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Math Review for Chemistry
Unit 1: Introduction to Chemistry
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Key Ideas
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Matter is classified as a pure substance or as a mixture of substances. (3.1q)
The three phases of matter (solids, liquids, and gases) have different properties. (3.1kk)
A pure substance (element or compound) has a constant composition and constant properties
throughout a given sample, and from sample to sample. (3.1r)
Elements cannot be broken down by chemical change. (3.1u)
Mixtures are composed of two or more different substances that can be separated by physical
means. When different substances are mixed together, a homogeneous or heterogeneous mixture
is formed. (3.1s)
The proportions of components in a mixture can be varied. Each component in a mixture retains
its original properties. (3.1t)
Differences in properties such as density, particle size, molecular polarity, boiling point and
freezing point, and solubility permit physical separation of the components of the mixture. (3.1nn)
A solution is a homogeneous mixture of a solute dissolved in a solvent. The solubility of a solute in
a given amount of solvent is dependent on the temperature, the pressure, and the chemical
natures of the solute and solvent. (3.1oo)
Energy can exist in different forms, such as chemical, electrical, electromagnetic, thermal,
mechanical, and nuclear. (4.1a)
Heat is a transfer of energy (usually thermal energy) from a body of higher temperature to a body
of lower temperature. Thermal energy is the energy associated with the random motion of atoms
and molecules. (4.2a)
Temperature is a measurement of the average kinetic energy
of the particles in a sample of material. Temperature is not a
form of energy. (4.2b)
The concepts of kinetic and potential energy can be used to
explain physical processes that include: fusion (melting),
solidification (freezing), vaporization (boiling, evaporation),
condensation, sublimation, and deposition. (4.2c)
A physical change results in the rearrangement of existing
particles in a substance. A chemical change results in the
formation of different substances with changed properties.
(3.2a)
Chemical and physical changes can be exothermic or
endothermic. (4.1b)
The structure and arrangement of particles and their
interactions determine the physical state of a substance at a
given temperature and pressure. (3.1jj)
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Math Review for Chemistry
Matter Activity
Station Number/
Identity of Substance
Description/Observations
Classification
(Element,
Compound,
Homogeneous Mixture,
Heterogeneous Mixture)
How do you know?
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Math Review for Chemistry
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Questions:
1. How could you tell a substance is an element?
2. What phases can elements be in?
3. How could you tell a substance is a compound?
4. What phases can compounds be in?
5. How could you tell a sample is a mixture?
6. What phases can mixtures be in?
7. How do you know the difference between a homogeneous and heterogeneous mixture?
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Math Review for Chemistry
Matter
Anything that has mass and volume (takes up space)
CAN be separated by
PHYSICAL means
Can NOT be separated
by physical means
PURE SUBSTANCES
(each piece looks the same
– PURE!)
-each piece has exact same
composition.
Can NOT be separated
by chemical means
ELEMENT (simplest
form of matter)
Example: Na, Cl2
MIXTURES (each piece is
different – not pure)
Same
Separated by
composition
chemical means,
throughout
only
Different
composition
throughout
COMPOUND or
MOLECULE
(2+ different elements
chemically combined)
HOMOGENEOUS
MIXTURE (uniform
throughout—distinct
pattern)
HETEROGENEOUS
MIXTURE (not
uniform throughout—
a pattern)
Example: NaCl (table
salt), H2O (water)
Example: saltwater,
iced tea
Example: Italian
dressing, concrete, soil,
chocolate chip cookie
Homo = same
Hetero = opposite
Particle
Diagram
Particle
Diagram
Particle
Diagram
Particle
Diagram
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Math Review for Chemistry
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Math Review for Chemistry
Matter Practice
Classify each of the following with the combination of terms listed below.
pure substance – element
mixture – homogeneous
pure substance – compound
mixture – heterogeneous
1. HCl (aq)
2. sugar (C11H22O11)
3. KBr (s)
4. Soil
5. Cl2 (g)
6. water
7. CH2(OH)2 (aq)
8. Sodium
9. Hg (l)
10. iron oxide
11.NH3 (l)
