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I. Measurement and Observation
There are two basic types of data collected in the lab:
Quantitative : numerical information (e.g., the mass of the salt was 3.45 g)
Qualitative : non-numerical, descriptive data (e.g., the color of the solution is magenta).
Uncertainty in Measurement
When you carry out an experiment or measurement you need to understand the true quality of your results. The terms scientists typically use are accuracy and precision—they are not the same.
1. Accuracy refers to degree of conformity with a standard (often called true, accepted
or theoretical) value. There are times when a calculated value will be used as the standard.
2. Precision refers to how close measurements are to one another. Repeated
measurements determine reproducibility or precision. Precision tells you how to report
results.
precision accuracy both neither
Accuracy and Precision Four lab groups performed the same experiment three times to determine the melting point of naphthalene (moth balls). The accepted melting point is 79.0°C. Indicate whether the following sets of data are precise, accurate, both or neither.
Precise, Accurate, Both or Neither
Reasoning Group Trial 1 Trial 2 Trial 3
accurate
Average of the trials is close to the accepted melting point of 79.
1 76.2°C 79.5°C 81.3°C
precise
All trials have values that are close to each other 2 76.2°C^ 76.1°C^ 76.3°C
neither
The trials are neither close to each other (precise) or close to the accepted value of 79.
3 86.4°C 82.8°C 81.2°C
both
All trials are precise and close to the accepted value of 79.
4 79.1°C 78.9°C 79.2°C
Glassware
Qualitative or Quantitative Function
Beaker qualitative
Large mouth glass containers used to contain approximate volumes of liquid.
Buret quantitative
Long tube with a stopcock that opens and closes. It is used to precisely deliver solutions, especially in a titration.
Erlenmeyer Flask qualitative
Glass container used to contain approximate volumes of liquid. Small mouth accommodates a stopper for storage or shaking.
Graduated Cylinder quantitative Used to measure and deliver approximate volumes of liquids.
Pipet quantitative Used to precisely deliver variable quantities of liquid.
Test Tube qualitative Glass cylinder that holds liquids being tested in an experiment.
Volumetric Flask quantitative Designed to precisely contain a specific volume. Commonly used
when accurately making aqueous solutions.
***In trying to decide which piece of equipment is the most accurate, always choose the one with the smallest measurement units and smallest diameter.
II. Measurement and Significant Figures
Results should always be reported to the correct number of significant figures. These will be
discussed in more detail in the next unit. When making a measurement in the lab, always report the number of digits necessary to express results of measurement consistent with the measured precision. This means you are to report all certain digits plus one uncertain digit.
Every time you take a measurement you should estimate between the lines. If
the measurement is on a line, add a zero to show that you are estimating it to be
exactly on the line. Always include one estimated digit.
Remember that liquids form a curved surface called a meniscus. Measure to the
bottom of the meniscus.
A buret precisely measures the amount of liquid that is released through the stopcock.
This is why a buret is marked “ upside-down ” compared to a graduated cylinder. The
numbers increase going down a buret. Be careful of this when reading burets.
III. Using Significant Figures
Significant figures indicate with how much confidence or estimation a measurement is known. For
example, the estimate “0.1” is quite different from the measurement “0.1000.” Likewise, the estimate “100” is quite different from the measurement “100.0.”
Counting Significant Figures
- All non-zero digits are significant (24 has two significant figures)
- Leading zeros are never significant ( 0.0024 has two significant figures)
- Middle or trapped zeros are significant ( 204 has three significant figures)
- nTail zeros are significant if and only if there is a decimal point in the number. ( 24.0 has three significant figures, 240 has 2 significant figures)
Example 2.3 Count and underline the significant figures in each of the following numbers:
4000 1 0.004 5 2 0.009 09 3 2.050×10^24 4
Rounding
A calculation cannot result in more significant figures than the numbers used to generate it. Jut because your calculator gives you an answer does not mean that answer is correct. You must round the answer correctly.
