Unit 2: Introduction to Unit 2: Introduction to ChemistryChemistry

All the background All the background needed for the rest of needed for the rest of

Chemistry 11Chemistry 11

2.1 Learning Outcomes2.1 Learning Outcomes

standard and scientific notation Calculators & exponents (EE,EXP, ^) conversion factors (CF)

2.1 Vocabulary Words2.1 Vocabulary Words

2.12.1 A AStandard notation (St. N), Standard notation (St. N),

scientific notation (Sc. N) and scientific notation (Sc. N) and using your calculatorusing your calculator

Sc. N is used to express very large or Sc. N is used to express very large or extremely small numbers as a extremely small numbers as a coefficient raised to a power of 10. coefficient raised to a power of 10.

The exponent for 10 can be a The exponent for 10 can be a positive number (lg numbers) or a positive number (lg numbers) or a negative number (sm. numbers). negative number (sm. numbers).

For example, the mass of the earth is For example, the mass of the earth is about about 1,317,000,000,000,000,000,000,000 1,317,000,000,000,000,000,000,000 pounds. This would be extremely pounds. This would be extremely difficult to write out each time. Using difficult to write out each time. Using scientific notation, we would write the scientific notation, we would write the same number as 1.317 x 10same number as 1.317 x 102424

Standard notation Scientific notation Using calculator(EE, EXP, ^)

1 100 000 000 1.1 x 10 9 1.1 EE 9

0.000 098 9.8 x 10-5 9.8 EXP -5

Rules for writing large numbers in Rules for writing large numbers in scientific notation:scientific notation:

Write 123,456,000 in scientific Write 123,456,000 in scientific notation notation

All whole numbers have a decimal point: All whole numbers have a decimal point: 123,456,000123,456,000..

Move the decimal point to the left: Move the decimal point to the left: 11..23456000 23456000

Count the number of spaces moved the Count the number of spaces moved the decimal point: 8 =exponent= 10decimal point: 8 =exponent= 1088

In scientific notation, our number is In scientific notation, our number is written as 1.23456 x 10written as 1.23456 x 1088

Rules for writing small numbers in Rules for writing small numbers in scientific notation:scientific notation:

Write 0.000000123 in scientific Write 0.000000123 in scientific notation notation

Move the decimal point to the right so Move the decimal point to the right so that the number to the left of the that the number to the left of the decimal point is greater than or equal to decimal point is greater than or equal to 1 and smaller than 10: 00000011 and smaller than 10: 0000001..2323

Count the number of spaces we moved Count the number of spaces we moved the decimal point: = 7 spaces to the the decimal point: = 7 spaces to the right= Our exponent will be 10right= Our exponent will be 10-7-7

In scientific notation, our number is In scientific notation, our number is written as 1.23 x 10written as 1.23 x 10-7-7

C. Practicing converting between C. Practicing converting between standard and scientific notation standard and scientific notation

1,897,432,000 1,897,432,000 3,874,000 3,874,000 1,000,000,000,000,000 1,000,000,000,000,000 256,000,000,000 256,000,000,000 875,932,745 875,932,745 2.3498456 x 10-4 2.3498456 x 10-4 1 x 10-13 1 x 10-13 2.034056 x 10-4 2.034056 x 10-4 2.1583 x 10-6 2.1583 x 10-6 8.64391 x 10-1 8.64391 x 10-1

B. Using your calculator…..B. Using your calculator…..

Which button on your calculator is Which button on your calculator is used for expressing “to the used for expressing “to the

power of 10” (EE, EXP, ^…)?power of 10” (EE, EXP, ^…)?

What steps do you need to take to What steps do you need to take to write a negative exponent? For write a negative exponent? For

example: 1.0 x 10example: 1.0 x 10-7-7

TIP:TIP:

- When calculating with power, the When calculating with power, the

EXP or EE button replaces the 1.0 EXP or EE button replaces the 1.0 x x 1010 99 in the number. in the number.

