Name _______________________ Period ___________

Chapter 2 Chemistry Notes

Scientific Notation

Technique Used to Express Very Large or Very Small Numbers

Based on Powers of 10

To write a large number in scientific notation:

1. Put the decimal after the first digit and drop the zeroes. 123,000,000,000

2. To find the exponent count the number of places from the decimal to the end of the number. The exponent is a positive number.

Example:

1. 75,000,000

To write a small number in scientific notation:

1. Put the decimal after the first non zero digit.

0.000000902

2. To find the exponent count the number of places the decimal moves. The exponent is a negative number.

Examples:

1. 0.0000000011

Express the Following in Scientific Notation:a) 0.00003 d) 55,000,000

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b) 0.000007 e) 8,000,000

c) 0.002 f) 65,000

Scientific to Standard Notation

If the exponent is negative, move the decimal to the left.

If the exponent is positive, move the decimal to the right.

Examples:

1. 2.75 x 10-7

2. 5.22 x 104

Measurements

Uncertainty in Measured Numbers

1. A measurement always has some amount of uncertainty

2. To understand how reliable a measurement is, we need to understand the limitations of the measurement

3. To indicate the uncertainty of a single measurement scientists use a system called significant figures

4. The last digit written in a measurement is the number that is considered to be uncertain

Ruler 1

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You will use various tools to record measurements in the lab.

You will always record all of the certain numbers plus one uncertain number using your tool.

What is the length using ruler 1? Remember record all certain numbers and then estimate the last number (uncertain number)

_________________ Circle the uncertain number

What is the length using ruler 2? Remember record all certain numbers and then estimate the last number (uncertain number)

_________________ Circle the uncertain number

Suppose that you measure liquid in two different graduated cylinders.3

Ruler 2

Cylinder A Cylinder B

What is the volume of graduated cylinder A (remember to estimate the last number)?

________________ circle the uncertain number

What is the volume of graduated cylinder B? (remember to estimate the last number)?

________________ circle the uncertain number

Rules for significant figures

1. Nonzero integers are always significant

a) 89.659

b) 0.281

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2. Zeros

A. Captive zeros are always significant

a) 1001.4

b) 55.0702

c) 0.4900008

B. Leading zeros never count as significant figures

a) 0.00048

b) 0.0037009

c) 0.0000000802

C. Trailing zeros are significant if the number has a decimal point

a) 22,000

b) 63,850.

c) 0.00630100

d) 2.70900

Determine the number of significant digits in each of the following:a) 6.571 g f) 30.07 g k) 54.52 cm

b) 0.157 kg g) 0.106 cm l) 0.12090 mm

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c) 28.0 ml h) 0.0067 g m) 2.690 g

d) 2500 m i) 0.0230 cm n) 43.07 cm

e) 0.0700000 g j) 26.509 cm

Multiplication/Division with Significant Figures

1. Count the number of significant figures in each measurement

2. Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures

14.593 cm ÷ 0.200 cm =

3.7 x 103 x 0.00340 =

Addition and subtraction with significant figures

1. Add or subtract the numbers in each measurement

2. Round the answer to the same number of decimal places as there are in the measurement with the least number of decimal places

5.0 + 10.624 =

34.2 - 5 =

Add:a) 16.5 + 8 + 4.37

b) 13.25 + 10.00 + 9.6

c) 2.36 + 3.38 0.355 + 1.06

Subtract:a) 23.27 - 12.058

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b) 13.57 - 6.3

c) 350.0 – 20.0

Multiply:a) 2.6 x 3.78 e) 3.08 x 5.2

b) 6.54 x 0.37 f) 0.0036 x 0.02

c) 3.15 x 2.5 x 4.00 g) 4.35 x 2.74 x 3.008

d) 0.085 x 0.050 x 0.655 h) 35.7 x 0.78 x 2.3

Divide:a) 35 / 0.62 d) 0.58 / 2.1

b) 3.76 / 1.62 e) 39 / 24.2

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c) 40.8 / 5.05 f) 0.075 / 0.030

Converting one unit to another unit

1. Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another

2. Conversion factors are relationships between two units

3. Conversion factors generated from equivalence statements

◦ e.g. 1000 mL = 1 L

4. Find the relationship(s) between the starting and final units.

5. Write an equivalence statement and a conversion factor for each relationship.

6. Arrange the conversion factor(s) to cancel starting unit and result in goal unit.

7. Check that the units cancel properly

8. Multiply all the numbers across the top and divide by each number on the bottom to give the answer with the proper unit.