If the digit to the right of the last digit to be kept is ≥ 5 , increase the last digit by 1.
If the digit to the right of the last digit to be kept is < 5 , the last digit stays the same.
Example 2.4 Round the following numbers to 3 significant figures:
Multiplication and Division with Significant Figures
In multiplication and division, the answer can have no more significant figures than are in the measurement
with the fewest number of significant figures. Exact numbers such as counting numbers and
conversion factors (a ratio used to convert from one unit to another) are not included when
counting significant figures.
Example 2.5 Perform the following mathematical functions and express the answers with the correct
number of significant figures:
0.006 760 ÷ 32 1,234,000 ÷ 0.0000345 278.4 × 25.2 89.554 × 43.
0.00021 3.58×
10
IV. Scientific Notation
Scientific notation is used to represent numbers that are very large or very small.
Rules for Scientific Notation
To convert from decimal form to scientific notation:
Move the decimal point to the left or the right so that only one nonzero digit remains to the left of the decimal point. The exponent is the number of places that you moved the decimal point. If you moved the decimal to the left, the exponent is positive. If you moved it to the right, the exponent is negative.
To convert from scientific notation to decimal form:
Move the decimal point to the right if the exponent is positive (add zeroes if needed). Move the decimal to the left if the exponent is negative (add zeroes if needed).
A calculator can automatically show numbers in scientific notation if it is in scientific
mode:
It can automatically show numbers in decimal form if it is in floating point mode:
Regardless of the mode in which the calculator is set, numbers in scientific notation should
be entered using the “ EE ” button. Do NOT enter scientific notation using “ × 10 ” or the
“ ^ ” or “ 10 x ” buttons. These will make it more difficult to get the correct order of
operations during calculations.
To enter 1.0×10-14^ in scientific notation:
Example 2.6 Convert the following numbers from decimal form to scientific notation:
7.51×
7
-2.349×
5
2.31×
-
-3.549×
-
2nd ◄
SCI/ENG DRG (^) select SCI
ENTER 2nd ◄ ═
SCI/ENG DRG (^) select SCI
ENTER ═
2nd ►
SCI/ENG
DRG select FLO
ENTER 2nd ► ═
SCI/ENG
DRG select FLO
ENTER ═
1. (^0) 2nd
EE x -1^ (^ –^ )^1
ENTER 1. (^0) 2nd ═
EE x -1^ (^ –^ )^1
ENTER 1. (^0) 2nd ═
EE x -1^ (^ –^ )^1
ENTER ═
XI. Density
Density is the mass of a substance per unit volume or how much it weighs per given volume. It is an intensive
physical property.
V
mass
D
The units for mass are grams. For liquids, the units for volume are milliliters and the units for density are grams/milliliter. For gases, the units for volume are liters and the units for density are grams/liter. Remember: 1 cm^3 = 1 mL.
Water has a density of about 1.0 g/mL. Substances with densities less than 1.0 g/mL float on water.
Substances with densities greater than 1.0 g/mL sink in water.
Example 2.11 Is ice more or less dense than liquid water?
Ice floats on water, therefore it is less dense.
Example 2.12 A certain solid has a volume of 35.7 cm^3 and a mass of 85 grams. What is its density?
cm^3
g
35.7 cm^3 2.
85 g
D
Example 2.13 The density of liquid mercury is 13.6 g/mL. What is the mass of 35.0 mL of mercury?
mass 13.6 g^ mL 35.0 mL 476 g
Example 2.14 If the density of gold is 19.3 g/cm^3 , what is the volume of 200 g of gold?
3
cm^3
19.3 g^10 cm
200 g
V
Example 2.15 Find the density of a 500. g rectangular solid whose dimensions are 3.4 cm by 1.2 cm by
1.7 cm.
