Transcript Significant Figures

Honors Chemistry I
84.135
Dr. Nancy De Luca
Course web site:
http://faculty.uml.edu/ndeluca/84.135
Matter
Matter is anything that has mass and
occupies space. It includes everything around
us, including the air that we breath, our skin and
bones, and the earth underneath us.
Properties of Matter
Matter can be described by its physical or
chemical properties.
Physical properties are a description of the
substance, and include mass, color, physical state
(solid, liquid or gas) at a specific temperature,
density, melting or boiling point, odor, solubility,
etc.
Properties of Matter
Mercury, a metal
that is a liquid at
room temperature,
reacts with iodine, a
black shiny solid, to
produce mercury (II)
iodide, a red
crystalline solid.
mercury
iodine
mercury(II)iodide
Properties of Matter

During a physical change, the chemical identity
of the substance or substances does not change.

Examples of physical changes include
evaporation, filtration, and changes of state.
Properties of Matter
When ice is melted and the liquid is then
evaporated, all three forms of water are
chemically the same, H2O.
When salt water is boiled, the salt remains,
and the water is removed as water vapor.
For either process, there is no change in the
identity of the substances. This is true for all
physical changes.
Physical Changes
When
water boils, its
chemical
composition
remains the
same. The
molecules are
now farther
apart.
Physical Change
The dissolving of sugar in water is a physical
change. The chemical identity of the water and the
sugar remain unchanged.
Filtration
During filtration,
liquids are separated
from solids by physical
means. The liquid and
solid maintain their
chemical identity.
Distillation
During distillation,
liquids may be
separated from other
liquids, or from
solids. The chemical
identity of each
component remains
unchanged.
Properties of Matter
Chemical properties are descriptions of how
a substance reacts chemically. Examples include
the rusting of iron in the presence of air and
water, the souring of milk, or the burning of
paper to form carbon dioxide and water vapor.
Chemical Changes
As iron rusts, the
iron atoms combine
with oxygen in the air
to form a new
substance, rust, or
iron (III) oxide.
Chemical Changes
During a chemical change, atoms rearrange the way
they are attached to each other, forming new
substances with properties that are often quite different
from the starting materials.
Intensive & Extensive Properties
Intensive properties do not depend on the
amount or quantity of matter. Melting point,
chemical formula and color are intensive
properties.
Extensive properties depend upon the
quantity of matter or sample size. Examples
include length, mass and volume.
The Elements
All matter is composed of approximately 100
elements, in various combinations, listed on the
periodic table.
The table groups elements with similar
chemical and physical properties.
The Periodic Table



Periodic tables group elements with similar
properties in vertical groups or families.
Metals are on the left side of the table, and nonmetals are on the right.
A bold line resembling a flight of stairs usually
separated metals from non-metals.
The Periodic Table
metal/non-metal line
Measurements
Scientists needed to establish a system of
measurement and units before they could
reproduce or communicate the results of their
experiments.
The Metric System is used, with the units of
grams (for mass) and milliliters (for volume)
commonly used in the chemistry laboratory.
Measurements
Prefixes Commonly used in Chemistry:
prefix name symbol
value exponential notation
kilo
centi
milli
micro
nano
pico
k
1,000
c 1/100 or .01
m 1/1,000 or .001
µ
.000001
n
p
103
10-2
10-3
10-6
10-9
10-12
Measurements- Units
SI or International System units are used.
Quantity
Unit
Symbol
Mass
kilogram
kg
Length
meter
m
Time
second
s
Temperature
kelvin
K

Measurement- Volume
Volume is a derived unit. A liter is a volume
that is 10cm x 10cm x 10cm, or 1000 cm3.
Therefore, a milliliter (mL) is the same as a cubic
centimeter (cm3 or cc).
Measurement - Temperature


