PHYSICAL SCIENCE
SLT STUDY GUIDE
Chemistry and Physics
2012-2013
How to convert between American and SI
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Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method)
is a problem-solving method that uses the fact that any number or expression can
be multiplied by one without changing its value. It is a useful technique.
Unit factors may be made from any two terms that describe the same or
equivalent "amounts" of what we are interested in. For example, we know that
1 inch = 2.54 centimeters
We can make two unit factors, each equaling 1 over 1 (or 1) from this information:
• Now, we can solve some problems. Set up each problem by
writing down what you need to find with a question mark.
Then set it equal to the information that you are given. The
problem is solved by multiplying the given data and its units
by the appropriate unit factors so that only the desired units
are present at the end.
• For example: You want meters, and are given the data in
inches. So –
Given Unit (inches) x Wanted Unit (meters)
Equal Amount in Given
Units (# inches in a meter)
The inches cancel-out leaving your answer in meters
• Example:
– Note the fraction you multiply by is equal to
one over one. (1 inch = 2.54 cm)
= You use an one/one fraction each time
regardless of what the conversion is!
= This is why learning the basic equivalences will
make life easier
• More examples: How many seconds in two years?
• What is the density (D) of mercury (13.6 g/cm3) in units of kg/m3?
ATOMIC MODELS
Protons (+ charge) and Neutrons (0 charge) make up the nucleus;
Electrons (- charge) around nucleus and held by electromagnetic
force. p+ and n made up of quarks.
Plum Pudding Model
Electron Cloud Model
Four Universal Forces
ISOTOPES
• All atoms of an element have the SAME
number of protons (p+)
• The p+ number is the atomic number (Z)
– This is a constant – it stays the same for that
element’s atoms
– For example: All Sodium (Na) atoms have 11 p+
– If an atom loses a proton, it becomes a different
element
• If Na loses 1 p+, then it has become Neon (Ne)
Z = atomic number = p+
• The number of protons identifies the atom
and which element it is
• In a stable atom:
– # p+ = # n0 = # e– Thus, Na in its stable form has 11 p+; 11 n0; and 11
e– If it has an unequal number of p+ and n0, then it is
called an ISOTOPE
The Carbon Isotope
IONS
• Ions are when an atom has an unequal
number of p+ and e• Metals form (+) ions and nonmetals (-) ions
• Remember – a stable atom has a neutral
overall charge due its equal number of p+ and
e• When an atom loses or gains an e-, its charge
changes accordingly
– Loss of e- means a + charge; gaining an e- means
a – charge for the atom
Losing or Gaining e- . . . . .
• If an atom loses an e-, then it has more p+ than
e- and it will have an overall positive charge
• Different elements’ atoms can lose 1, 2, 3, or
even 4 electrons depending on various factors
• If an atom has LOST e-, then it is called a
CATION or a positive ion
– A Cation would be written as Al+ (the one being
understood) or Al+3
• Atoms can also gain electrons
• If an atom gains electrons (from 1 up to 4), then it
will have more e- than p+ and will end up having
an overall negative charge
• A negatively charged ion is called an ANION
• (A positively charged ion is called a CATION)
• The NOBLE GASES will not form ions and thus will
not bond
• The Transition Metals can form various numbers
of positive ions – got to learn these!
• The losing or gaining of electrons determines
what type of bonds the atoms will form, and
which atoms will bond to others
Using the Periodic Table
• Elements in the Main Groups (A), form fairly
consistent ions
• Group IA will form +1 ions; Group 2A form up to +2;
Group 3A form up to +3 ions
• Group 4A will form either up to -4 or +4 ions
• Group 5A will form up to -3 ions; Group 6A up to -2;
Group 7A form -1; and Group 8A will not form ions at
all
• Those elements in the B group (transition metals)
vary in their + charges meaning they can form
different ions
Group Names - Periodic Table
Know These!
