Chem 400 Chapter 1 Lecture Notes Part 2
Measurements, Metric System, SI Units, and Scientific Notation
• In the lab, we make measurements, that is we collect data with numbers and units.
• The basic types of measurements with simple units are _________, __________, ________,
__________, __________, ____________, and _____________.
• Although there are many different ways of expressing these measurements, there is an approved
system of units, the SI system. That way, any scientist can communicate with and understand the
measurements that any other scientist makes.
Here is a table of these measurements, the SI system, and our US system.
Measurement
SI Unit and abbreviation
US Unit and abbreviation
• To go between very small numbers and large numbers, we use the metric system of prefixes:
Prefix
giga
mega
kilo
hecto
deka
--deci
centi
milli
micro
nano
pico
femto
Abbreviation
G
M
k
h
da
--d
c
m
μ
n
p
f
Math Meaning
1x109 or 1,000,000,000
1x106 or 1,000,000
Example
1GW = 1x109W
1Mm = 1x106m
1 (Base Unit)
----
1x10-15 or 0.000 000 000 000 001
*Memorize the bolded ones. Fill in the blanks.
• Another way to express large or small numbers without using prefixes is by scientific notation
(regular number format is actually called floating notation).
• Scientific notation is a type of exponential notation where there is exactly 1 digit to the left of the
decimal.
• Write the following numbers in scientific notation (See handout):
• Important Note: Almost all numbers in chemistry have units! Remember this: numbers without
units are garbage!
• Mass and Weight:
• What’s the difference between mass and weight!
• Although they are different, and we truly measure mass in the lab, it is very common to say the
word weight instead as it is common usage.
• Temperature Scales and Temperature Conversions:
• In the US, there are 3 common units for temperature, which is how we measure heat.
• Fahrenheit Scale:
• Celsius Scale:
• Kelvin Scale:
• Absolute Zero:
• Here’s how you convert (memorize):
• °C = K – 273.15
so
K = °C + 273.15
• °F = (9/5)°C + 32
so
°C = (5/9)(°F – 32)
What’s the temperature of absolute zero in °C and in °F?
Derived SI Units or Compound Units
• The above units were simple units, but we also make measurements with compound or derived units.
That is, the unit contains more than 1 of the basic SI units.
• For example, volume is a compound unit of cubic meters or m3. Area is square meters or m2.
Fill in the following Table with common chemistry compound units:
Name and abbreviation
Area
Volume, V
Density, d
Speed, v
Pressure, P
Energy, E, H, G
SI Unit
Other common Chem units
• Density is mass/volume or d = m/V. For chemists, the common units for solids or liquids is g/mL or
g/cm3 (1 mL = 1 cm3). For gases, the common unit is g/L.
• Densities are intensive physical properties which give an idea of how closely packed the particles in
an object are.
• Density is temperature dependent, and densities typically increase as the substance goes from the gas
phase to the liquid phase to the solid phase. Water is an exception as the density of ice is lower than
the density of liquid water at room temperature. This is of course why ice floats!
Accuracy, Precision and Significant Figures (In Lab)
• When we use a balance to measure mass, or when we read a buret to measure volume, there is
uncertainty attached to that number. It is NOT an exact number, it is estimated or uncertain. This is
because of equipment inaccuracies as well as your errors. Reading volumes is somewhat objective
and there will often be 2 or more slightly different readings of the same pipet or buret.
• The last place which you read is the uncertain place or the estimated place.
• Even equipment with digital readouts are not EXACTLY correct, as the equipment is internally
estimating the last place.
• What’s accuracy?
• What’s precision?
• What does this look like graphically?
• The number of significant figures (sig figs) in a measurement is the total digits in that measurement.
• So if a digital centigram balance gives a reading of 3.56g, this measurement has 3 sig figs.
• If an analytical balance gives a reading of 3.5607g for the same object, this measurement now has 5
sig figs.
• Which balance do you think is more accurate and precise (assuming both are working correctly)?
• So the number of sig figs in a number is directly related to the quality, precision, and accuracy of the
equipment used to take the measurement.
• In the lab, you must always be careful to record the correct sig figs, remembering that when you take
a measurement on a buret or pipet or ruler, you must estimate between the lines (estimate to the next
place).
• What do you think the correct reading of this buret is? How many sig figs does this measurement
have?
• Counting sig figs is usually simple, but zeros may be problematic. Because of this, there are zero
rules:
• Sandwiched Zeros:
• Leading Zeros:
• Trailing Zeros (slightly different than what is in the book):
• Sig figs not only reflect the accuracy and precision of the equipment, but they help us round answers
to calculations involving measurements.
• Say you want to find the density of a solid. You determine the mass to be 1.94721 g and the
volume to be 5.25 mL. What’s the density and how should you correctly round the number to the
correct sig figs?
• The above is the multiplication and division rule, there is also a subtraction and addition rule.
• Now you weigh a crucible with Mg ribbon and it weighs 12.0456 g. You burn the ribbon in air so
that it reacts with oxygen gas to produce MgO. After the ribbon has completely combusted, you
weigh the crucible and the MgO product and it weighs 13.2700g. What’s the mass of oxygen
which combined with the ribbon and how should you correctly round this calculation to the correct
sig figs?
Dimensional Analysis or Problem Solving with Units
• Chemists are always solving problems.
• Some are relatively simple metric conversions, while others may be longer stoichiometry problems.
• Because some problems may involve multiple steps, chemists use a unit-based technique called
dimensional analysis.
• For example, if the density of a solution is 1.003 g/mL and you weighed out 90.7450g, how many
L of the solution did you measure out?
• What is the given starting quantity (how much do we have)?
• And what is 1.003 g/mL; can it take us between mass and volume?
• So you see, we let the units guide us and we always check whether the correct units cancel out and
whether we are left with the correct units.
• Your turn:
1) Convert 64.9 nL to mL.
2) Convert 33.2 km/hr to m/s.
3) How many seconds are in 14 centuries?
4) A medicine tablet contains 50.mg of the active ingredient. The correct dosage for an adult is
125mg/kg bodyweight. If a person weighs 62.8 kg, how many tablets should they take?
5) What’s the mass of a gold nugget in kg if its volume is 1.2 m3? (dAU = 19.3 g/cm3)