- For example if I am to enter 1.79 x For example if I am to enter 1.79 x 10102323 into my calculator, I would into my calculator, I would enter: 1.79 EXP 23enter: 1.79 EXP 23

Try these calculations:Try these calculations:

5x105x1033 g x 0.2 g g x 0.2 g 6.02 x 106.02 x 102323 atoms x 3 atoms atoms x 3 atoms 27 / 1.9 x 1027 / 1.9 x 10-21-21

1.7 x 101.7 x 102424 x 2.7 x 10 x 2.7 x 10-17-17

Remember, these are ways to represent Remember, these are ways to represent REALLY big or small numbers….x10…REALLY big or small numbers….x10…means to the power of __, not means to the power of __, not times 10times 10

2.1 B. 2.1 B. Conversion Factor using old Conversion Factor using old

fashion Word Problemsfashion Word Problems: :

Sample Questions: Sample Questions:

If a car can go 80 km in 1 hour, how far can If a car can go 80 km in 1 hour, how far can it go in 8.5 hours?it go in 8.5 hours?

Answer: Answer:

# km = 8.5 hours x # km = 8.5 hours x 80 km80 km = 680 km = 680 km

1 hour 1 hour

How many milligrams are in 8 kg of sugar?How many milligrams are in 8 kg of sugar?

Answer: Answer:

# mg = 8 kg x # mg = 8 kg x 1x101x1033gg x x 1 mg1 mg = 8 x 10 = 8 x 1066 mgmg

1 kg 1x101 kg 1x10-3 -3 gg

Conversion factor (CF): a fractional Conversion factor (CF): a fractional expression relating expression relating or connecting or connecting two two different units or prefixesdifferent units or prefixes

A fraction with a value = 1A fraction with a value = 1 CF are used to change from one unit to CF are used to change from one unit to

another another always include units in every stepalways include units in every step

For every unit conversion use the For every unit conversion use the

following steps: following steps: U = I x CFU = I x CF

Identify the Identify the UUnknown amount and unitsnknown amount and units

Identify the Identify the IInitial amount and unitsnitial amount and units

List the List the CFCF(s) that will relate or connect (s) that will relate or connect the I units to the U unitsthe I units to the U units

Solve (the units of the I must cancel with Solve (the units of the I must cancel with the units of the bottom of the CF)the units of the bottom of the CF)

See SWB examples on page 10 – 14See SWB examples on page 10 – 14

If a car can go 80 km in 1 hour, how far If a car can go 80 km in 1 hour, how far can it go in 8.5 hours?can it go in 8.5 hours?

Answer: Answer:

# km = 8.5 hours x # km = 8.5 hours x 80 km80 km = 680 km = 680 km

1 hour 1 hour

How many milligrams are in 8 kg of How many milligrams are in 8 kg of sugar?sugar?

Answer: Answer:

# mg = 8 kg x # mg = 8 kg x 1x101x1033gg x x 1 mg1 mg = 8 x 10 = 8 x 1066 mgmg

1 kg 1x101 kg 1x10-3 -3 gg

2.1 C2.1 CMultiple CF’s:Multiple CF’s:

Always create a plan:Always create a plan:

L L gal gal $ $ oror mL mL L L kL kL Each “Each “” represent a CF” represent a CF can be computed in separate steps can be computed in separate steps

or all in one stepor all in one step See SWB examples on page 14-15See SWB examples on page 14-15

Sample Question with many CF’sSample Question with many CF’s

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

Sample QuestionSample Question

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

U

Sample QuestionSample Question

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

U I

Sample QuestionSample Question

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

U I

CF

Sample QuestionSample Question

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

U I

CFOther CF?

Sample QuestionSample Question

How many days would it take to fly How many days would it take to fly to mars in a space shuttle if it had to mars in a space shuttle if it had enough supplies? Mars is 90 million enough supplies? Mars is 90 million km from Earth (the shuttle in Earth km from Earth (the shuttle in Earth orbit travels at 28 164 km/h). orbit travels at 28 164 km/h).

U I

CFOther CF? =

1 day 24

hours

One step answer:One step answer:

# days = # days = 9.0 x 109.0 x 1077 km x km x 1 hour1 hour x x 1 day

28 164 km 24 hrs

= 133.15 days

Two step answer:Two step answer:

# hours = # hours = 9.0 x 109.0 x 1077 km x km x 1 hour1 hour = 3.2x10 = 3.2x1033hrshrs 28 164 km

# days = 3.2x103 hrs x 1 day = 1.3x102 days 24 hrs