12. salt water
13. Matter that is composed of two or more different elements chemically combined in a fixed proportion is
classified as
(1) a compound
(2) an element
(3) a mixture
(4) a solution
14. A compound differs from an element in that a compound
(1) is homogeneous
(2) has a definite composition
(3) has a definite melting point
(4) can be decomposed by a chemical reaction
15. A compound differs from a mixture in that a compound always has a
(1) homogeneous composition
(2) maximum of two elements
(3) minimum of three elements
(4) heterogeneous composition
16. A heterogeneous material may be
(1) an element
(2) a compound
(3) a pure substance
(4) a mixture
17. Which statement is an identifying characteristic of a mixture?
(1) a mixture can consist of a single element
(2) a mixture can be separated by physical means
(3) a mixture must have a definite composition by weight
(4) a mixture must be homogeneous
18. Which must be a mixture of substances?
(1) solid
(2) liquid
(3) gas
(4) solution
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Math Review for Chemistry
19. Which substance can be decomposed by chemical means?
(1) aluminum
(2) octane
(3) silicon
(4) xenon
20. Which substance can be decomposed by chemical means?
(1) ammonia
(2) oxygen
(3) phosphorus
(4) silicon
21. Which substance can not be broken down by a chemical reaction?
(1) ammonia
(2) argon
(3) methane
(4) water
22. Two substances, A and Z, are to be identified. Substance A can not be broken down by a chemical change.
Substance Z can be broken down by a chemical change. What can be concluded about these substances?
(1) Both substances are elements.
(2) Both substances are compounds.
(3) Substance A is an element and substance Z is a compound.
(4) Substance A is a compound and substance Z is an element.
23. Which terms are used to identify pure substances?
(1) an element and a mixture
(2) an element and a compound
(3) a solution and a mixture
(4) a solution and a compound
24. Two different samples decompose when heated. Only one of the samples is soluble in water. Based on this
information, these two samples are
(1) both the same element
(2) two different elements
(3) both the same compound
(4) two different compounds
25. Tetrachloromethane, CCl4, is classified as a
(1) compound because the atoms of the elements are combined in a fixed proportion
(2) compound because the atoms of the elements are combined in a proportion that varies
(3) mixture because the atoms of the elements are combined in a fixed proportion
(4) mixture because the atoms of the elements are combined in a proportion that varies
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Math Review for Chemistry
Drawing Particle Arrangements
Draw a diagram of a:
pure diatomic
element
pure diatomic
compound
mixture of
two elements
mixture of
an element &
a compound
mixture of
two diatomic
elements &
a compound
1.) In terms of composition/type of atoms, what is the difference between a monatomic element, a diatomic
element, and a diatomic compound?
2.) Use the following key for parts a-c.
a.) 8 atoms of element X in gaseous form
= element X
= element Z
b.) 4 molecules of compound X2Z in liquid form
c.) Homogeneous mixture of element Z with element X (10 atoms of each element).
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Math Review for Chemistry
Phases and Phase Changes
Directions: Using the boxes provided below as your container, place six circular molecules in each container
representing the given phase. Then on each line with the arrow label which phase change is occuring. Last fill in
the chart below about phases using the words provided in the parenthesis.
SOLID (s)
LIQUID (l)
Solid
GAS (g)
Liquid
Gas
Shape
(Has a fixed shape or
takes the shape of the
container)
Volume
(Has a fixed volume or
takes the volume of the
container)
Density
(high or low)
Particle arrangement
(rigid or free)
Attraction
(particles are highly
attracted and close or
weakly attracted and
spread out)
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Math Review for Chemistry
Unit 1 Review
Regents Chemistry
METRIC
1. Using tables on page one of your reference table you should be able to identify which unit is used to measure
each quantity and you should be able to convert between units using the prefixes. Locate the prefix assigned to
the measurement unit that you are starting with and then find the prefix that you want to convert to. Count the
number difference between the factors and then move your decimal that many places.
a. Identify the unit used for each quantity:
(1) mass
_________
(4) temperature
__________
(2) volume
_________
(5) length
__________
(3) energy
_________
(6) time
__________
b. Convert the following:
(1) 568 mL to L
___________________
(2) 0.00897 g to mg
___________________
(3) 45700 mm to km ___________________
2. Density is the measurement of mass divided by volume. A substance’s density can help identify it. For
example, water’s density is 1.00g/mL. Substances float in water of they have low densities, and sink when their
densities are greater than 1.00 g/mL.
a. Calculate the density of 5.00 gram sample of an unknown substance, which has a volume of
5.15mL.
b. Using table S, identify the unknown substance in question (a) above. __________________________
c. Calculate the mass of a substance with a density of 2.50 g/mL and a volume of 23.0mL.
d. Calculate the volume of a metal rectangle with a height of 2.0cm, a length of 3.0cm, and a width
of 1.0cm.