9. Round your answer to the correct number of significant figures.

10.Check that your answer makes sense!

Steps using metric conversions

1. Locate the starting unit and final unit on the chart. 2. Determine the number of spaces you move up or down the chart. Each space

is a power of 10. a. Move 3 spaces= 103= 10X10X10= 1000

3. Determine which unit is larger and which is smaller (largest units start at the top and progressively get smaller as you move down the chart).

4. Write equivalence statements. The larger unit will have a 1 in front of it and the smaller unit will have the power of 10 number in front of it.

5. Use factor labeling method to convert between units. Make sure all units cancel out until you are left with your goal unit.

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Metric Conversions

Prefix Symbol

exa- E

peta- P

tera- T

giga- G

mega M

kilo k

hector h

deka da

Grams ,liters, meters

Grams= g Liters= L Meters= m

deci d

centi c

milli m

micro µ

nano n

pico p

femto f

atto a

Examples:

1. 250 mL to L

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2. 1.75 kg to µg

3. 682 mg to pg

4. 3.5 L to dag

5. 9.1 X 10-15 km to am

Temperature Scales

1. Fahrenheit Scale, °F

◦ Water’s freezing point = 32°F, boiling point = 212°F

2. Celsius Scale, °C

◦ Water’s freezing point = 0°C, boiling point = 100°C

3. Kelvin Scale, K

◦ Water’s freezing point = 273 K, boiling point = 373 K

Temperature Conversions10

Fahrenheit to Celsius oC = 5/9(oF -32)

Celsius to Fahrenheit oF = 1.8(oC) +32

Celsius to Kelvin K = oC + 273

Kelvin to Celsius oC = K – 273

Examples:

1. 86oF to oC

2. -5.0oC to oF

3. 352 K to oC

4. 53 oF to K

Density

1. Density is a property of matter representing the mass per unit volume

2. Units for Density are as follows:

Solids = g/cm3

1 cm3 = 1 mL

Liquids = g/mL 11

Gases = g/L

1. What is the density of a metal with a mass of 11.76 g whose volume occupies 6.30 cm3?

2. What volume, in mL, of ethanol (density = 0.785 g/mL) has a mass of 2.04 g?

3. What is the mass, in g, of aluminum (density = 2.70 g/mL) that has a volume of 35.7 mL?

Density and conversions

1. A cube of metal has a mass of 1.45 kg and a volume of 542 mL. What is the density, measured in g/mL) of this metal?

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2. Mercury is a liquid metal used in thermometers. Mercury has a density of 13.6 g/cm3. What is the mass, in kg, of a 0.125 L sample of mercury?

3. The density of silver is 10.5 g/cm3. What is the volume, in mL, of a 525 centigram silver sample?

4. What is the volume, in L, of a 5320 µg sample of sodium chloride. The density of sodium chloride is 2.16 g.cm3.

5. Benzene has a density of 0.880 g/cm3. What is the mass, in milligrams, of a 2.50 L sample of benzene?

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Determining Volume by displacement

1. Fill a graduated cylinder with water and record the volume.

2. Add the solid and record the change in volume.

3. The volume change = volume of the solid.

Example:

A student attempting to find the density of copper records a mass of 17.92 g. Observe the volume displacement below. What is the density of the copper in g/mL?

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The actual density of copper is 8.92 g/mL. To determine the error in the student’s measurement, we can calculate the percent error. We use the equation below:

% error = measured value – accepted value x 100%

accepted value

Accepted value – correct value based on reliable sources.

Experimental (measured) value – value physically measured in the lab.