Ions and Isotopes in Review
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Stable atom: #p+ = #n0 = #eAtomic Mass: #n0 = # p+
If charge is 0, then #p+ = #eIf charge is positive, then #p+ > #e- Cation
If charge is negative, then #p+ < #e- Anion
Mass measured in AMU (Atomic Mass Units)
based on the C-12 atom
Examples:
• Li-1 has gained an electron, meaning there is
one more negative charge than positive ones
– It has 3 p+ and 4 e-
• Li+1 has lost an electron, meaning there is one
more positive charge than negative ones
– It has 3 p+ and 2 e• REMEMBER: The # of p+ DOES NOT CHANGE
• Only the number of n0 (isotope) and e- (ion) change
• Cf-3 has an atomic number of 98
– This means it has 98 p+
– Its atomic mass is 216
– It has 118 n0, (216 – 98), making it an ion and an
isotope!
– Since it has a -3 charge, the number of e- will be
101; (98 + 3)
– Zn+1 has 30 p+ and n0; but due to the +1 charge, it
has only 29 e-
On the Periodic Table:
The top number is Z, the Atomic Number or
number of p+
The Element’s Symbol
The element average atomic weight set by isotopes
and abundances
Counting Atoms in a Molecule
In the example, NH3, the subscript 3 only applies to the hydrogen.
– Therefore: there is 1 N and 3 H in ammonia
In the example, 3Ca3(PO4)2, the number of atoms changes due to the
Coefficient is always in front of the whole molecule!!
-The subscript 2, multiplies the P (2) and O (4 x 2 = 8) since it is
outside the parenthesis
-The subscript 3 only goes with the Ca
-The coefficient 3 is multiplied to the Ca, P and O after you do the
subscripts
-Therefore, this molecule has (3 x 3) Ca + (3 x 2) P + (3 x 4 x 2) 0
which equals 39 atoms
3Ca3(PO4)2
Ionic Bonds
• These are the bonds between a metal and a
nonmetal
• The metal Ion is positively charged and called
a cation
• The nonmetal Ion is negatively charged and
called an anion
• The bonded molecule should be neutrally
charged when finished
Knowing where the metals and nonmetals are on the
table will make your life easier
Covalent Compounds
• These can be monatomic or polyatomic
compounds
• It is a bond between two nonmetals
• They share a pair of electrons
• They can be subgrouped into polar or
nonpolar
• If a binary compound (2 atoms) – use the
same naming rules as in Ionic Compounds
Naming Covalent Compounds
Process:
1. Prefix Indicating # + full name of first
nonmetal
2. Prefix Indicating # + root name of second
nonmetal + suffix “ide”
3. Watch for polyatomics and use their proper
names
• If it has more than two atoms – need to use
the prefixes
Number Prefix
1
Mono
2
Di
3
Tri
4
Tetra
5
Penta
6
Hexa
Number
7
8
9
10
11
12
Prefix
Hepta
Octa
Nona
Deca
Undeca
Dodeca
For Example:
NOTE THESE ARE ALL NONMETALS WITH NONMETALS!
• P4S10 becomes Tetraphosphorous Decasulfide
• P2O5 becomes Diphosphorous Pentaoxide
• SF6 becomes Sulfur Hexafluoride
• N2O3 is Dinitrogen Trioxide
• CO is Carbon Monoxide
• SO2 is Sulfur Dioxide
• SiBr4 becomes Silicon Tetrabromide
• Water is really Dihydrogen Monoxide!
Naming Ionic Compounds is really simple:
1. Name the cation (metal) using its proper name; if it is a
polyatomic, do the same
2. Then, using the stem of the anion (nonmetal), simply add
the suffix “ide” to it
3. If a transition metal with different possible ions, a roman
numeral will tell you which one it is – and it changes the
molecular formula!
Examples:
Iron (II) Sulfide = Fe+2 and S-2 combined
Zinc + Chlorine = Zinc Chloride
Iron + Oxygen = Iron Oxide
Lithium + Cyanide = Lithium Cyanide
Ammonium + Fluorine = Ammonium Fluoride
Cobalt + Phosphorous = Cobalt Phosphide
Balancing Compounds
In an Ionic Compound – balance the molecule
using the criss-cross rule. Switch oxidation
numbers, making them into subscripts and
DROP charges.
Mg
+2
+
-1
Cl
Mg Cl2
The one is understood.
