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Chemistry P Unit 1 – Scientific Measurement

1. Define matter and distinguish between a pure substance and a mixture; an element and a compound; a homogeneous mixture

and a heterogeneous mixture (by definition and with examples).

Chemistry = Study of matter

Matter = Anything that has mass and takes up space

1. Pure Substance = Every sample in the substance is identical to every other sample. (Examples: Water, H2O, O2, Au)

a. Pure substances are either elements or compounds.

i. Element = Pure substance made of only one type of atom. (Example: Au)

ii. Compound = Pure substance composed of two or more different elements chemically combined.

(Examples: H2O, O2)

2. Mixture = Type of matter composed of two or more substances physically combined. (Examples: A bowl of Raisin Bran cereal, Air (oxygen, nitrogen))

a. Homogeneous Mixture (SOLUTION) = Mixture that is the same throughout; uniform appearance and composition. (Examples: Pitcher of Kool Aid, Air (oxygen, nitrogen), metal alloys)

b. Heterogeneous Mixture = Mixture that is NOT the same throughout. (A bowl of Raisin Bran cereal)

Separation of Mixtures 3. Since mixtures are physically combined, they can be separated by physical methods, which are methods based on physical

properties. a. Filtration = The separation of a mixture based on particle size. b. Distillation = Separation based on boiling point.

i. A mixture of different liquids can be separated as long as they have different boiling points.

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2. Compare physical changes and chemical reactions by listing the key characteristics of each and giving examples.

1. Chemical Change = A change in the chemical composition of a substance. Atoms or molecules are rearranged. Bonds are

broken and formed.

a. Example: the formation of rust:

i. 4Fe + 3O2 2Fe2O3

2. Physical Change = A change in the physical state. The atoms or molecules are NOT rearranged. Bonds are NOT broken and

formed.

a. Example: the freezing of water:

i. H2O(l) H2O(s) + energy

3. Chemical Properties = Characteristics which can be seen as one substance is chemically transformed into another.

a. A chemical’s reactivity with another chemical

b. Examples: iron’s tendency to rust (Fe is becoming Fe2O3), flammability

4. Physical Properties = Anything that can be observed without changing the identity of the substance.

a. Examples: smell, color, solubility, boiling point, volatility

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1-3. Compare the three phases of matter (solid, liquid, and gas) in terms of molecular speed and molecular spacing, and be able to

draw a simple diagram for each state.

Solid Liquid Gas

Volume Definite Definite Takes volume of container

Shape Definite Takes shape of its container

Takes shape of its container

Molecular Speed

Slowest (vibrational)

Medium Fastest

Molecular Spacing

Closest Medium Farthest apart

Draw particle diagrams of Solid, Liquid, Gas

Solid Liquid Gas

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1-4. Convert between scientific notation and standard form of a number.

1. To convert from scientific notation to decimal notation:

a. If the exponent is positive, move the decimal to the right the number of places equal to the value of the exponent.

2 x 103 = 2000

b. If the exponent is negative, move the decimal to the left the number of places equal to the value of the exponent.

2 x 10-3 = 0.002

2. To convert from decimal notation to scientific notation:

a. Multiply the number in decimal notation by 100

2100

2100 x 100

b. Move the decimal of the significand (the number in decimal notation) to just after the first non-zero digit.

i. If you moved the decimal to the right, making the number in decimal notation larger, you want to make

the exponent smaller by the same number of digits.

ii. If you moved the decimal to the left, making the number in decimal notation smaller, you want to make

the exponent larger by the same number of digits.

Example: Convert 2100 to scientific notation:

2100 x 100

2.100 x 100 (moved the decimal 3 places to the left)

2.100 x 103 (since the decimal was moved to the left 3 places, the exponent was raised 3 places, from 0 to 3)

Example: Convert 0.051 to scientific notation:

0.051 x 100

5.1 x 100 (moved the decimal 2 places to the right)

5.1 x 10-2 (since the decimal was moved to the right 2 places, the exponent was lowered 2 places, from 0 to -2)

3. To convert from exponential notation to scientific notation:

a. Move the decimal of the significand to just after the first non-zero digit.

i. If you moved the decimal to the right, making the number in decimal notation larger, you want to make

the exponent smaller by the same number of digits.

ii. If you moved the decimal to the left, making the number in decimal notation smaller, you want to make

the exponent larger by the same number of digits.

