Chemistry is where you
learn 2 + 2 = 10
or something.
—Dennis Rodman
Chemistry Math With Chemistry-specific graphs
S
Chemistry = Memorization?
FALSE!
http://www.magazine-agent.com/officials-logic-problems/magazine
S Look at the following numbers. How easy
would it be to memorize this list and
regenerate it in a week or so on a quiz?
S 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365,
2731, 5461, 10923, 21845
S Pretty hard? Pretty Easy? Why?
S Easy huh?
S OK, what’s the next number in the
sequence?
S How about the next 5 numbers?
1, 3, 5, 11, 21, 43, 85, 171, 341, 683,
1365, 2731, 5461, 10923, 21845
http://www.antiqueradiomuseum.org/RR%20Rule%20Book%20for%20CMSP&P%20RR.jpg
S The numbers don’t seem to follow any
kind of pattern.
S But, what if you knew a rule? It
wouldn’t just be memorization then.
S OK, good point! The rule is:
S
S
S
S
You just wish it
was that EASY!
Start with 1.
Double and add 1.
Double and subtract 1.
And so on.
Learn HOW to do the problem;
don’t just memorize the steps!
http://familyfun.go.com/Resources/printable-previews/previews/beaver_memorygame_august2.jpg
Don’t
S Doesn’t “knowing the rule” make
the list easier to memorize?
S You don’t have to memorize a bunch
of unrelated numbers.
S IF YOU KNOW the rule, you can
generate the number list on the test
easily. Anytime! Anywhere!
Can you make sense out of
NONSENSE?
S Force
Hour
Cis
Neigh
S Koran
Fodder
Count
Shun
S Heaven
Brat
An
S Ye
Farth
Ent
S Sago
Upon
Anew
S Figured it out yet?
The Gettysburg Address
http://www.old-picture.com/defining-moments/pictures/Abraham-Lincoln-Antietam-Battlefield.jpg
http://en.wikipedia.org/wiki/Gettysburg_Address
S “Four score and seven years ago our fathers
brought forth on this continent a new nation,
conceived in Liberty, and dedicated to the
proposition that all men are created equal.”
S Being able to look at something
Yes, Ms Rackley, I
know this was
Antietam, but it’s a
nice picture.
new, and make sense of it is an
important skill for the rest of this
course.
S You have to be able to DO
chemistry in your mind.
Unfortunately (for you) I’m not
Bill Nye
http://www.tvgasm.com/newsgasm/Bill-nye.jpg
What
would
Bill Nye
do?
S In Chemistry, when we have
numbers, most of the time we do
one of three things:
S Multiple 2 x 3
S Divide 2 / 3
S Divide 3 / 2
S If you can figure out which
operation to do when, you can
actually solve the problem.
S That’s our goal.
Units TELL you the right ANSWER
S If your units don’t work
out right, your answer is
wrong.
S Don’t just ignore wrong
units. It is a big clue for
you.
S LISTEN to the units!
Graphing Variables
Slope = rise/run
Slope = mass/volume
Slope = density
Line of Best Fit
Real data never
(almost never) falls
exactly on the line!
The line is an “average”
Once you know the line of best fit, you
can use it to predict other values.
The line represents the data.
We never “connect the
dots” in a graph.
Don’t connect the dots. The line
of best fit doesn’t have to go
through ANY of the data points.
However, some points might be
exactly on the line.
Ideally the points above the line
= the points below the line
y = mx + b
S To graph without your calculator,
you need 2 points to define a line.
S Use the y-intercept for the first point
(x = 0 so y = b)
S Set y = 0 to find the second point
S (x = − b/m when y = 0).
S Use a RULER to draw your lines!
Accuracy & Precision
S Accuracy is how close you are to the true
value. Think of a “bullseye” in darts.
S Precision is how close all your measurements
are to each other.
S Can you be accurate but not precise?
S Can you be precise but not accurate?
Density
S Anyone remember
the formula for
density?
S Anyone remember
the “density heart?”
D=m/V
OMG, we just zoomed into Chapter 3
S We don’t use x to solve Chem problems.
S We use real variables that mean something
S D = density
S m = mass (units of grams)
S V = volume (units of mL or L or cm3)
D=m/V
Write this down
and learn it!
OMG, we just zoomed into Chapter 3
S Density equals mass divided by volume. That’s what
the formula is telling you. (Most of you probably
already knew that).
S Density has units of “g/mL” or “g/cm3”
S But what does density really mean? Density tells
you how much 1 milliliter (volume) is going to
weigh.
S One mL of water weighs 1 g. One mL of gold
weighs 19.3 g.