What is the student’s percent error in this case?

Example:

The accepted value for the density of lead is 11.34 g/cm3. When you experimentally determined the density of a sample of lead, you found that a 85.2 gram sample of lead displaced 7.35 mL of water. What is the percent error in this experiment?

A student places a 52.4 grams of iron in a graduated cylinder with an initial volume of 75.0 mL. After the iron is added, the volume rises to 81.2 mL. The accepted value of iron’s density is 7.87 g/cm3. What is the percent error of the student?

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A student placed a 2.78 gram sample of copper in a graduated cylinder with an initial volume of 50.0 mL. The volume rose to 52.5 mL. The accepted value of copper’s density is 8.96 g/cm3. What is the student’s percent error?

Energy

1. Capacity to do work

chemical, mechanical, thermal, electrical, radiant, sound, nuclear

2. Energy may affect matter

e.g. raise its temperature, eventually causing a state change

All physical changes and chemical changes involve energy changes

Energy Transfer (heat)

Types of energy transfers

1. Exothermic = A process that results in the evolution of heat.

2. Endothermic = A process that absorbs energy.16

Measuring Energy

Units: Calories & Joules

1. joule (J)

4.184 J = 1 cal

1.184 = 1 kcal

2. Calories

1 Cal = 1 kcal

Example:

1. Convert 60.1 joules to calories

2. How many kilojoules are there in 4.80 x 103 calories of energy?

3. How many kilocalories are in 3.25 X 102 joules of energy?

4. How many calories are in 7.98 X10-1 kilojoules of energy?

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5. How many joules of energy are in 8.90 X 102 calories?

Specific Heat (Cp)

Specific Heat (Cp) is the amount of energy required to raise the temperature of one gram of a substance by one Celsius degree

It takes 4.184 J of energy to raise one gram of water 1 °C

Equation for Specific Heat

q = mΔTCp

q= amount of heat

m= mass

ΔT= change of temperature = final temp. - initial temp

Cp= Specific heat

Amount of Heat = Mass x Temperature Change x Specific Heat

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Examples

1. Calculate the amount of heat energy (in joules) needed to raise the temperature of 7.40 g of water from 29.0°C to 46.0°C. (Specific heat of water 4.184 J/g°C)

2. A 1.6 g sample of metal that appears to be gold requires 5.8 J to raise the temperature from 23°C to 41°C. What is the specific heat of the metal?

Is the metal pure gold? The specific heat of pure gold is 0.13 J/goC.

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3. What is the temperature change when 10.0 g sample of aluminum (Cp = 0.90 J/goC) absorbs 425 J of energy?

4. Calculate the mass of water used if 6,234 cal of energy are released when a pan of water is cooled from 85oC to 54oC. (Specific heat of water 4.184 J/g°C)

Is this process endothermic or exothermic?

5. A 1.29 g piece of lead is cooled from 26.0 °C to 14.5 °C. The specific heat of lead is 0.128 J/g°C. Determine the energy released?

Is this process endothermic or exothermic?

Calorimetry – an accurate and precise measurement of heat change for chemical and physical processes.

the heat gained by a system or the surroundings equals heat lost by the system or the surroundings.

q lost = - q gained

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Examples

1. A 19.6-gram sample of a metal was heated to 61.7oC. When the metal was placed into 26.7 grams of water in a calorimeter, the temperature of the water increased from 25.0oC to 30.0oC.

How much heat is absorbed by the water?

How much heat is released from the metal?

What is the student’s measured value of the specific heat of this sample?

Look at the table below: Which metal did the student use?

Metal Specific Heat J/g°C

Nickel 0.444

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Silver 0.235

Aluminum 0.900

2. A 183 g sample of iron is heated to 100. °C. The sample of iron is placed in a calorimeter containing 425 g of water at 25.0 °C. The water temperature rises to 28.5 °C.

How much heat is absorbed by the water?

How much heat is released from the metal?

What is the student’s measured value of the specific heat of iron?

The accepted value for the specific heat of iron is 0.450 J/g°C. What is the student’s percent error?

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