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Ch. 1: Measurements

Chem 20-1204

El Camino College

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Units

Units of Lengthmeter (m), centimeter (cm), inch (in.)1 m = 100 cm1 m = 39.4 in.2.54 cm = 1 in.

Ex. Which is larger, a meter or a cm?

Ex. Which is larger, an in. or a meter?

a meter

a meter.

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Units

Units of Volumeliter (L), milliliter (mL), quart (qt)1 L = 1000 mL1 L = 1.06 qt946 mL = 1 qt

Ex. Which is larger, a milliliter or a liter?

Ex. Which is larger, a quart or a liter?

a liter

a liter.

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Units

Units of Massgram (g), kilogram (kg), pound (lb)1 kg = 1000 g1 kg = 2.20 lb454 g = 1 lb

Ex. Which is larger, a g or a kg?

Ex. Do you weigh a higher number ofpounds or kilograms?

a kg

lbs

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Units

Units of TemperatureFahrenheit (oF), Celsius (oC), Kelvin (K)freezing pt of H2O is 32 oF, 0 oC, 273 K

boiling pt of H2O is 212 oF, 100 oC, 373 K

Ex. What is being measured: length, volume, mass, or temp?

292 K

23 mL

0.004 cm.temp

volumelength

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For Very Large or Small Numbers

Scientific notation has a specific form a.bcd x 10e

a.bc (the number must be 1 to <10)10e (the e is the exponent)

x 101 = x 10

x 102 = x 100

x 103 = x1000

x 10-1 = x .1

x 10-2 = x .01

x 10-3 = x .001

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Solved Examples

Write 53 in scientific notation Convert to a.bc form (between 1 and 10) 5.3 To go from the a.bc form to 53, the decimal

moves 1 place to the right 5.3 x 101

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Solved Examples

Write 8769 in scientific notation Convert to a.bc form (between 1 and 10) 8.769 To go from the a.bc form to 8769, the decimal

moves 3 places to the right 8.769 x 103

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Solved Examples

Write 100.30 in scientific notation Convert to a.bc form (between 1 and 10) 1.0030 To go from the a.bc form to 100.30, the

decimal moves 2 places to the right 1.0030 x 102

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Solved Examples

Write 0.00367 in scientific notation Convert to a.bc form (between 1 and 10) 3.67 To go from the a.bc form to 0.00367, the

decimal moves 3 places to the left 3.67 x 10-3

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Examples

Write these in scientific notation 501 = 3,256,000 = 0.042 = 0.0005395 =

5.01 x 102

3.256 x 106

4.2 x 10-2

5.395 x 10-4

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Solved Examples

Write 1.0389 x 102 in decimal form 1.0389 x 102 means that the decimal moves 2 places to the

right 103.89 Write 8.0 x 10-3 in decimal form 8.0 x 10-3 means that the decimal moves 3 places to the left .0080

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Examples

Write these in decimal notation 3 x 100 = 6.022 x 104 = 5.33 x 10-3 = 9.99 x 101 =

3

60220

0.00533

99.9

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On Your Calculator

Don’t use the 10x key Don’t press “x 10” You must use the EE or EXP key 5.62 x 10-3 is 5.62 exp 3 +/- Try this calculation. If you get a different

result, see me after class

5.62 x 10-3

8.84 x 104 = 6.36 x 10-8

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Place Names

___ ___ ___ . ___ ___ ___ hundreds tens ones tenths

hundredths

thousandths

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Dimensional Analysis How many minutes are in 2.0 hrs? The 2.0 hrs is your given information The conversion (60 min/1 hr) is called a conversion factor Always start with the given information Write the conversion factor so the units to be cancelled are

on the bottom.

2.0 hrs 60 min1 hr

= 120 min

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Dimensional Analysis

936.2 sec 1 min60 sec

= 15.60 min

How many minutes in 936.2 sec?

How many hrs in 53 min?

53 min 1 hr60 min

= 0.88 hr

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Dimensional Analysis If you need two conversions, don’t stop in the middle. Write one conversion after the other. Hit the times (X) key between numerators Hit the divide (/) key between denominators

How many hours in 9365 sec?

9365 sec 1 min60 sec

= 2.601 hr1 hour60 min

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Dimensional Analysis

5,877 sec 1 min60 sec

How many hrs in 5,877 sec?

= 1.633 hr1 hour60 min

0.052 days 24 hrs1 day

How many minutes in 0.052 days?

