Download Mathematics-based Chemistry for Science, engineering

Mathematics-based Chemistry
for
Science, engineering
&
preprofessional majors
WHAT IS CHEMISTRY ????
Chemistry is the Study Of _________
& the ______________________
• Matter is defined as anything that
has both _________________________
Matter Classification
Matter can be subdivided into mixtures and pure
substances.
Homogeneous & Heterogeneous
• Homogeneous matter has the SAME
________, ___________ and _________
throughout.
• Heterogeneous matter has VISIBLY
DIFFERENT ______ that can be seen, or
_________ that vary through the substance.
SAMPLE EXERCISE
White gold, used in jewelry, contains two
elements, gold and palladium.
• The material is uniform throughout, it is
_______________
• Composition varies therefore, it
__________________
• It must be a
_____________________
Mixtures vs Pure Substances
• A mixture is two or more pure substances
that can be separated by ______________.
• Pure substances
– cannot be separated into separate parts by a
________ change
– have a distinct set of physical and chemical
_________.
Which of the following is a pure
substance?
(a) air
(b) concrete
(c) blue-cheese salad dressing
(d) Nitrogen
(e) None of these
Matter is formed from one
or more of the Elements
• Elements Are Fundamental Substances
That Can Not Be Broken Down _________
• Elements Are Symbolized By One Or
Two Letter ___________
See Table 1.2
H
F
Cl
I
N
O
Elemental
Elemental
Elemental
Elemental
Elemental
Elemental
Hydrogen
Fluorine
Chlorine
Iodine
Nitrogen
Oxygen
• A COMPOUND Is A PURE Substance
Formed When TWO or More _______
Combine
• EVERTHING Is Made Of Chemicals.
There Is NO Meaningful Distinction
Between a “NATURAL” Substance
And A “____________” One
Passing an electric current through a
certain substance produces oxygen and
sulfur. This substance cannot be a(n)
(a) Pure substance
(b) mixture
(c) compound
(d) element.
Name
Nitrogen
Oxygen
Argon
Carbon Dioxide
Neon
Helium
Krypton
Xenon
Formula
N2
O2
Ar
CO2
Ne
He
Kr
Xe
Table 1.1
1.
2.
3.
4.
5.
6.
7.
8.
Important Compounds
Sulfuric Acid
Nitrogen
Oxygen
Calcium Oxide
Ammonia
Phosphoric Acid
Chlorine
Sodium Hydroxide
H2SO4 (aq) NOTE
N2
O2
CaO
NH3
H3PO4 (aq) NOTE
Cl2
NaOH
Properties
• Can be determined without _________the
chemical make–up of the sample.
• Some typical physical changes are:
Melting, Freezing, Boiling, Condensation,
Evaporation, Dissolving, Stretching,
Bending, Breaking
Intensive & Extensive Properties
Intensive Properties have values that
___ _____ depend on the amount of
substance. {e.g. temperature
Extensive Properties have values that
____ depend on the amount of
substance {e.g. weight
CHEMICAL Properties
• are those that ______ the chemical make–up
of the sample.
• Burning, Cooking, Rusting, Color change,
Souring of milk, Ripening of fruit, Browning
of Apples, Taking a photograph, Digesting
food
• Note: Chemical properties are actually chemical
changes.
Pick the chemical change that occurs when a
match is held over a piece of metal
(a)
(b)
(c)
(d)
water condensing on the metal
burning a match
metal getting hot
smoke deflecting light
Chemistry is the study of Matter
& the Changes it undergoes
Changes can be EITHER
Physical Changes Ice ______
or
Chemical Changes Gasoline ________
How Do We Study Chemistry ?
by using the Scientific Method
The scientific method is a systematic approach to
solving problems that involves
1. Making observations (_______________)
2. Devise a hypothesis to (_____________)
3. ____ing these hypotheses with experiments
4. Formulating a _________
HYPOTHESIS , LAW & THEORY
HYPOTHESIS __________Explanation
LAW Concise ___________of Fact
THEORY ____________ of Facts
scientific method
• A hypothesis is a suggested explanation of a
phenomenon, based on whatever resources are
available.