This applies even if using a polyatomic ion
NH4+ +
O-2
(NH4)2O
The parentheses are used to keep
the polyatomic together; the 1 is understood
Pb+4 +
CO3-2
Pb2 (CO3)4
Pb(CO3)2
and this can be simplified by
reducing the subscripts to
Chemical Equations
• The chemical equation is the rxn formula
• Reactants  Products
– Each component will have a phase indicator:
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(g) meaning it is in its gaseous phase (not just gassy)
(l) meaning it is in its liquid phase
(s) in its solid phase
And (aq) meaning the substance is in a solution of
water, aq meaning aqueous
• Must remember which elements are normally
diatomic (N2, O2, F2, Cl2, Br2, I2, and H2)
• All molecules in an equation must be balanced
first!!
– Remember the criss-cross rule!!
• You may not adjust any subscripts from the
original formula
• You may add and adjust, as you will see, the
coefficients in front of each item in the
equation
Example:
• H2 + O2  H2O
– This is the skeleton equation
– According to the Law of Conservation of Matter,
both sides of the arrow must have the SAME
number of atoms for each and every element –
NO EXCEPTIONS
– The  can be treated like an = sign
– In reality, it indicates that some sort of process
occurred to cause the reaction
– So. . . . .
• To balance this simple equation:
– We ARE NOT ALLOWED TO CHANGE SUBSCRIPTS
– We CAN ADJUST COEFFICIENTS ONLY
– The subscripts are the numbers after and below
each element’s symbol
– The coefficients are number in front of a unit
(atoms or molecules) and tell how many units
there are
– The coefficients are multiplied out to each and
every unit’s atom they are in front of
– So. . . . .
H 2 + O 2  H2O
• There are 2 H and 2 O on the reactant side of
the equation (the left side)
• There are 2 H and only 1 O on the product
side (the right side)
• Each side must balance
• You may add, adjust, finagle, cram, etc. any
coefficient in front of any and/or all units to
get the equation to balance
• Therefore: 2 H2 + O2  2 H2O
2H2 + O2  2H2O
• Now this is balanced!
• It means it takes 2 hydrogen molecules and
one oxygen molecule to form 2 water
molecules
Balancing Equations Steps:
• First identify all the reactants and products in
the equations
• Remember – subscripts indicate how many of
each element’s atoms are present – with 1
being understood
• Remember to multiply out all subscripts that
are outside a unit in parentheses!
• YOU CAN’T CHANGE SUBSCRIPTS
• COEFFICIENTS HAVE TO GO IN FRONT OF A
UNIT
• Let’s take the unbalanced equation of:
KClO3  KCl + O2
• List the elements and how many for both
sides of the arrow
K 1  K 1
Cl 1
Cl 1
O 3
O 2
• Obviously, everything is fine except for oxygen
– This is where we have to adjust
• We can only use coefficients
– So we try to multiply each Oxygen by a number to
get them to equal out
– These multipliers become coefficients
K 1
 K 1
Cl 1
Cl 1
O 3x2=6
O 2x3=6
• So the new equation is:
2 KClO3  KCl + 3 O2
• This changes the number of K and Cl now
• You have to readjust again. . . . . .
2 KClO3  KCl + 3 O2
• Now we have:
K 2  K 1
Cl 2
Cl 1
O 6
O 6
• Multiply the product KCl by a coefficient of 2 and it
balances
• Let’s check:
2 KClO3  2KCl + 3O2
K 2  K 2
Cl 2
Cl 2
O 6
O 6
• It’s Balanced! Finally.
Another Example:
C2H6 + O2  CO2 + H2O
• List the atoms and numbers:
C 2
C 1
H 6
H 2
O 2
O 2+1=3
• Let’s go with C first by multiplying CO2 by a
coefficient of 2
C2H6 + O2  2 CO2 + H2O
• This gives us:
C 2
C 1x2=2
H 6
H 2
O 2
O 4+1=5
• Now, let’s balance H by multiplying H2O by 3
• This gives us: C2H6 + O2  2 CO2 + 3 H2O
C 2
C 2
H 6
H 2x3=6
O 2
O 4+3=7
• It’s still not balanced!