V = (3.4 cm)(1.2 cm)(1.7 cm) = 6.936 cm^3
(Don’t round significant digits until the end.)
cm^3
g
6.936cm^3
500.g
D
Example 2.16 An empty graduated cylinder weighs 26.5 grams. When it is filled with an unknown liquid
up to the 45.8 mL mark, the cylinder and the liquid together weigh 70.0 grams. What is the density of
the unknown liquid?
mass = 70.0 g – 26.5 g = 43.5 g
mL
0.950g
45.8mL
43.5 g
D
VII. Units of Measurement
In 1960, scientists all over the world decided to begin using a standard system of seven base units for all measurements. They are known as the SI (Le Système International d’Unités).
mass kilogram (Kg) amount mole (mol)
length meter (m) electric current Ampere (amp)
time second (s) luminous intensity candela (cd)
temperature Kelvin (K)
Mass (measure of quantity
of matter)
kilogram - The only standard which is still defined by an artifact. It is a metal
cylinder, called the International Prototype Kilogram, which is kept in the International Bureau of Weights and Measures at Sevres, France.
Length (distance covered
by a straight line segment connecting two points.)
meter - Defined in terms of the distance light travels in a vacuum in a specific
period of time.
Time (interval between two
occurrences)
second - Defined in terms of electron transition in an atom. A very accurate
timepiece is called a chronometer, solid state digital timer or atomic clock.
Temperature (measure
of kinetic energy)
Kelvin - Defined as the same size as the Celsius degree—1/100 of the
difference between the freezing and boiling points of water. The Kelvin scale starts in a different place so that there are no negative temperatures. The lowest temperature possible in the universe is 0 K.
Derived Units
Notice that the liter is not listed as a unit of volume. Volume is a derived unit which is sometimes expressed in cubic units or in liters. The standards that we will use are:
Volume L (liter) or mL or cm^3 (milliliter and cubic centimeter are the same size)
Pressure Pa (Pascal)
Energy J (Joule)
Metric System
Prefix Abbr. Sci. Not. Meaning Memorize
giga G 1×10^9 1,000,000,000 1 G* = 1,000,000,000 *
mega M 1×10^6 1,000,000 1 M* = 1,000,000 *
kilo k 1×10^3 1,000 1 K* = 1,000 *
hecto h 1×10^2 100 1 H* = 100 *
deca da 1×10^1 10 1 D* = 10 *
deci d 1×10-^1 0.1 10 d* = 1 *
centi c 1×10-^2 0.01 100 c* = 1 *
milli m 1×10-^3 0.001 1,000 m* = 1 *
micro μ 1×10-^6 0.000 001 1,000,000 μ* = 1 *
nano n 1×10-^9 0.000 000 001 1,000,000,000 n* = 1 *
* = g (gram) or L (liter) or m (meter)
Example 2.22 How many kiloliters are there in 4.56×10-7^ L?
4.56 10 kL
1,000L
4.56 10 -7 L 1 kL 10
Example 2.23 Convert 88.1 km to meters.
8.81 10 m
1 km
88.1 km1,000m 4
Metric system units (two step)
If the two units in the problem are both metric units, but neither of the units is a base unit (g, L or m), the problem is a two-step conversion.
Follow the directions for dimensional analysis to convert from the given unit to the base unit.
Add another section to the grid. Repeat dimensional analysis to convert from the base unit to the desired unit.
Example 2.24 Convert 231 mm to km.
2.31 10 km
1,000m
1 km
1,000mm
231 mm 1 m -
Example 2.25 Convert 5.43 kL to dL.
5.43 10 dL
1 L
10 dL
1 kL
5.43 kL1,000L 4
Example 2.26 Convert 6.99×10^8 kg to cg.
6.99 10 cg
1 g
100 cg
1 kg
6.99 108 kg1,000g 13
Example 2.27 How many kilometers are there in 45.2 centimeters?
4.52 10 km
1,000m
1 km
100 cm
45.2 cm 1 m -