Example: Convert 756 x 10-2 to scientific notation.

7.56 x 10-2 (move the decimal to just after the first non-zero digit)

7.56 x 100 (Since the decimal was moved to the left 2 places, the exponent is raised 2 places).

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Example: Convert 0.03450 x 10-4 to scientific notation.

3.450 x 10-4 (move the decimal to just after the first non-zero digit)

3.450 x 10-6 (Since the decimal was moved to the right 2 places, the exponent is lowered 2 places).

WS #2 (Learning Target 1-4. Convert between scientific notation and standard form of a number)

Directions: Write the number(s) given in each problem in decimal form.

1. The age of earth is approximately 4.5 x 109 years. __________________________yr

2. The weight of one atomic mass unit (a.m.u.) is 1.66 x 10-27 kg.

_____________________________________kg

Directions: Write each number in scientific notation.

3) 0.00000216

4) 5400000

5) 60

6) 0.63 × 102

7) 6.7

8) 0.0000002

9) 2000000

10) 71 × 103

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4. When you add or subtract numbers in scientific notation, they must have the same exponentials. If they do not have the

same exponentials, you need to convert one of them so that they do.

a. Convert the exponential of the smaller number to the exponential of the larger number.

b. Since you are raising its exponential, you need to move the decimal of its significand to the left the same number

of places.

Example: 1.70 x 103 + 3.75 x 105 = ?

In this example, we need to raise the exponential of 1.70 x 103 to match the exponential of 3.75 x 105. Since we are raising the exponential two places, we need to move the decimal two places to the left. 1.70 x 103 0.0170 x 105 Since these two number have identical exponentials, now we can add them together. 3.75 x 105

+ 0.0170 x 105

4.7670 05

5. Here are the rules for multiplying and dividing exponents.

a. When you multiply exponentials, you add the exponents.

b. When you divide exponentials, you subtract the exponents.

Example: Multiply 2.00 x 10-2 by 2.00 x 103.

(2.00 x 10-2)(2.00 x 103) = (2.00 x 2.00) (10-2 x 103) = (4.00)(10-2+3)

= 4.00 x 101

Example: Divide 2.00 x 10-2 by 2.00 x 103.

(2.00 x 10-2) ÷ (2.00 x 103) = (2.00 ÷ 2.00) (10-2 ÷ 103) = (1.00)(10-2-3)

= 1.00 x 10-5

6. When raising exponentials to a power, multiply the exponents.

Example: (2.00 x 10-2)3 = (2.00)3 x (10-2)3 = 8.00 x 10-6

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WS #3 (Learning Target 1-4. Convert between scientific notation and standard form of a number)

Directions: Perform the following calculations without a calculator. Write all answers in scientific notation.

11. 7.0 x 103 + (0.0070 x 106)

12. 8.5 x 102 - 2.0 x 10 -1

13. (4 x 10-3) (4 x 10-2)

14. (9.0 x 10-3) ÷ (3.0 x 106)

15. (5.0 x 10 6)2 ÷ (2.5 x 10-9)

16. (4 x 103)(2 x 104)

17. 8.74 x 102 – 2.3 x 103

18. (6.0 x 104)(7.0 x 102)

19. 2.4 x 10-1 – 4.0 x 10-3

20. (2.0 x 102)3 – (8.0 x 105)

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1-5. Convert from one metric unit to another using a metric scale.

Metric Base Units

Measurement Metric Base Unit

Length Meter

Mass Gram

Volume Liter

Basic Metric Prefixes

“times” (x) base unit Exponential Notation

Milli – (m) 1/1000 10-3

Centi – (c) 1/100 10-2

Deci – (d) 1/10 10-1

Deka – (da) 10 101

Hector – (h) 100 102

Kilo – (k) 1000 103

Useful Scientific Metric Prefixes

“times” (x) base unit Exponential Notation

Tera – (T) 1012 1012

Giga – (G) 1 000 000 000 109

Mega – (M) 1 000 000 106

micro – (µ) 0.000001 10-6

nano – (n) 0.000000001 10-9

pico – (p) 10-12 10-12

femto – (f) 10-15 10-15

Other Relationships to Memorize

Is equal to:

1 cm3 1 mL

1 dm3 1 L

1 g H2O at 1ᵒC 1 mL

How do we convert from ANY metric prefix to another?

