Mathematics in Chemistry

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Mathematics in Chemistry
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Learning Target

• I can identify the metric units of measurement
  used in chemistry.

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Units of Measurement

• Many properties of matter are quantitative
  associated with numbers
• A measured quantity must have BOTH a number and a
  unit
• The units most often used for scientific
  measurement are those of the metric system

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• The loss of the the Mars Climate Orbiter on
  September 23, 1999, was a most unfortunate and
  highly avoidable event.
• The cause of the mishap has been traced to a
  mix-up over units. Preliminary findings indicated
  that one team used English units (e.g., inches,
  feet and pounds) while the other used metric
  units for maneuvers required to place the
  spacecraft in the proper Mars orbit.
• The 'root cause' of the loss of the spacecraft
  was the failed translation of English units into
  metric units.
• For nearly three centuries, engineers and
  scientists have been struggling with English
  units.

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SI Units

• 1960 All scientific units use Système
  International dUnités (SI Units)
• There are seven base units
• Smaller and larger units are multiples of the
  base units

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7 Base Units
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The motto for the metric system was For all
people, for all time
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Derived SI Units

• These are formed from the 7 base units
• Area length x width
• Volume length x width x height
• Density mass/volume

m x m m2
m3
kg/m3 but typically g/mL
Important The liter is not an SI unit. Density
mass
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Target CheckI can identify the metric units of
measurement used in chemistry.

• State the physical quantity expressed by each of
  the following measurements.
• metric ruler
• 10.0 mL
• thermometer
• 75.4 s
• graduated cylinder

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Learning Target

• I can define the common metric prefixes and
  convert between units.

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Since we have 10 fingers, a number system
based on 10 was developed.
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Metric Prefixes
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Metric Prefixes
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How it works!

• The number always goes in front of the base unit
• The 1 (one) always goes in front of the prefix
• For Example
• 1 x 10-12 m 1 pm
• 1 TA 1 x 1012 A

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Target CheckI can identify the metric units of
measurement used in chemistry.

• Fill in the blanks with the appropriate number.
• ________ kg ________ g
• ________ Ms ________ s
• ________ m ________ pm
• ________cd ________dacd
• ________mm ________ m

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Learning Target

• I can explain what causes uncertainty in
  measurements.
• I can compare accuracy and precision.

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Making Measurements

• 2 Types of Numbers
• Exact numbers (known as counting or defined)
• Inexact numbers (derived from measurement)
• ALL measurements have some degree of uncertainty
  associated with them
• 2 Reasons for Uncertainty
• Measuring instruments are never completely free
  of flaws
• Measuring always involves some degree of
  estimation

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Reliability in Measurement

• Measurements that are close to each other are
  precise.
• Measurements that are close to the true value are
  accurate.

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Accuracy vs. Precision
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Target CheckI can explain what causes
uncertainty in measurements.I can compare
accuracy and precision.

• Three students measure the room to be 10.2 m,
  10.3 m and 10.4 m across.
• Were they precise?
• Were they accurate?

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Learning Target

• I can explain how to determine significant
  figures

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Significant Figures

• The number of digits reported in a measurement
  reflect the accuracy of the measurement and the
  precision of the measuring device.
• All the figures known with certainty plus one
  extra figure are called significant figures.

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Significant Figures

• When we measure something, we can (and do) always
  estimate between the smallest marks.
• What is the measurement?

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Significant Figures

• The more marks the better we can estimate.
• Scientists always understand that the last number
  measured is actually an estimate.
• What is this measurement?

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Significant Figures

• The measurements we write down tell us about the
  ruler we measure with
• What is the smallest mark on the ruler that
  measures 142.13 cm?

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Significant Figures

• What is the smallest mark on the ruler that
  measures 142 cm?

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• 140 cm?

• Here theres a problem. Is the zero significant
  or not?

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• 140 cm?

• Scientists needed a set of rules to decide which
  zeros count.
• All nonzero numbers do count.