• Any useful hypothesis will enable predictions.
Once predictions are made, they can be tested
by experiments. If test results contradict
predictions, then the hypotheses are called into
question and explanations may be sought.
WE “DO” EXPERIMENTS
What do we “do” in EXPERIMENTS ?
We _____________ things
“GOOD” ARE THE
MEASUREMENTS?
An object was weighed three times
1. 13.036 grams
2. 13.040 grams
3. 13.031 grams
What do you report as the weight ?
ACCURACY & PRECISION
• ACCURACY refers to how closely a
measured value agrees with the correct
value
• PRECISION refers to how closely
individual measurements agree with one
another.
ACCURACY & PRECISION
Weight
Should record weight in ___________
Length
Should record length in ________
Temperature
Should record temperature in __________
Amount
Should record amount in __________
S I Base Units
(See Table 1.4 Text)
Mass
Length
Time
Temperature
Amount
Kilogram
kg
Meter
m
Second
s
Kelvin
K
Mole
mol
Some Derived Quantities
Quantity
Definition
Area
Length times Length
• .
Derived Unit
2
m
m
3
Volume
Area times Length
Density
Mass per unit
kg / m 3
Speed
Distance per unit
m/s
Must Know Prefixes
Used in Science
Metric System
See Table 1.5 Text
Metric to Metric
Convert pm to meters
Let the UNITS solve the problem
?? m
?? pm χ
= ??? meters
? pm
English to Metric
Convert inches to cm
Let the UNITS solve the problem
?? cm
?? inches χ
= ?? cm
?? inches
English to English
Convert 5.68762 x 10 3 feet to miles
• Inches in a foot ?
• Feet in a mile ?
See Back of Book
For useful conversions
Exponential Notation
In Scientific Notation, Numbers Are
Written in The EXPONENTIAL Format
n
A x 10
5687.62 feet = 5.68762 x 10 3 feet
= 5.68762 Kilo feet
= 5.68762 kft
CONVERSION FACTORS
You MUST Know A Conversion Factor For
• Length : Metric ↔ English
• Mass : Metric ↔ English
• Volume : Metric ↔ English
• See Text For Useful Conversion Factors
TYPES OF NUMBERS
Some Conversions are EXACT Numbers
12 inches ≡ 1 foot
4 quarts ≡ 1 gallon
1 pound ≡ 16 oz
Many Conversion Are APPROXIMATE
1 pound ≈ 453.59 grams
TYPES OF NUMBERS
1. EXACT ( COUNTED ) NUMBERS
e.g. 54 STUDENTS, 100 BOOKS, 6 ANTS
2. APPROXIMATE ( MEASURED )
NUMBERS
e.g. 54 LITERS, 100 METERS, 6 GRAMS
SIGNIFICANT FIGURES
1. Digits of a measured number that have
uncertainty only in the last digit
2. The NUMBER Of Digits That Are
KNOWN With CERTAINTY
3. Digits that indicate the precision of
measurements
DETERMINING THE NUMBER OF
SIGNIFICANT FIGURES
ALL Digits Are SIGNIFICANT
EXECPT TWO TYPES
1. ZEROS That Come BEFORE The First
NONZERO Digit e.g. 047.54
2. ZEROS That Come AFTER The LAST
NONZERO Digit (Most Of The Time)
How many significant figures do each
of the following have ?
1.
2.
3.
4.
5.
6.
7.
8.
13.036 grams
13.230 grams
13.217 grams
12.947 grams
12.949 grams
12.758 grams
12.967 grams
13.122 grams
?
How many significant figures do
each of the following have ?
(a)0.0360653 meters
________
(b)7.2100 x 10-3 gms
________
(c)7210000000 sec
________
(d)$25.03
_______
Rounding Off Numbers
1. If the digit to be removed is LESS than 5
number is left unchanged.
2. If the digit to be removed is 5 or greater,
number is increased.