Example: How many µL is 25 mL?

1. First determine what we have and what we want to get

2. Take the number we have and multiply by its multiple

3. Divide by the multiple of the unit we want to get

4. Write the result with the new unit

1. First determine what we have and what we want to get

25 mL = ______ µL

2. Take the number we have and multiply by its multiple

25 mL = 25 x 10-3 L

3. Divide by the multiple of the unit we want to get

9

25 × 10−3

10−6

4. Write the result with the new unit

25 × 10−3

10−6= 25 × 103 = 2.5 × 104𝜇𝐿

Example: 92 meters is how many centimeters?

Example: How many milliliters is 27.4 L?

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WS #4 (Learning Target 1-5. Convert from one metric unit to another using a metric scale.)

Directions: Perform the following conversions.

1. 42 mg = ______________ cg

2. 1.385 x 102 mm = ______________ μm

3. 87.2 cg = ______________ kg

4. 4.67 x 104 km = ______________ dm

5. 88.5 g = ______________ mg

6. 7.43 x 105 m = _______________ pm

7. 687 500 000 ng = ______________ mg

8. 1.30 x 106 mm = ______________ cm

9. 0.048 5 kg = ______________ g

10. 3.95 x 10-3 km = ______________ m

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1-6. Convert temperature between Fahrenheit, Celsius, and Kelvin.

Conversion Factors

℉ =9

5℃ + 32

℃ =5

9(℉ − 32)

𝐾 = ℃ + 273.15

Sample Problem: Convert 10 ᵒC to ᵒF.

Sample Problem: Convert 32 ᵒF to ᵒC.

Sample Problem: Convert -50o C to Kelvin.

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WS #5 (Learning Target 1-6. Convert temperature between Fahrenheit, Celsius, and Kelvin.)

Convert the following to Fahrenheit

1) 10o C ________

2) 30o C ________

3) 40o C ________

4) 37o C ________

5) 0o C ________

Convert the following to Celsius

6) 32o F ________

7) 45o F ________

8) 70o F ________

9) 80o F ________

10) 90o F ________

11) 212o F ________

Convert the following to Kelvin

12) 0o C ________

13) -50o C ________

14) 90o C ________

15) -20o C ________

Convert the following to Celsius

16) 100 K ________

17) 200 K ________

18) 273 K ________

19) 350 K ________

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1-7. Solve conversion problems using dimensional analysis.

1. Sample Problem: How many hours are in a year?

2. Sample Problem: You're throwing a pizza party for 15 and figure each person might eat 4 slices. You call up the pizza place

and learn that each pizza will cost you $14.78 and will be cut into 12 slices. How much is the pizza going to cost you?

3. Sample Problem: How many months are in 5 years? (Use dimensional analysis to solve)

Wanted:

Given:

Conversion Factor(s):

? ___________ = ____________ x

4. Sample Problem: How many liters are in 350 mL?

Wanted:

Given:

Conversion Factor(s):

? ___________ = ____________ x

5. Sample Problem: How many hours are equal to 390 min?

Wanted:

Given:

Conversion Factor(s):

? ___________ = ____________ x

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WS #6 (Learning Target 1-7. Solve conversion problems using dimensional analysis. )

Make the following conversions.

1) 484 days to years

2) 125 mL to liters

3) 5 x 103 kg to grams

4) 0.12 hrs to min.

5) 1.35 nm to meters

6) 25.3 millimol to mol

7) How many yards are there in a mile (1 mile = 5280 feet)?

8) How many hours are there in a fortnight (1 fortnight = 14 days)?

9) 0.025 km to cm

10) 923 cL to GL

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1-8. Read metric scales to the correct number of significant figures and with an appropriate unit.

Sample Problem: Read the balance to the appropriate number of digits.

Sample Problem: Read the graduated cylinder to the appropriate number of digits.

Sample Problem: Read the ruler to the appropriate number of digits.