D=m/V
S If you know 2 of those 3 variables, you can solve for
(calculate) the remaining one. This is basic, basic
algebra 1.
S Rearrange the formula so that mass is by itself.
S Rearrange the formula so that volume is by itself.
D=m/V
S If you know 2 of those 3 variables, you can solve for
(calculate) the remaining one. This is basic, basic
algebra 1.
S Rearrange the formula so that mass is by itself.
S Rearrange the formula so that volume is by itself.
m=VxD
D=m/V
S If you know 2 of those 3 variables, you can solve for
(calculate) the remaining one. This is basic, basic
algebra 1.
S Rearrange the formula so that mass is by itself.
m=VxD
S Rearrange the formula so that volume is by itself.
V=m/D
D=m/V
S If you know 2 of those 3 variables, you can solve for
(calculate) the remaining one. This is basic, basic
algebra 1.
S Rearrange the formula so that mass is by itself.
m=VxD
S Rearrange the formula so that volume is by itself.
V=m/D
S Write these into your notes. You don’t need to
memorize all 3. Memorize the top one and
rearrange when you need one of the others!
K = °C + 273
S This formula converts Celcius temperature into Kelvin temperature.
S This will be on the SOL.
S For some problems in Chemistry, we need to use Kelvin temperature.
S We don’t use Fahrenheit temp. If this is first semester, it’s probably
about 80°F outside (maybe 30°F it is second semester). But you do need
to know how to convert from Celcius to Kelvin (and vice versa).
S What is the formula if you want °C by itself ?
S Answer:
°C = K − 273
Helpful Formulas
for Unit 1
S Density
S D = m/V
S Temperature Conversions
S K = °C + 273 (note K does not have a ° symbol)
S °C = K − 273
S °C = (°F − 32) ÷ 1.8 (won’t be on test)
S ΔT = T2 − T1
or
ΔT = Tfinal − Tinitial
Directly Proportional
S Directly proportional means that as one goes up,
the other goes up too.
S For matter, kinetic energy (KE) is directly
proportional to Kelvin temperature (K)
S If you graph these variables, you will get a
straight line with a POSITIVE slope.
Inversely Proportional
S Inversely proportional means that as one goes
up, the other goes down (and vice versa).
S For any gas, pressure (P) is inversely
proportional to volume (V)
S If you graph these variables, you will get a
straight line with a NEGATIVE slope
(sometimes a curve with a negative slope).
Let’s Do Some
Math!
S Density
S If a marble weighs 10.0 g and has a volume of 5.0
mL what is the density of the marble? Use correct
units.
S Another marble with the same density has a mass of
15.0 g. What is the volume of that marble? Use
correct units.
S A different marble has a density of 3.0 g/mL. If that
marble has a volume of 10.0 mL, what is the mass of
that marble? Use correct units.
Let’s Do Some
Math!
S Temperature
S If it is 104°F in Fredericksburg, what is the temp in
°C?
S What is the temp in K?
S If it is -40°F in Fredericksburg, what is the temp in
°C?
S What is the temp in K?
S If a sample of matter is 298K, what is the temp in
°C?
Helpful Formulas
Unit 1
S How to Figure out your Quiz Grade:
S Your Grade ÷ 25 × 100 = SCORE
S Calculating Error
S Error = |Your Number − True Number|
S % Error = Error ÷ True Number × 100
Let’s Do Some
Math!
S Error Analysis
S The accepted value for the density of a penny is 7 g/cm3.
S You measure 3 pennies and calculate the density as
S 7.20 g/cm3
S 6.90 g/cm3
S 7.40 g/cm3
S What is the average density? What is the error? What is the
percent error?
Helpful Formulas
Unit 1
S SI Units and Conversions
S Need to know what these prefixes mean
S Kilo (k)
S Centi (c)
S Milli (m)
S Micro (μ)
S Nano (n)
ex 1 kg = 1000 g
ex 100 cm = 1 m
ex 1,000 mL = 1 L
ex 1,000,000 μg = 1 g
ex 1,000,000,000 nm = 1 m
Dimensional
Analysis
S The base unit can change, but the prefix means
the same thing
S 1,000 mm = 1 m
S 1,000 mg = 1 g
S 1,000 mL = 1 L
S Milli- ALWAYS means that there are 1,000 divisions of
the base unit.
Let’s Do Some
Math!: First, plan!
S Convert 45 cm to mm?
S To do this you need to know the conversion factors
S 100 cm = 1 m
S 1,000 mm = 1 m.
S First step: convert cm to meters.
S Second step: convert meters to mm.
S To find the answer: cancel out units until you have the units
you are looking for.
Let’s Do Some Math!
Then, use the calculator.
S Convert 45 cm to mm?