• Let’s try readjusting Oxygen to get it the same amount
• So, if we change the reactant oxygen to 7 and
the product water to 6, we get:
C2H6 + 7 O2  2 CO2 + 6 H2O
• This also changes our product hydrogen.
• Therefore, change the reactant C2H6 and the
product CO2 to balance and you get:
2 C2H6 + 7 O2  4 CO2 + 6 H2O
C 4
C 4
H 12
H 12
O 14
O 14
Reaction Types
• SYNTHESIS (or Direct Combination or
Composition) REACTIONS
– 2 + reactants join together to form a single
product
– Resulting compound is based on common
oxidation numbers of the reactant elements
– There is typically an electron transfer from the
element with the lower EN to the one with the
higher EN
– So: A + B  AB or AB + C  ABC
– If two nonmetals involved – a covalent bond
formed
– If two metals – a metallic bond
– If metal with a nonmetal – ionic bond
• DECOMPOSITION REACTIONS
– Compounds break down into components
• AB  A + B
or
ABC  AB + C
• Examples. . .
CaCO3  CaO + CO2
2 KClO3  2 KCl + 3 O2
H2CO3  H2O + CO2
Ca(OH)2  CaO + H2O
2 NaCl  2 Na + Cl2
• REPLACEMENT REACTIONS (2 types)
Single Replacement (Displacement Rxn)
– Key Rule: Metals Replace Metals
• A + BC  AC + B
– If Nonmetal – a transfer of e- from more reactive
to lesser one
– Halogens Replace Halogens also
– Metals replace H in H2O  Metal OH- + H2 (g)
– Metals replace H in Acids  salt + H2(g)
• Al + H2SO4  AlSO4 + H2(g)
• 2 Sc(s) + 6 HCl (aq)  2 ScCl2(aq) + 3 H2(g)
• DOUBLE REPLACEMENT
Example:
– FeCl3 + 3 NaOH  3 NaCl + Fe(OH)3
OH goes with FE
Cl goes with Na
• Cations exchange anions with each other
– No change in oxidation numbers
– Better know your ions and polyatomics
– Remember the criss-cross rule and balance each
compound after exchanging anions!
– So: AB + CD  AC + BD
• COMBUSTION
– An exothermic rxn (gives off energy)
– Usually find CO2 and H2O in products
– O2 usually found in reactants
• CH4(g) + 2 O2  CO2(g) + 2 H2O(g) + heat
• 2 C4H10(g) + 13 O2(g)  8 CO2(g) + 10 H2O(g)
• ACID/BASE REACTIONS
An acid + base  salt + H2O
– Acids lose a H+ ion and the bases lose OH- ion
• These make up one of the products, water
– Process is called neutralization
– The produced salt does not have to be NaCl and
can be any ionic compound
– Measure acid with pH scale (1 strong, 7 neutral
and 14 is a base)
– Measure base with pOH scale
Acid (pH) and Base (pOH)
• Strong Acid (1)
Weak Acid
• Neutral (7)
Weak Base
• Strong Base (14)
Speed, Velocity and Acceleration
• The speed of an object is the distance the object
travels per unit of time. Speed is a rate which tells
you the amount of something that occurs or
changes in one unit of time.
• Speed=distance over time
• Speed can be divided into two subtitles constant
speed & average speed. Constant speed is the
speed that does not change. Average speed is the
total distance divided by time.
• Velocity is a speed in a given direction
Velocity
• V1 represents the initial or starting velocity
– If the object starts from a rest, V1 will = 0
• V2 represents the final velocity of an object
– If the object ends with a stop, then V2 right at the
end will be a zero, but not just a millisecond
before that!
–V = d/t
– And this means d = vt; and t = d / v
Acceleration
• The acceleration of an object as produced by a
net force is directly proportional to the
magnitude of the net force, in the same
direction as the net force, and inversely
proportional to the mass of the object.
• Acceleration (a) = ΔV / Δt -or• Acceleration = force over mass
Newton's 1st Law of Motion
• An object at rest tends to stay at rest and an object in motion
tends to stay in motion with the same speed and in the same
direction unless acted upon by an unbalanced force.