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WS #7 (Learning Target 1-8. Read metric scales to the correct number of significant figures and with an appropriate unit.)

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1.9 Define density using a mathematical equation and give the appropriate units.

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =𝑚𝑎𝑠𝑠

𝑣𝑜𝑙𝑢𝑚𝑒

𝑚𝑎𝑠𝑠 =

𝑣𝑜𝑙𝑢𝑚𝑒 =

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1.10 Perform calculations involving density, mass, and volume, giving answers with the appropriate units.

Sample Problem: Calculate the density in g/mL of aluminum if a 13.7 mL block weighs 37.0 g.

Sample Problem: Calculate the mass of a 100. cm3 block of silver with a density of 10.5 g/cm3.

Using the density equation:

Sample Problem: Calculate the mass of a 100. cm3 block of silver with a density of 10.5 g/cm3.

Using dimensional analysis:

Sample Problem: Calculate the volume of a 10.0 g cube of iron with a density of 7.80 g/cm3.

Using the density equation:

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Sample Problem: Calculate the volume of a 10.0 g cube of iron with a density of 7.80 g/cm3.

Using dimensional analysis:

Sample Problem: You perform an experiment in which you place a rod of an unknown metal weighing 5.40 g in a graduated cylinder full of water. The rod displaces the water 2.0 mL. Identify the unknown metal. On the next slide are densities of various substances.

Substance Density (g/mL)

Water 1.00

Aluminum, Al 2.70

Iron, Fe 7.80

Gold, Au 19.30

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WS #8 (Learning Target 1-10. Perform calculations involving density, mass, and volume, giving answers with the appropriate

units.)

Directions: Answer each of the following questions in the space provided.

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =𝑚

𝑉

𝑚 = 𝐷𝑉

𝑉 =𝑚

𝐷

Substance Density (g/mL or g/cm3 )

water 1.00

Ethanol 0.800

Aluminum 2.70

Iron 7.86

Lead 11.34

Gold 19.30

Tin 7.31

Silver 10.50

Chromium 7.20

Copper 8.95

(1) (a) Calculate the density of a metal having a mass of 108 g and a volume of 15.0 cm3 . (b) Identify the metal.

D = ____________ metal = ____________

(2) (a) Find the density of aluminum. (b) Calculate the mass of 16.0 cm3 of aluminum.

D = ____________ m = ____________

(3) (a) Find the density of silver. (b) Calculate the volume of a silver block with a mass of 25.2 g.

D = ____________ V = ____________

(4) (a) Find the density of copper. (b) Calculate the mass of 40.0 cm3 of copper. (c) What is the mass of the copper in kg?

D = ____________ m = ____________ m = ____________kg

(5) (a) Find the density of iron? (b) What volume will 393 g of iron occupy? (c) Calculate the volume in Liters.

D = ____________ V = ____________ V = ____________L

(6) (a) A block of lead measures 2.00 cm by 5.00 cm by 5.00 cm. What is the volume of the block? (b) Find the density of lead? (c) What is the mass of the block? (d) What is the mass in kilograms?

V = ____________ D = ____________ m = ____________ m = ____________kg

(7) (a) An ice cube has sides with a length of 2.00 cm. Calculate the volume of the ice cube. (b) If the mass of the ice cube is 7.36 g, calculate the density of ice. (c) Find the density of water. (d) Ice will ________ in water because the density of ice is ________ than the density of water.

V = ____________ D = ____________ D = ____________

(8) (a) A ring weighing 38.6 g is placed in a graduated cylinder. The water in the graduated cylinder rises from 2.00 mL to 4.00 mL. What is the volume of the ring? (b) Calculate the density of the ring. (c) Of what metal is the ring composed?

