¸ 5.00 / 11000 / 55000 has 2 sig figs / 1.1x104
c) / (6.7 x 10-2)(3 x 10-5) / 2.01x10-6 / 3x10-5 has 1 sig fig / 2x10-6
d) / (6.7 x 10-2)(3.0 x 10-5) / 2.01x10-6 / Both #s have 2 sig figs / 2.0x10-6
e) / (6.7 x 10-2)(3.00 x 10-5) / 2.01x10-6 / 6.7x10-2 has 2 sig figs / 2.0x10-6
f) / (6.7 x 10-2)+(3.00 x 10-5) / 0.0670300 / .067: thousandth’s place / 0.067

Try It #5: Report each answer using the correct number of sig figs: a) 250,000 ¸ 250; b) 15956 - 72.7; c) (7.92 x 10-2)(-3.0 x 105)

Unit Conversions

Always show all units and how they cancel out in conversions. Exercise 15 illustrates how to set up a calculation.

Exercise 8: A Canadian traveler wishes to convert a $50 bill to Euros. The exchange rate is 0.7813 Euros per 1 dollar. How many Euros will the traveler receive?

Strategy: Set up a conversion factor: 0.7813 Euros = 1 dollar.

Solution: 39.07 (4 sig figs in answer based on exchange rate data). The $50 bill and the $1 bill are exact numbers, so they are infinitely significant. They do not limit sig figs.

Notice in Exercise 15 that the given information (50 dollars) is written first and that the conversion factor is set up so that the units “dollars” will cancel and we’ll be left with units of lire. If we were converting from Euros to dollars, the conversion factor would be flipped:

Helpful Hints

·  When converting units, start with what you’re given then multiply that number by the appropriate conversion factor to get the units to cancel out.

·  Always show units when setting up conversion calculations so that you can track what units you have.

Exercise 9: An automobile consumes gasoline at a rate of 7.8 L/100 km. 1.00 L of gasoline produces about 2.35 kg of CO2 when burned. What mass of CO2 would be produced if the vehicle drove 1365 km?

Strategy: Arrange the given information such that units of kg of CO2 remain.

Solution: The automobile will emit 2.5 x 102 kg of CO2.

1.3 chemical problem solving

Any time you encounter a problem that you can’t figure out how to attack, break it down using the 7-step method, as outlined in the text. Exercise 10 illustrates the 7-step approach.

Exercise 10: The radius of one atom of carbon is 77 pm. (1 pm = 1x10-12 m). How many carbon atoms lined up next to each other would it take to span 1.0 inch?

1. Determine what is asked for. The number of carbon atoms that can line up in one inch.