Round off the following measurements
(a) 3.774499 L to four significant figures ____
(b) 255.0974 K to three significant figures ____
(c) 55.265 Kg to four significant figures ______
MATHEMATICAL SKILLS
ONLY A FEW Mathematical Skills
Are Required For General Chemistry,
But a THOROUGH
UNDERSTANDING
Of Them Is Necessary
ADDITION And SUBTRACTION
• The Number Of Significant Figures to
the RIGHT of the DECIMAL POINT
in the Final Sum or Difference is
determined by the SMALLEST number
of Significant Figures to the RIGHT of
the DECIMAL POINT in ANY of the
ORIGINAL NUMBERS
Examples
1. 89.332 m Five Significant Figures
+ 1.1 m ONE Sig. Fig. After Decimal
90.432 m = ???? m
2. 2.097 m
Four Significant Figures
- 0.12 m TWO Sig. Fig. After Decimal
1.977 m = ???? m
How many significant figures are
in the following summation ?
6.220
+ 1.0
+ 125
(a)
(b)
(c)
(d)
(e)
2
3
4
5
6
A “practical” Example
MEASUREMENT
DATA
Mass Of Solid + Weighing paper….13.6801 g
Mass Of Weighing paper…………….0.12 g
What do you report weight solid to be?
Multiplication And Division
The WEAKEST Link DETERMINES
The STRENGTH Of The CHAIN
The Number Of SIGNIFICANT FIGURES
in the Final Product or Quotient is
determined by the ORIGINAL Number
that has the SMALLEST number of
SIGNIFICANT FIGURES
How Many Significant Figures in
6 ft x 6 ft = ?
6.0 ft x 6 ft = ?
6.0 ft x 6.0 ft = ?
6.00 ft x 6.0 ft = ?
6.000 ft x 6.0 ft = ?
6.0000 ft x 6.0 ft = ?
Examples
1. 2.8 m x 4.5039 m = 12.61092 m 2 = ???????
2. 6.85 m 2
112.04 m
=
0.0611388789 m
=
0.0611 m = 6.11 x 10 –2 m
3. 2.5 m x 4 m = ? (a) 10.0 m2 (b) 1 m 2
(c) none of these
How many significant figures are there
in the result of the following
multiplication:
(2.54) × (6.2) × (12.000)= ???
(a)
(b)
(c)
(d)
2
3
4
5
A “practical” Example
MEASUREMENT
DATA
LENGTH
6.45 cm
WIDTH
2.50 cm
THICKNESS
3.1 cm
(6.45)(2.50)(3.1) = 49.9875 cm3
What do you report volume = ?
SAMPLE EXERCISE 1.11 page 28
Earth’s oceans contain about 1.36 × 109 km3
of water. Calculate the volume in liters.
Dimensional–Analysis method for
SOLVING PROBLEMS makes
use of conversion factors
Use UNITS
To Solve Problems !!!!!!
In Dimensional Analysis
Ask 3 Questions
1. What do you want to know
2. What information are you given?
3. What conversion factors are available to take us
from what we are given to what we want?
An average adult has 5.2 Liters of Blood
How many quarts of Blood?
How many gallons of Blood?
ML
UNITS first, then numbers
??? mL
??? L ×
= ??? mL
??? L
Convert pounds to milligrams
What do you want to know
??? grams ??? mg
??? lbs ×
×
= ??? mg
??? lbs
??? grams
Now put in numbers
Convert Liters to pints
What do you want to know
??? quarts ??? pints
??? liters ×
×
= ??? pints
??? liters ??? quarts
Now put in numbers
5.850 gal/hr to L/s
UNITS first, then numbers
gal
? qt ??? L ? hr ? min
???
×
×
×
×
= ???
hr
? gal ??? qt ? min ? sec
If the volume of an object is 5.0 ft3 what
is it in cubic meters?
3
 12 inches   2.54 cm 
 
volume = (5.0 ft )

 1 foot   1 inch 
3
3
 1m 


 100 cm 
Volume = 0.14158422 cubic meters
Is that the correct answer?