V = ____________ D = ____________ metal = ____________

(9) (a) An empty beaker weighs 200 g. When the beaker is filled with ethanol it weighs 420 g. What is the mass of the ethanol? (b) Find the density of ethanol. (c) What is the volume of the ethanol in mL? (d) What is the volume in cm3

m = ____________ D = ____________ V = ____________ ? = ____________cm3

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(10) (a) An empty graduated cylinder has a mass of 150.0 g. When 40.0 mL of acetone are poured into the graduated cylinder, the mass increases to 181.6 g. What is the mass of the acetone? (b) Calculate the density of acetone. (c) A piece of titanium weighing 22.7 g is placed in a graduated cylinder. The water in the graduated cylinder rises from 5.00 mL to 10.00 mL. What is the volume of the titanium? (d) Calculate the density of titanium. (e) Titanium will ________ in acetone because the density of titanium is ________ than the density of acetone.

m = ____________ D = ____________ V = ____________ D = ____________

Answers: (1) (a) 7.20 g/cm3 (b) chromium (2) (a) 2.70 g/cm3 (b) 43.2 g (3) (a) 10.50 g/cm3 (b) 2.40 cm3 (4) (a) 8.95 g/cm3 (b) 358 g (c) 0.358 kg

(5) (a) 7.86 g/cm3 (b) 50.0 mL (c) 0.0500 L (6) (a) 50.0 cm3

(b) 11.34 g/cm3 (c) 567 g (d) 0.567 kg

(7) (a) 8.00 cm3 (b) 0.920 g/cm3 (c) 1.00 g/cm3 (d) float, less (8) (a) 2.00 mL (b) 19.3 g/mL (c) gold

(9) (a) 220 g (b) 0.800 g/mL (c) 275 mL (d) 275 cm3 (10) (a) 31.6 g (b) 0.790 g/mL (c) 5.00 mL (d) 4.54 g/mL (e) sink, greater

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WS #9 (Unit 1 Review)

Directions: Complete the questions in the space provided. Show all work, with any equations used, and answer with appropriate

units and significant figures.

(1) Give the name for each unit.

(a) nm (b) ks (c) µL (d) Mg

(2) Give the symbol for each unit.

(a) milligram (b) deciliter (c) centisecond (d) gigameter

(3) Convert the numbers between scientific notation and standard form.

(a) 45600000 = _________________ (b) 8.3 x 10-4 = _________________

(c) 0.0000571 = _________________ (d) 2.8 x 103 = _________________

(e) 9.7x105 = _________________ (f) 0.00000000018 = _________________

(g) 4.6x10-7 = _________________ (h) 230000000 = _________________

(4) Complete the following metric conversions.

(a) 890 µm = _________________ mm (b) 0.065 daL = _________________ hL

(c) 150000 cs = _________________ ks (d) 0.0090 Mg = _________________ g

(e) 0.0060 Gm = _________________ km (f) 150 mL = _________________ L

(g) 750000 µg = _________________ cg (h) 0.0018 ds = ________________ ns

(5) Complete the following temperature conversions.

(a) 90 °C = ____ F = ____ K (b) ____ °C = -115 F = ____ K (c) ____ °C = ____ F = 433 K

(6) Complete the following density calculations.

(a) A block of wood measures 10.0 cm by 8.00 cm by 2.50 cm. What is the volume of the block? If the density of the wood is

0.525 g/cm3, what is the mass of the block in g? in kg?

(b) A necklace weighing 200.0 g is placed in a graduated cylinder. The water in the graduated cylinder rises from 21.15 mL

to 40.18 mL. What is the volume of the necklace? What is the density of the necklace in g/mL? What metal is the necklace

composed of?

(c) An empty beaker has a mass of 150 g. When it is filled with water, the mass of the beaker and the water is 200 g. What is

the mass of the water? What is the density of water? What is the volume of water in the beaker in mL? in µL

Answers:

(1) (a) nanometer (b) kilosecond (c) microliter (d) megagram

(2) (a) mg (b) dL (c) cs (d) Gm

(3) (a) 4.56x107 (b) 0.00083 (c) 5.71x10-5 (d) 2800 (e) 970000 (f) 1.8x10-10 (g) 0.00000046 (h) 2.3x108

(4) (a) 0.890 mm (b) 0.0065 hL (c) 1.5 ks (d) 9000 g (e) 6000 km (f) 0.150 L (g) 75 cg (h) 180000

(5) (a) 194 F, 363 K (b) –81.7 ºC, 191.3 K (c) 160 ºC, 320 F

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(6) (a) 200 cm3, 105 g, 0.105 kg (b) 19.03 mL, 10.51 g/mL, silver (c) 50 g, 1.00 g/mL, 50 mL, 5.0x104 µL