• Sometimes referred to as the “Law of Inertia."
– Inertia is the state of rest or resisting a force that may cause motion or
a change in velocity
• Frame of Reference – how the observer sees the change in
velocity
• Frame of Reference (Point of View) can be stationary or
moving depending on the observer
• Example: When a car stops suddenly, all the loose objects will
continue forward until they hit something that stops them
(have you ever had coffee do this at a stoplight?)
Newton's 2nd Law of Motion
• The second law states that the acceleration of an
object is dependent upon two variables - the net
force acting upon the object and the mass of the
object.
• It explains the relation of force, mass & acceleration.
• Force=mass x acceleration (F = ma)
• Weight is also a force = m x g
• The net force on an object is equal to the product of
its acceleration and its mass.
Force
• Force is measured in the SI unit called a
Newton (N)
– 1 N = 1 kg x 1 m / s2
1 N = .225 lbs
1 lb. = 4.448 N
• Forces usually are in equilibrium (balanced)
• Weight is a Force (wt = m g)
Force Continued. . .
• By definition it is a push or pull
• It can be divided into two subsets: unbalanced
and balanced
• Unbalanced force can cause an object to start
or stop moving; or change its acceleration,
velocity or direction
• A balanced force is equal forces on an object
that will not change the object’s motion
Acceleration - Due to Gravity
• agrav or just plain g, has a value of 9.80665
m/s2
– We’ll round this off to 9.81 m/s2
• Use 10 for guesstimating!
– Believe it or not – agrav at the equator is
9.7804 m/s2 and at the poles it is 9.8321
m/s2
Free Fall Acceleration
• If v1 (initial velocity is zero or the object is at
rest then falls):
– V2 = gt
– V2 = √2gh
– H = ½ gt2
– H = v2 t
2
If v1 does not equal zero. . . the object
is thrown down or is shot downwards
• V2 = v1 + g t
• V22 = v12 + 2 g h
• H = v1t + ½ g t2
• H = v2 + v 1 t
2
Momentum (ρ)
• Momentum is the product of an object’s mass
and velocity
• It is directly proportional to mass and velocity
• It’s the tendency for an object to keep in
motion
–p = mv
– F t = m v; where F t is the impulse or change in
momentum
Newton’s 3rd Law
• Basically – the law means that for every action
there is an equal and opposite reaction
• A rocket launch – the Fthrust downwards
(action) forces the rocket upwards (reaction)
against the Fgravity
•
Remember:
Action  Equal/Opposite Reaction
Vectors
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Properties of Vectors
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–
–
–
Vectors can be rearranged into a diagram
Size and Direction can not be changed
Use the tip to tail method of rearranging vector arrows – addition
To subtract vectors – add one to its opposite
– Example: One Dimension
A(6m)
(5 m) + B
(6 m) = R (Resultant)
of 11 m to the right (same direction = addition)
A
(4m) + B
(-3m) = R of 1 m to
the left (opposite directions = subtraction)
Some Key Concepts
• Mass – the amount of matter something has
• Weight – mass affected by the force of gravity
(m x g) – this a Force!
• Density – how much mass per volume
(d = m / volume)
Can be determined through math or
through the displacement of fluid method
*(Remember Archimedes and the crown)
Work, Power, Energy
Work
• Work is a force applied to an object that causes displacement
• W = FΔd
– Measured in Newton-meters (Nm) or Joules (J)
– Kg m2 / s2 is also called a Joule
Power
• Power is the rate at which work is being done
• Measured in Joules per Second or Watts (W) and 1 J/s = 1 W
• Power (P) = Work / Time
– P = W/t = Fd/t
Energy
• Potential Energy
– The stored energy of position, inertia, or ability to do work
– PE = m g h
• Kinetic Energy
– Energy of motion
– KE = .5 m v2
– KE = F d
KE / PE Example
• As KE increases, PE decreases and versa vice
• As it moves upwards, height increases and PE increases; as it moves
downwards, velocity increases and KE increases
• The pendulum at the two highest points have high PE, but no KE until it
starts to move towards the center again.