3
Density
• Density relates the mass of an object to its
volume.
weight
Density =
volume
If you have equal volumes of the following,
which will have the largest mass?
Au, density = 19.3 g/cm3
Pb, density = 11.3
g/cm3
Ag, density = 10.5 g/cm3
Cu, density = 8.92 g/cm3
Al, density = 2.70 g/cm3
How
do
you
know
If you have equal masses of the following,
which will occupy the largest volume?
Au, density = 19.3 g/cm3
Pb, density = 11.3 g/cm3
Ag, density = 10.5 g/cm3
Cu, density = 8.92 g/cm3
Al, density = 2.70 g/cm3
How
do
you
know
Densities (g/cc)
Air
Balsa wood
Water
Table sugar
Aluminum
Iron
Gold
0.001185
0.16
1.00
1.59
2.7
7.9
19.32
Two Practical Examples
Involving DENSITY
• Example 1: What is the material
• Example 2: Is the material Gold
MEASUREMENT
DATA
Mass Of Solid + paper …….. 13.6801gm
Mass Of Weighing paper ….. 0.12 gm
LENGTH ………. 6.45 cm
WIDTH ………… 2.50 cm
THICKNESS …… 3.1 mm
DENSITY = WEIGHT
VOLUME
Weight = 13.6801 – 0.12 = ????
Volume = L x W x T = ????
V = 6.45 cm x 2.50 cm x 3.1 mm
V = 6.45 cm x 2.50 cm x ? cm
V = 6.45 cm x 2.50 cm x 0.31 cm
DENSITY = WEIGHT
VOLUME
Wt = 13.6801 – 0.12 = 13.5601 gm
V = 4.99875 cc
Density = 13.5601 gm / 4.99875 cc
Density = 2.71267817 g/ml
Density = ????
What is the solid ?
1.
2.
3.
4.
5.
6.
7.
8.
13.036 grams
13.230 grams
13.217 grams
12.947 grams
12.949 grams
12.758 grams
12.967 grams
13.122 grams
Weights of
Unknown
Material
Average Weight ?
13.02825 ?
Size of Unknown Material
LENGTH ………. 4 inches
WIDTH ………… ¾ inches
THICKNESS …… 1 mm
Is the material Gold?
Is the material Gold?
YES If the density is 19.3 grams / cc
NO If the density is not 19.3 grams/cc
DENSITY = WEIGHT
VOLUME
Weight = 13.028gm
Volume = L x W x T = ????
Length = 4 inches x 2.54 cm/in = 10.16cm
Width = ¾ inches x 2.54 cm/in = 1.905cm
Thickness = 1 mm x 1/10 cm/mm = 0.1 cm
DENSITY = WEIGHT
VOLUME
Weight = 13.028gm
Volume = L x W x T = ????
V = 4 inches x ¾ inch x 1 mm
V = 10.16 cm x 1.905 cm x 0.1 cm
V = 1.93548 mL
DENSITY = WEIGHT
VOLUME
Density = 13.028 gm / 1.93548 cc
Density = 6.7311467 g/mL
WELL
IS IT GOLD ???????
Thermometers
If you were given a thermometer in
which all the markings had been
removed, how would you calibrate it ?
Temperature Conversions
1.
Kelvin (K)
↔
Celsius (°C)
Kelvin (K) = °C + 273.15
2.
Celsius (°C) ↔ Fahrenheit (°F)
5
°C = (° F − 32) and
9
9 
° F =  °C  + 32
5 
Carry out the indicated
temperature conversions
98.6°F = ? °C
oC
98.6°F = ? K
K = °C + 273.15 = ?????
37.0°C = ? °F
°F = oC (9/5) + 32 = ????
310 K = ? °C
°C = K – 273.15 = ????
= (°F –32) (5/9) = ?????
What are you suppose to get out of
Chapter 1 ?
In Text
1. Strategies in Chemistry - Page 29
2. Summary & Key Terms -Page 30