Measurement
Chemistry is a quantitative
discipline.
Significant Figures
• The numerical value of every observed
measurement is an approximation. The accuracy
of every measurement is limited by the accuracy
of the measuring instrument. The last digit is an
estimated figure and is considered significant.
• Some numerical values are considered to be
exact and have as many significant digits as
desired. These are usually conversion factors
specified by definition, e.g., 1 kg = 1000 g.
Zeros as significant figures
• Embedded zeros are significant – 1008 has four
significant figures.
• Leading zeros used as place holders are not
significant. 0.0028 has two significant figures.
• Trailing zeros may or may not be significant
depending on the decimal point. 1500 has two
significant digits. 87.60 has four significant
digits. 650. has three significant digits.
Arithmetic and Significant Figures
• Adding and subtraction – the answer
should be rounded off after adding or
subtracting so as to retain digits only as far
as the column with the lowest accuracy.
• Multiplication and division – the answer
should be rounded off to contain only as
many significant figures as contained in
the least exact factor.
Example
• Add the following
156.67
90.124
432.098
Divide the following: 45.67 / 80.2
Scientific Notation
• Scientific notation – method used to succinctly and
accurately write very large or very small numbers.
• Standard format –
• m.mmm x 10power
• m.mmm is a number and < 10
• power is an integer (whole number that may be positive,
negative, or zero)
• We will see later that this format works well with
evaluating logarithms. Also the number of significant
figures is fully expressed in the leading factor.
Example
• Convert 0.000 145 to scientific notation.
• Covert 7,789,000 to scientific notation.
• Multiply these two numbers in scientific
notation form and convert back to regular
notation.
Example
• Convert 6.30 x 10-3 to standard decimal
form.
• Convert 8.998 x 105 to standard decimal
form.
Measurement Units
• All of the sciences use the metric system
(SI system)
• SI system originally developed in France
in the French Revolution and spread
throughout Europe by Napoleon
Bonaparte.
Fundamental Units and Measures
•
•
•
•
•
Length – meter (about 7% longer than a yard)
Volume – liter (about 6% larger than a quart)
Mass – kilogram (about 2.2 pounds)
Time – second (no difference)
Temperature – Celsius degree (1.8 of a
Fahrenheit degree). Same magnitude as a
Kelvin degree, but different zero points.
• Note: 1 liter = 1000 cm3 and that 1 ml = 1 cm3
Metric units
• All metric units are based on making multiples or
fractions based on 10. It is a decimal system –
like money.
• Prefixes on the base unit indicate the multiple or
fractional nature of the quantity.
• Multiples (using Greek) –
• deka (10), hecto (100), kilo (1000), mega
(1,000,000)
• Fractions (using Latin) –
• deci (0.1), centi (0.01), milli (0.001), micro
(0.000001)
Conversion of Units
• Use factor-label method (a.k.a. dimensional analysis)
• One goes from a given unit to the desired unit by
multiplying by a fraction called the unit-factor in which
the numerator and the denominator represent the same
quantity.
• For example, we are given that 2.54 cm is one inch
(exactly). To convert from inches to cm, we multiply by
the factor
• 2.54 cm / 1 inch.
• To convert from cm to inches, we multiply by
• 1 inch / 2.54 cm.
Example
• Convert 5.00 inches to centimeters.
Example
• A tourist goes shopping in Austria and
purchases items totaling 135 euros. How
many dollars is this purchase? (assume
that $1 = 0.75 euro)
Example
• What is the weight in grams of seven nails
when the nails weigh 0.765 kg / gross?
Example
• Find the capacity in liters of a tank 0.6 m
long, 10 cm wide, and 50 mm deep.
Temperatures
• Scientific temperatures are recorded in
either Celsius or Kelvin temperatures, not
Fahrenheit.
5
• Formulae
TC  (TF  32)
9
TF  1.8TC  32
TK  TC  273.15
Example
• You are in Wisconsin in January and it is
-20 oF at a bus stop. What is the
temperature in oC?
Example
• The boiling point of a liquid is found to be
67 oC. What is this temperature in
Fahrenheit and in Kelvin?
Density
• For solids and liquids, usually expressed
as grams / cm3 or grams / milliliter.
• Density expresses a unit conversion
factor.
• Density of mercury is 13.6 g / cm3
• This means that 13.6 g Hg describes the
same quantity as 1 cm3 of Hg. Both the
numerator and denominator describe the
same quantity.
Example
• Battery acid has a density of 1.285 g / cm3
and contains 38.0% by weight sulfuric
acid. How many grams of pure sulfuric
acid are contained in a liter of battery
acid?
Example
• A preparation of concentrated nitric acid is
69.8% by weight pure nitric acid. It has a
density of 1.42 g / cm3. What volume of
the concentrated acid contains 63.0 g of
pure nitric acid?