e. If the metal in question (d) above is iron, calculate the mass. (Hint: density is on table S)
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Math Review for Chemistry
SCIENTIFIC NOTATION
3. Scientific Notation is used to represent very small or very large numbers. Convert the following to scientific
notation:
a. 0.00000345
____________________________
b. 1098000000
____________________________
c. 0.000345
____________________________
d. 0.000005677
____________________________
SIGNIFICANT FIGURES
4. All whole numbers 1-9 count. Preceding zeros never count, trapped zeros always count, and trailing zeros
count IF THERES A DECIMAL before the zero. Count the number of significant figures:
5678
0.09809
0.00345
0.0712
0.0987
10000
10200
102.0986
5. When rounding, your answer can only be as precise as your least precise measurement. When adding or
subtracting numbers, round your answer to the lowest decimal place given. When multiplying or dividing,
round your answer to the least number of significant figures. Calculate and round to the correct number of
significant figures:
a. 4.567 + 1.2 = _____________
d. 67065/87.2 = ________________
b. 678.345-234.98 = ______________
e. (54.0-32.34)/1.202 = ________________
c. 45 x789 = _____________
f. 3.108*(98.70-8.20) = __________________
ELEMENTS, COMPOUNDS, AND MIXTURES
6. Matter is anything that has a mass and takes up space. An element is the simplest form of matter, which
cannot be broken down any further. Elements are listed on Table S and the periodic table. Their symbols start
with an uppercase letter.
a. Which of the following is not matter? _____________________
Magnesium
Calcium Carbonate
Salt water
Heat
b. Which of the above is an element? _____________________
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Math Review for Chemistry
7. Compounds are composed of two or more elements. They can only be decomposed chemically. Elements
and compounds are also known as substances.
a. Which of the choices in number one was a compound? ________________________
b. How can compound be broken down? __________________________________________________
c. Which of the choices in question one are substances? ______________________________________
8. Mixtures are physical combinations of two or more substances (elements and/or compounds). Mixtures can
be homogeneous (completely mixed, cannot see the parts) or heterogeneous (unevenly mixed, can see the
parts). Mixtures can be separated by physical means. Label each as homogeneous or heterogeneous:
Sand: ____________________
Brass: ______________________________
Milk: ____________________
Oil and water: ________________________
9. Compounds must be separated chemically but mixtures can be separated easily using physical methods.
a. Match each method with its name.
Distillation
Filtration
Decant
Chromatography
Separated by differences in particle size
To pour off the top layer of an uneven mixture
Separated by differences in boiling point.
Just a test for purity
b. Which of the above processes only work if the mixture is heterogeneous? _____________________
10. Mixtures are composed of solutes that dissolve and solvents that do the dissolving. The solute should be the
smaller quantity.
a. In iced tea, what is the solute? ___________________ solvent? ________________________
b. In air, name a solute: _________________
c. Do all solvents have to be water? Explain. _______________________________________________
SOLIDS, LIQUIDS, AND GASES
11. A solid has a definite shape and volume. Solids are arranged in a geometric pattern. Liquids have a definite
volume but take the shape of the container they are in. Gases have an indefinite shape and volume; they take the
shape and volume of the container. Gases are easily compressed.
a. Draw particle diagrams for a solid, liquid, and a gas using at least 5 particles:
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Math Review for Chemistry
b. Which has a definite shape?
HCl(g)
H2O(l)
Cu(s)
c. Which has a definite volume?
LiF(g)
Br2(l)
Mg(s)
12. Vapors are the gas phase of substances that are normally solid or liquid at room temperature. Which can be
a vapor?
Carbon dioxide ______
Water _____
Oxygen _____
13. Phase changes occur when heat is given to or taken from a sample. For each of the following, give the
phases involved and if it is endothermic or exothermic.
Evaporation
___________________________
__________________________
Melting
___________________________
__________________________
Deposition
___________________________
__________________________
Boiling
___________________________
__________________________
Condensation
___________________________
__________________________
Sublimation
___________________________
__________________________
CHANGES IN THE LAB
14. Physical changes are changes where the substance retains its properties. Chemical changes will make
substances change into new substances and change properties.
a. Label the following as physical (P) or chemical (C) properties:
Texture
____
flammability ____
boiling point:
____
Odor
____
color
chemical composition:
____
____
b. Label the following as physical (P) or chemical (C) changes:
Corrosion: ____
melting:
____
mixing:
____
Freezing:
cutting:
____
decaying:
____
____
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