Measurements are made by scientists to determine size, length and other properties of matter.
For measurements to be useful, a measurement standard must be used.
A standard is an exact quantity that people agree to use for comparison.
SI (Metric) system is the standard system of measurement used worldwide by scientists.
SI BASE UNITS:
There are 7 base SI units. Five of these are of importance in the study of chemistry.
Quantity Measured
Metric Units
Symbol
English Units
Length
Meter
m
yd
Mass
Kilogram
kg
lb
Time
Seconds
s
s
Temperature
Kelvin
K
Amount of substance
Mole
mol
mol
DERIVED UNITS:
In addition to the fundamental units above, several useful derived units are commonly used in SI system.
Quantity Measured
Units
Symbol
Volume
Liter
L
Density
grams
ERROR IN MEASUREMENTS
Two kinds of numbers are used in science:
Counted or Defined: exact numbers; no uncertainty
Measured: are subject to error; have uncertainty
8.6 cm
Every measurement has uncertainty because of instrument limitations and human error.
The last digit is the estimated one.
Significant numbers are the certain and uncertain digits.
SIGNIFICANT FIGURE RULES
Significant (all non-zero digits)
Significant (trailing zeros after decimal)
Examples:
Determine the number of significant figures in each of the following measurements:
461 cm
93.500 g
1025 g
0.006 m
0.705 mL
5500 km
Rounding Off Rules
If the rounded digit is , the digit is simply dropped.
If the rounded digit is , the digit is increased.
Examples:
3 sig. figs
2 sig. figs.
8.4234 rounds off to
8.42
8.4
14.780 rounds off to
14.8
15
3256 rounds off to
3260
3300
SIGNIFICANT FIGURES AND CALCULATIONS
The results of a calculation cannot be more precies than the least precise measurement.
For multiplication and division, the answer must contain the same number of significant figures as there are in the measurement with the fewest significant figures.
For addition and subtraction, the answer must have the same number of decimal places as there are in the measurement with the fewest decimal places.
106.8 (rounded answer)
Examples:
SI PREFIXES
The SI system of units is easy to use because it is based on multiples of ten.
Common prefixes are used with the base units to indicate the multiple of ten that the unit represents.
SI PREFIXES
Prefixes
Symbol
Multiplying factor
mega-
M
kilo-
k
1000
centi-
c
0.01
milli-
m
0.001
micro-
CONVERSION FACTORS
Many problems in chemistry and related fields require a change of units.
Any unit can be converted into another by use of the appropriate conversion factor.
Any equality in units can be written in the form of a fraction called a conversion factor. For example:
Equality:
Conversion factors:
Equality:
Conversion factors:
Sometimes a conversion factor is given as a percentage. For example:
Percent quantity: 18% body fat by mass
Conversion factors: or
CONVERSION OF UNITS
Problems involving conversion of units and other chemistry problems can be solved using the following step-wise method:
Determine the intial unit given and the final unit needed.
Plan a sequence of steps to convert the initial unit to the final unit.
Write the conversion factor for each units change in your plan.
Set up the problem by arranging cancelling units in the numerator and denominator of the steps involved.
Examples:
How many mg are equivalent to ?
Step 1: Given Need mg
Step 2:
Step 3: or
Step 4:
A doctor orders 0.50 g of Chloromyedin to be given to a patient. Chloromedin comes in 250 mg tablets. How many tablets should be given to this patient?
Step 1:
Given
Need
Step 2 & 3:
Step 4:
3. The order is to give a patient 250 mg Keflin. The bottle's direction is to add 9.5 mL of sterile water to the vial to yield . How many mL should be given to the patient to fill this order?
Step 1: Given 250 mg Need mL
4. An order is given to infuse 250 mL of IV solution in 100 minutes. If the IV tubing delivers at a rate of 15 drops , what should be the flow rate of the IV in drops ?
5. The dosage for Mannitol is , and it is available in solution. How many mL of this solution should be given to a patient weighing 137 lb ? ( )
VOLUME & DENSITY
Volume is the amount of space an object occupies. Common units are or liter (L) and milliliter ( mL ).
Density is mass per unit volume of a material. Common units are or .
Density is directly related to mass of an object, and indirectly related to the volume of an object.
Mass, 10.0 g
(a)
Comparison of the volume of equal masses of 3 materials with different densities
Volume,
(b)
Comparison of the masses of equal volumes of 3 materials with different densities
VOLUME & DENSITY
Examples:
A copper sample has a mass of 44.65 g and a volume of . What is the density of copper?
A silver bar with a volume of has a mass of 294 g . What is the density of this bar?
m =
d =
If the density of gold is , how many grams does a nugget weigh?
Step 1: Given Need
4. If the density of milk is , what is the mass of 0.50 qt of milk? ( )
Step 1: Given Need
Step 2:
Step 3:
Step 4:
What volume of mercury has a mass of 60.0 g if its density is ?
DENSITY & FLOATING
Objects float in liquids when their density is lower relative to the density of the liquid.
The density column shown below was prepared by layering liquids of various densitites.
The greater the density of the liquid, the lower it layers itself.