• Then, the PE decreases until the bob hits the bottom and KE is at its
highest
•No medium needed
•All are transverse waves
•Have an electrical and magnetic field at right angles to each other
•Longest Wavelengths  Shortest λ
•Lowest f  Highest f
•Lowest energy (eV)  Highest eV
•Velocity is the same throughout = c = 300 000 km/s
Waves: f = Hz; λ = wavelength
Differences between Gravitational and Electromagnetic
radiation
There are two principal differences between gravity and
electromagnetism, each with its own set of consequences for the
nature and information content of its radiation, as described.
• Gravity is a weak force, but has only one sign of charge.
Electromagnetism is much stronger, but comes in two opposing
signs of charge.
This is the most significant difference between gravity and
electromagnetism, and is the main reason why we perceive these
two phenomena so differently.
• Significant Gravitational fields are generated by accumulating bulk
concentrations of matter. Electromagnetic fields are generated by
slight imbalances caused by small (often microscopic) separations
of charge.
• Gravitational charge is equivalent to inertia.
Electromagnetic charge is unrelated to inertia.
SOUND Equations
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•
•
•
Vsound = 331.5 + .61 (Co)
v = d/t
d = vt
t = d/v
If no temp given, assume 343 m/s
 Denser the material, faster the sound!
•
•
•
•
f
λ
v
v
=v/λ
In Hertz (Hz)
= v/f
= fλ
= λ / T (period)
• Intensity (I) = Power (P) / Area (A)
– Intensity (I) = P / 4 π r2
In Watts / meter2
• Power = I (4 π r2)
In Watts
• Doppler Effect = fo = (v + vd / v + vs) fs
Light, Mirrors and Lenses
Convex Mirror
Concave Mirror
Concave Mirror
Electricity and Magnetism
Magnitude of Charge
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•
•
•
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•
Coulomb’s Law
FElectric = K q q’
r2
K = 8.988 x 109 Nm2/c2
q and q’ are charges of objects
r is distance between objects
Coulomb (c) and Amperage (I)
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•
•
•
•
Amount of charge flowing through a wire in 1 second with a current of 1 ampere
Ampere is 1 Coulomb per second, the intensity (I) of the electrical current
Based on the charge of an electron
1 coulomb = 6.242 x 1018 e– Current (I) = Q / t in amperes
• Measuring the intensity of the electric current
Charge of an electron (e-) = 1.60218 x 10-19 c = 1 eV
Potential Difference (V)
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•
•
Amount of work in an electric field to take the charge of 1 coulomb from one point to another
Volt is the potential difference across a conductor that carries a current of 1 amp
V = W/Q
– V is potential difference in Volts
• One volt = J/c
– W is work done in Joules
– Q is charge in Coulombs
Resistance (R)
• Measured in Ohms  Ω
• R = V/I
– I ohm (Ω) = 1 V / Amp
• Ohm’s Law  V = I R
– Voltage = Current in Amps x Resistance in Ohms
• Resistance in Series
– R1 + R2 + R3 + …. = RTotal
• Resistance in Parallel
– 1/R1 + 1/R2 + 1/R3 + …. = 1/RTotal
Capacitance (C)
• C = Q/V
• Measured in farads (1 coulomb per volt)
• Parallel Capacitance
– C1 + C2 + C3 + … = CTotal
• Series Capacitance
– 1/C1 + 1/C2 + 1/C3 + … = 1/CTotal
Work and Power
• Work (WE) = q V
– In Joules
• Power (P) = V q / t
– In Watts (J/s)
– Power also = V I = I2 R = V2 / R
Magnetism
• Based on charges of atom’s particles
• It is a field force – line go from N to S (Faraday Lines)
– Measured in Teslas or Gauss (1T = 100000G);
– Earth = .0001T
• All magnets have two poles – if cut it makes new poles!
• Can lose magnetism if it is heated past material’s “Curie
Temperature” and it returns when cooled
• Types of Magnetism:
– Diamagnetic: no magnetism in material
– Paramagnetic: magnetic only when in a magnetic field
– Ferromagnetic: due to e- sea model of metal, it can be
permanently magnetized