= 75 min60 min1 hr

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Metric Prefixes to Memorizeprefix symbol multiple

kilo k 1000 g / 1 kg

centi c 1 m / 100 cm

milli m 1 L / 1000 mL

micro 1 g / 1 x 106 g

nano n 1 m / 1 x 109 nm

also useful is 1 cm = 10 mm

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Metric Conversion Factors

There are many ways to write conversion factors

Make sure you know which unit is biggerMany small units = one big unitA fraction of a big unit = one small unit

1 m100 cm

100 cm1 m

1 x 102 cm1 m

1 cm.01 m

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Examples: Use Dimensional Analysis

Always put the number by itself before the conversion factor How many cm in 4.6 m?

100 cm1 m

4.6 m = 460 cm

1 kg1000 g

54.8 g = 0.0548 kg

How many kg in 54.8 g?

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Examples How many kL in 4,329,647 L?

1 kL1000 L

4,329,647 L = 4329.647 kL

How many m in 0.33 m?

How many kg in 828 mg?

1 g1000 mg

828 mg = 8.28 x 10-4 kg1 kg1000 g

0.33 m = 3.3 x 105 m1 x 106 m1 m

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English Units

These are the most common US unitsmass: ounce, poundlength: inch, foot, yardvolume: cubic inch, fl. oz., gallon

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Metric-US Conversions: Don’t Memorize

1 lb = 454 g 1 oz = 28.3 g 2.20 lb = 1 kg

1 in. 2.54 cm 39.4 in. = 1 m 0.621 mi = 1 km

1.06 qt = 1 L 1 qt = 946 mL

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Examples

How many liters are in 2.98 quarts?

2.98 qt 1 L1.06 qt

= 2.81 L

How many ounces are in 500.0 g?

500.0 g 1 oz28.3 g

= 17.7 oz

How many cm in 8.994 in.?

8.994 in. 2.54 cm1 in.

= 22.84 cm

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Place Names

___ ___ ___ . ___ ___ ___ hundreds tens ones tenths

hundredths

thousandths

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Significant Figures

Sig figs apply to measured amounts Sig figs don’t apply to counted things

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Significant Figures

For any apparatus, read 1 place past the smallest mark

The last significant digit is estimated (the doubtful digit).

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Significant Figures

0 oC10o20o30o40o50o

The smallest mark is in the tens placeOne place past the smallest mark is the ones.

28 oC

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Ex. Read These

3.6 oC

110 oC

4.7 oC

5.5 oC

meas-4

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Right on the Line? Always read to one place past the smallest mark Always read a piece of equipment to the same place.

Note: Read the meniscus (the bottom of the belly for water)

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Right on the Line?

3.0 mL

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Conversion Factors in Problems

Read the problem carefully, then write a conversion factor

When solving, write a number by itself first, then write the conversion factor

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Example

A car is traveling 65.9 miles per hour. How many miles will it go in 13.3 hrs?

65.9 miles1 hourThe conversion factor is or 65.9 miles

1 hour

13.3 hrs 65.9 miles1 hour

= 876 miles

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A car is traveling 38.8 miles per hour. How many hrs will it take to go 51.0 miles?

51.0 mi 1 hr38.8 mi

= 1.31 hr

A pool empties at 4.2 gal per sec. How many min will it take to empty 3200 gal?

3200 gal 1 sec4.2 gal

= 13 min1 min60 sec

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Density

Density is mass/volume D =

mv

5.8 g3.8 mL

= 1.5 g/mL

Note: 1 mL 1 cm3 1 cc

Find the density of 3.8 mL of liquid that has a mass of 5.8 g.

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The density of gold is 19.3 g/cm3. Find the mass of 87.3 cm3 of gold.

87.3 cm3 19.3 gcm3

= 1685 g

Find the volume of 0.53 g of gold using the density of 19.3 g/cm3.

0.53 g 1 cm3

19.3 g= 0.027 cm3

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Density and Solids The mass of a solid is measured on a balance or

scale The volume of a solid may be measured by

volume displacementMeasure the vol of water in a cylinderAdd the solidMeasure the vol of water again

Vfinal - Vinitial = Vsolid

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A cylinder contains 11.3 mL water. A piece of aluminum is added, and the water level rises to 16.0 mL. What is the volume of the aluminum?

16.0 mL - 11.3 mL = 4.7 mL If the Al has a mass of 12.7 g, what is the

density of the Al?

12.7 g4.7 mL

= 2.7 g/mL

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Example

A cylinder contains 35.5 mL water. A piece of zinc is added, and the water level rises to 45.0 mL. If the mass of the zinc is 68.60 g, what is the density of the zinc?

Volume 45.0 mL - 35.5 mL = 9.5 mL Density 68.60 g

9.5 mL= 7.2 g/mL