In the chemistry lab,
temperature is measured
in degrees Celsius or
Centigrade. The
temperature in Kelvins is
found by adding 273.15
The Fahrenheit scale has
180 oF/100 oC. This is
reason for the 5/9 or
9/5 in the conversion
formulas.
Measurement - Units
Common English-Metric Conversion Factors
2.54 cm = 1 inch
1 lb = 453.6 g
1 qt = 943 mL
Significant Figures
When writing a number, the certainty with
which the number is known should be reflected
in the way it is written.
Digits which are the result of measurement
or are known with a degree of certainty are
called significant digits or significant figures.
Significant Figures
The goal of paying attention to significant
figures is to make sure that every number
accurately reflects the degree of certainty to
which it is known.
Likewise, when calculations are performed,
the final result should reflect the same degree of
certainty as the least certain quantity in the
calculation.
Significant Figures
If someone says “There are roughly a
hundred students enrolled in the freshman
chemistry course,” the enrollment should be
written as 100 or 1 x 102.
Either notation indicates that the number is
approximate, with only one significant figure.
Significant Figures
If the enrollment is exactly one hundred
students, the number should be written with a
decimal point, as 100. , or
1.00 x 102.
Note that in either form, the number has
three significant figures.
Significant Figures
The rules for counting significant figures:
1. Any non-zero integer is a significant figure.
Significant Figures
2. Zeros may be significant, depending upon
where they appear in a number.
a) Leading zeros (one that precede any nonzero digits) are not significant.
For example, in 0.02080, the first two zeros
are not significant. They only serve to place
the decimal point.
Significant Figures – Zeros (cont’d)
b) Zeros between non-zero integers are always
significant. In the number 0.02080, the zero
between the 2 and the 8 is a significant digit.
c) Zeros at the right end of a number are
significant only if the number contains a decimal
point. In the number 0.02080, the last zero is
the result of a measurement, and is significant.
Significant Figures
Thus, the number 0.02080 has four
significant figures.
If written in scientific notation, all significant
digits must appear. So 0.02080 becomes
2.080 x 10-2.
Significant Figures
3. Exact numbers have an unlimited number of
significant figures. Examples are 100cm = 1m,
the “2” in the formula 2πr, or the number of
atoms of a given element in the formula of a
compound, such as the “2” in H2O.
Using an exact number in a calculation will not
limit the number of significant figures in the
final result.
Significant Figures - Calculations
When calculations are performed, the final
result should reflect the same degree of certainty
as the least certain quantity in the calculation.
That is, the least certain quantity will
influence the degree of certainty in the final
result of the calculation.
Significant Figures - Calculations
There are two sets of rules when performing
calculations. One for addition and subtraction,
and the other for multiplication and division.

For Multiplication and Division:
The result of the calculation should have the
same number of significant figures as the least
precise measurement used in the calculation.
Significant Figures - Calculations
Multiplication & Division:
Example: Determine the density of an object
with a volume of 5.70 cm3 and a mass of 8.9076
grams.
Significant Figures - Calculations
Multiplication & Division:
Example: Determine the density of an object
with a volume of 5.70 cm3 and a mass of 8.9076
grams.
δ = mass/volume = 8.9076 g/5.70 cm3
δ = 1.5627368 = 1.56 g/cm3
Significant Figures - Calculations

Addition and Subtraction:
The result has the same number of places
after the decimal as the least precise
measurement in the calculation.
For example, calculate the sum of:
10.011g + 5.30g + 9.7093g = 25.0203 = 25.02g
Significant Figures - Measurement


All measurements involve some degree of
uncertainty. When reading a mass from a digital
analytical balance, the last digit (usually one-ten
thousandth of a gram) is understood to be
uncertain.
When using other devices in the laboratory, such
as a ruler, graduated cylinder, buret, etc., you
should estimate one place beyond the smallest
divisions on the device.
Significant Figures - Measurements


The volume should be
estimated to the nearest
hundredth of a milliliter,
since the buret is marked
in tenths of a milliliter.
The correct reading is
20.15 (or 20.14 or 20.16)
mL. It is understood
that the last number is
uncertain.
Significant Figures - Measurements


The value of 20.15 mL
indicates a volume in
between 20.1 mL and
20.2 mL.
If the liquid level were
resting right on one of
the divisions, the reading
should reflect this by
ending in a zero.
Conversion of Units
Many chemical calculations involve the
conversion of units. An example is calculating
how many grams of a product can be obtained
from a given mass of a reactant. The calculation
involves going from mass of reactant to moles
of reactant to moles of product to grams of
product. You should write in your unites for all
calculations, and make sure they cancel properly.
Metric Conversion Factors
These conversion factors are useful and
worth learning.
I inch = 2.54 cm
1 lb = 454.6 g
1 L = 1.0567 qt
Problem
The density of mercury is 13.6 g/mL. What
is the weight, in lbs, of a quart of mercury?
Accuracy & Precision
Most experiments are performed several
times to help ensure that the results are
meaningful. A single experiment might provide
an erroneous result if there is an equipment
failure or if a sample is contaminated. By
performing several trials, the results may be
more reliable.
Accuracy & Precision
If the experimental values are close to the
actual value (if it is known), the data is said to be
accurate.
If the experimental values are all very similar
and reproducible, the data is said to be precise.
The goal in making scientific measurements
is to that the data be both accurate and precise.
Accuracy & Precision
Data can be precise, but inaccurate. If a
faulty piece of equipment or a contaminated
sample is used for all trials, the data may be in
agreement (precise), but inaccurate. Such an
error is called a systematic error. If the scientist has
good technique, the results will be similar, but
too high or too low due to the systematic error.
Random Error
In many experiments, data varies a bit with
each trial. The variation in the results is due to
random error. Examples might be estimating the
last digit for the volume in a buret. Random
errors have an equal probability of being too
high or too low. As a result, if enough trials are
performed, the random error will average itself
out.
Random and Systematic Errors