S 45 cm ×
1m
100 cm
S 45 cm ×
1m
100 cm
× 1,000 mm =
?
1m
× 1,000 mm =
450 mm
1m
SThe framework works!
Let’s Do Some Math!
You try some!
S Convert 345 μg to kg?
S Convert 14.6 mL to L?
S Convert 1 hour to seconds?
S Convert 100 cm3 to mL
S Convert 500 nm to mm?
Some Other Chemistry
Graphs
Phase Diagrams
Heating Curves
Radioactive Decay
Reaction Progress
Phase Diagram for H2O
Critical Point
Triple
Point
A phase is a “state” of
matter.
Solid phase
Liquid phase
Gas phase
We don’t “do” plasma.
Phase Diagram for H2O
Critical Point
Triple
Point
The triple point is the
only point on the graph
where all 3 phases are
at equilibrium.
The critical point is the
END of the graph.
Phase Diagram for H2O
Boiling Point
Melting
Point
The lines show the
pressure/temperature
points where the phase
changes from one to the
other.
When P = 1 atm, you
can read the MP and
BP right off the graph.
Heating Curve for H2O
Solid between A&B,
liquid between C&D,
gas between E&F
Heating Curve for H2O
Melts between B & C
Boils between D & E
Why doesn’t the temp rise when water is melting?
Radioactive Decay
After 1 half life, 50% remains. After 2 half lives, 25% remains.
HALF of whatever is left decays during each half life.
Sometimes, just reading the
graph is enough!
The point where vapor pressure crosses atmospheric pressure
(101.3kPa) = boiling point. The lower the vapor pressure, the
higher the boiling point.
Rxn =
abbreviation
for reaction
Rxn Progress
Rxn Progress
Significant Figures
aka Sig figs
S If you didn’t know the
exact amount of
coffee, is adding one
more drop significant?
S In other words, by
adding one more
drop, do you now
know that it’s exactly
200.05mL?
Sig Fig Rules
S 1. All digits except for zero are ALWAYS significant.
S How many sig figs does 12.34 have?
S How many sig figs does 45.6 have?
S 2. Zero is SOMETIMES significant.
S 0’s between other numbers are significant.
S
S
100.3 has 4 sig figs.
10101010101 is totally significant. Every one of the digits is significant. Make
sense?
S 0’s at the end of a number are significant IF they are also to the right of the
decimal point.
S
BOTH things must be true. End of the number. AND, to the right of the decimal
point.
S Zeros are the beginning of a number are never significant
Sig Fig Rules
S Therefore.
S 14.50 has 4 sig figs (end of the number
AND right of the decimal point).
S 1,450 has 3 sig figs (zero is at end of the
number BUT to the LEFT of the decimal
point).
S 0.02345 has 4 sig figs (zeros are at the
beginning of the number).
Sig Figs
S How many sig figs do each of the following have
S 1234.0
S 0.000000000000000000001
S 0.000100
S 50
S 50.0
S 60 min = 1 hour
S
How many sig figs does 60 have?
S
How many sig figs does 1 have?
Rules for Sig Figs if you take
the measurement yourself.
S All of the digits you can read directly off the measuring instrument
are significant.
S The first digit you can ESTIMATE is also significant.
S Suppose you have water in a graduated cylinder. The meniscus is
EXACTLY on 20 mL. The next mark up is 20.1 mL. What should
you record the volume as?
S Suppose the meniscus was between 20 and 20.1 mL. What then?
Rules for Sig Figs when
doing math problems.
S When adding/subtracting, use the number of decimal places to
decide.
S 2.22 + 3.333 = 5.553.
S 2.22 has 2 decimal places. 3.333 has 3 decimal places. Your answer can only
have 2 (because 2 is less than 3).
S Your answer is 5.55.
S When multiplying/dividing, use the least number of sig figs for the
numbers you are working with.
S 2.00 x 6 = 12.00
S 2.00 has 3 sig figs. 6 has only 1 sig fig. Your answer can only have 1 (because
1 is less than 3).
S What is your answer? The answer CANNOT be 12, since that has 2 sig figs!!
Scientific Notation
S Put the following in scientific notation.
S 150,000
S 0.000045
S Put the following in regular notation
S 4.05 x 108
S 2.34 x 10-4
Let’s Do Some Math!
Answer from above.
S Answers:
S Convert 345 μg to kg? 3.45 x 10-7 kg
S Convert 14.6 mL to L? 0.0146 L
S Convert 1 hour to seconds? 3,600 sec
S Convert 100 cm3 to mL 100 mL
S Convert 500 nm to mm? 5 x 10-4 mm
Homework
1. Stay tuned! Because there will be some.
The End