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Sig Fig Rules

• Nonzero numbers are always significant
• Captured zeros are significant (e.g. 302)
• Leading zeros are never significant (e.g. 0.002)
• Trailing zeros are only significant if there is a
  decimal somewhere in the number (e.g. 130.)
• All number in scientific notation (except the
  factor of 10) are significant

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Target Check I can explain how to determine
significant figures.

• Determine the number of sig figs in the following
  numbers.
• 5.432 cm
• 0.319 g
• 1460 cm3
• 50. L
• 23.20 g/mL

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Sig Figs in CalculationsMultiplication and
Division

• Report to the least number of sig figs
• Example
• 6.221 cm x 5.2 cm 32 cm2

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Sig Figs in CalculationsAddition and Subtraction

• Report to the least number of decimal places
• Example
• 20.4 g 1.322 g 19.1 g

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Sig Figs in CalculationsNOTE

• In multiple step calculations, always retain an
  extra significant figure until the end to prevent
  rounding errors

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Target Check I can explain how to determine
significant figures.

• Calculate the following and report the answer
  with the proper number of sig figs.
• 6.000 g x 0.004 g
• 0.085 cm 0.062 cm 0.14 cm

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Learning Target

• I can calculate percent error.

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Error
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Target Check I can calculate percent error.

• A student determines the density of a sample of
  iron to be 7.49 g/mL. The known density of iron
  is 7.86 g/mL. What is the percent error?

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Learning Target

• I can define the common metric prefixes and
  convert between units.
• I can explain how dimensional analysis and
  conversion factors are used to solve problems in
  chemistry .

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Dimensional Analysis

• A method used to convert from unit to another
• YOUR BEST FRIEND IN THIS CLASS
• Given units are multiplied by conversion units to
  give the unknown units

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Conversion Factors

• Simple ratios
• Example 1 x 10-3 m 1 mm
• Can be written two ways as a ratio

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Conversion Factors

• The unknown unit is always on top and the known
  unit is on the bottom of the conversion factor
• e.g.
• The word per implies a fraction
• 100 cm per m 100 cm/ 1 m or 1 m/ 100 cm

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D.A. Questions

• 3 questions to ask when solving a problem
• What is the known?
• What is the unknown?
• What conversion factors are available to take us
  from the known to the unknown?

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Example

• How many mm are in 0.36 m?
• Known 0.36 m
• Unknown mm
• Conversion Factor 1x10-3m 1mm

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Solving the Problem

• Always start with the known
• Multiply the known by the appropriate conversion
  factor(s)

1 mm
0.36 m
x

3.60 x 102 mm
1x 10-3 m
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Example

• How many g are in 2.33 x 10-4 kg?
• Known 2.33 x 10-4 kg
• Unknown g
• Conversion Factor 1 kg 1 x 103g

1x 103 g
2.33 x 10-4 kg
x

2.33 x 10-1 g
1 kg
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Target Check

• I can define the common metric prefixes and
  convert between units.
• I can explain how dimensional analysis and
  conversion factors are used to solve problems in
  chemistry .

• Convert 329 mg to g.
• 0.329 g or 3.29 x 10-1 g

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Using 2 or More Conversion Factors

• Convert 35.47 m to in

1 cm
1 in
x
35.47 m
x
1396 in

1x 10-2 m
2.54 cm
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Target Check

• I can define the common metric prefixes and
  convert between units.
• I can explain how dimensional analysis and
  conversion factors are used to solve problems in
  chemistry .

• Convert 39.82 mg to µg

1 x 10-3 g
1 µg
39.82 mg
x
x
39820 µg

1 mg
1 x 10-6 g
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Conversions Involving Volume

• Use density to convert between mass and volume
• Example
• What is the mass in g of 2.00 in3 of gold given
  that the density of the gold is 19.3 g/cm3?

(2.54 cm)3
19.3 g
633 g
2.00 in3
x
x

(1 in)3
1 cm3
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D.A. Practice

• What is the capacity in liters of a gasoline tank
  that holds 18 gallons?
• A car is traveling 65 miles per hour. How many
  meters will it travel in one second?
• A car has a fuel efficiency rating of 38.9 miles
  per gallon. What is that rating in kilometers
  per liter?