# Topic 1 Introduction_ Measurement_ Mathematical Operations

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Introduction: Measurement,
Mathematical Operations; Introduction
to Chemistry
Measurement
Measurement, from the Greek word
"metron", meaning limited proportion is
the estimation of the magnitude of
some attribute of an object, such as its
length or weight, relative to a unit of
measurement

It involves using a measuring
instrument, such as a ruler or scale,
which is calibrated to compare the
object to some standard, such as a
meter or a kilogram

Metrology is the scientific study of
measurement
Units of Measurements
Imperial system
early used as English units then Imperial units
came to known as US Customary Units
have at times been called foot-pound-second systems

Metric System
a decimalised system of measurement based on the
metre and the gram
it has a single base unit for each physical quantity
all other units are powers of ten or multiples of ten of this
base unit

SI Units
Système International d'Unités
modern, revised form of the metric system
two types of SI units, Base and Derived Units
SI Base Units
Name      Symbol           Quantity

metre       m               Length

Kilogram     kg               mass

second       s                time

ampere       A           electric current

kelvin      K      thermodynamic temperature

mole       mol        amount of substance

candela      cd         luminous intensity
SI Prefixes
yotta,   (Y),    meaning 1024   deci,    (d),   meaning 10-1
zetta,   (Z),    meaning 1021   centi,   (c),   meaning 10-2

exa,     (E),    meaning 1018   milli,   (m),   meaning 10-3

peta,    (P),    meaning 1015   micro,   (u),   meaning 10-6

tera,    (T),    meaning 1012   nano,    (n),   meaning 10-9

giga,    (G),    meaning 109    pico,    (p),   meaning 10-12

mega,    (M),    meaning 106    femto,   (f),   meaning 10-15

kilo,   (k),    meaning 103    atto,    (a),   meaning 10-18

hecto,   (h),    meaning 102    zepto,   (z),   meaning 10-21

deka,    (da),   meaning 101    yocto,   (y),   meaning 10-24
Instruments used for measuring
Example

Convert the following measurements:

1.   34 L = _____ cc
2.   25°F = _____ °K
3.   2.0 mg = _____ kg
4.   3.5 hrs = ______ s
5.   1 x 10-5 mol = ______ mol
Example

Convert the following measurements:
1. 34 L = 34, 000cc
2. 25°F = 244.48 °K
3. 2.0 mg = 0.0000020 kg
4. 3.5 hrs = 12600 s
5. 1 x 10-5 mol = 0.01 mmol
Basic Mathematical Operations
MDAS rule
Perform multiplication/division first before

e.g.
Solve the following:

1.    32(6+5) – 4/2 + (35+8)
2.    {3[4+8]/6} – (2+5(6)-12)
Basic Mathematical Operations
MDAS rule
Perform multiplication/division first before

e.g.
Solve the following:

1.    32(6+5) – 4/2 + (35+8) = 393
2.    {3[4+8]/6} – (2+5(6)-12) = -14
Rounding-off Figures
Rule 1: If the digit after that being retained is
LESS than 5, the retained digit is unchanged.

Rule 2: If the digit after that being retained is
GREATER than 5, the retained digit is
increased by one.

Rule 3: f the digit after that being retained is
EQUAL to 5, what follows determines how to
round the number.
If even number, retained
If odd number, increase by 1
Example

Round to the nearest hundredths:

1.   2.3560   =   _____
2.   2.3460   =   _____
3.   2.3452   =   _____
4.   2.3453   =   _____
5.   2.3423   =   _____
Example

Round to the nearest hundredths:
1. 2.3560 = 2.36
2. 2.3460 = 2.35
3. 2.3452 = 2.34
4. 2.3453 = 2.35
5. 2.3423 = 2.34
Significant Figures
Guidelines for Using Significant Figures
1.  Any digit that is not zero is significant.
2.  Zeros between nonzero digits are significant.
3.  Zeros to the left of nonzero digit are not significant.
4.  If a number is greater than 1, all zeros written after the
decimal point is significant.
5.  If a number is less than 1, zeros before the nonzero digit is
not significant.
6.  For numbers that do not contain decimal point, the trailing
zeros (zero after the nonzero digit) may or may not be
significant.
7.  In addition and subtraction, the number of significant
figures in the answer is determined by the digit that has the
least number of decimal places.
8.  In multiplication and division, the number of significant
figures in the product or quotient is determined by the
original number that has the least number of significant
figures.
Significant Figures
Example:

1.   5.01
2.   0.02120
3.   7,100
4.   7.10 x 103
5.   2.456
Significant Figures
Example:

1.   5.01 = 3
2.   0.02120 = 4
3.   7,100 = 2
4.   7.10 x 103 = 3
5.   2.456 = 4
Significant Figures
Example:

1.   12,524.1 + 0.1193
2.   8.60 x 2.1335
3.   0.0154 / 1.3
Significant Figures
Example:

1.   12,524.1 + 0.1193 = 12524.2
2.   8.60 x 2.1335 = 18.3
3.   0.0154 / 1.3 = 1.2 x 10-2
Scientific Notation

In observance of significant figures, scientist
used scientific notation to express
extremely large or small numerical values.
All can be expressed in the form:

N x 10n
Scientific Notation
Step 1: Find n

Step2: Count the number of places that the
decimal point must be moved to give the
number N.

Step 3: If the decimal point has to be
moved to the left, n is a positive integer or
to the right, n is a negative integer
Scientific Notation

Example:

1.   568213.5
2.   18162.07
3.   0.000092
Scientific Notation

Example:

1.   568213.5 = 5.682135 x 105
2.   18162.07 = 1.816207 x 104
3.   0.000092 = 9.2 x 10-5
Accuracy and Precision

Accuracy     determines    how     close a
measurement is to the true value of the
quantity that is being measured.

Precision refers to the closeness of two or
more measurements of the same quantity
with one another.
Error
Error refers to a difference between actual
behavior or measurement and the norms
or expectations for the behavior or
measurement

Two types:
1. Systematic Error (determinate)
2. Random Error (indeterminate)
Error
Chemistry

History
began with the discovery of fire

leads to the purification of metals
(metallurgy)

alchemy
Alchemy
Mission:
protoscience

to discover the elixir of
life
(fountain of youth)

to create gold through
transformation
Alchemy

Failure:

no scientific method
unable to established nomenclature
unable to reproduce experiments
Timeline

First chemists – the Moslems
Geber – the father of chemistry

Robert Boyle – alchemist turned chemist
differentiate alchemy and chemistry

Antoine Lavoisier
Timeline
Aristotle
“atomos”

John Dalton

J. J. Thomson

Ernest Rutherford
Timeline

Niels Bohr

E. Schrodinger

Dmitriv Mendeleyeev
Divisions of Chemistry
   Inorganic chemistry is the      study of the
properties  and    reactions     of  inorganic
compounds.

   Organic chemistry is the study of the structure,
properties, composition, mechanisms, and
reactions of organic compounds. In other words,
it is the study of those substances that contain
carbon.
Divisions of Chemistry
   Analytical chemistry is the analysis of material samples
to gain an understanding of their chemical
composition and structure. Analytical chemistry
incorporates standardized experimental methods in
chemistry.

   Biochemistry is the study of the chemicals, chemical
reactions and chemical interactions that take place in
living organisms.

   Physical chemistry is the study of the physical basis of
chemical systems and processes. In particular, the
energetics and dynamics of such systems and
processes are of interest to physical chemists.
Divisions of Chemistry
Other subdivisions:

Astrochemistry             Atmospheric chemistry
Chemical Engineering       Chemo-informatics
Electrochemistry           Environmental chemistry
Geochemistry               Green chemistry
History of chemistry       Materials science
Medicinal chemistry        Molecular Biology
Molecular genetics         Nanotechnology
Organometallic chemistry   Petrochemistry
Pharmacology               Photochemistry
Phytochemistry             Polymer chemistry
Supramolecular chemistry   Surface chemistry
Thermochemistry            Theoretical Chemistry
Nuclear Chemistry

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