### Chem Math - Fredericksburg City Public Schools

```Chemistry is where you
learn 2 + 2 = 10 or something.
—Dennis Rodman
Chemistry Math With Chemistry-specific graphs
Variables
 Independent
 Variable “I” change
 Graphed on “x” axis
 Dependent
 Variable which “Depends” on independent variable
 Tested during experiment
 Graphed on “y” axis
 Control
 Variables you control so they do not change and mess up
 Never graphed
Graphing Variables
Slope = rise/run
Slope = mass/volume
Slope = density
We don’t graph just to graph; the graph and
the data tells us something meaningful.
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
 To graph without your calculator,
you need 2 points to define a line.
 Use the y-intercept for the first
point (x = 0 when y = b)
 Set y = 0 to find the second point
(x = − b/m when y = 0).
 Use a RULER to draw your lines!
Unit 1
 Density
 D = m/V
 Temperature Conversions




K = °C + 273 (note K does not have a ° symbol)
°C = K − 273
°C = (°F − 32) ÷ 1.8
ΔT = T2 − T1
or ΔT = Tfinal − Tinitial
Directly Proportional
 Directly proportional means that as one goes
up, the other goes up too.
 For matter, kinetic energy (KE) is directly
proportional to Kelvin temperature (K)
 If you graph these variables, you will get a
straight line with a POSITIVE slope.
Inversely Proportional
 Inversely proportional means that as one goes
up, the other goes down (and vice versa).
 For any gas, pressure (P) is inversely
proportional to volume (V)
 If you graph these variables, you will get a
straight line with a NEGATIVE slope.
Let’s Do Some
Math!
 Density
 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.
 Another marble with the same density has a mass
of 15.0 g. What is the volume of that marble? Use
correct units.
 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!
 Temperature
 If it is 104°F in Fredericksburg, what is the temp in
°C?
 What is the temp in K?
 If it is -40°F in Fredericksburg, what is the temp in
°C?
 What is the temp in K?
 If a sample of matter is 298K, what is the temp in
°C?
Unit 1
 Calculating Error
 Error = |Your Number − True Number|
 % Error = Error ÷ True Number × 100
Let’s Do Some
Math!
 Error Analysis
 The accepted value for the density of a penny is 7 g/cm3.
 You measure 5 pennies and calculate the density as






7.50 g/cm3
7.20 g/cm3
6.90 g/cm3
7.40 g/cm3
6.90 g/cm3
What is the average density? What is the error? What is the
percent error?
Let’s Do Some
Math!
 What is the average density? 7.18 g/cm3.
 What is the error? |7.18 − 7| = 0.18 g/cm3.
 What is the percent error? 0.18 ÷ 7 x 100 = 2.57142857
rounding.
Unit 1
 SI Units and Conversions
 Need to know what these prefixes mean





Kilo (k)
Centi (c)
Milli (m)
Micro (μ)
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
 The base unit can change, but the prefix means
the same thing




100 cm = 1 m
100 cg = 1 g
100 cL = 1 L
Centi ALWAYS means that there are 100 divisions of
the base unit.
Let’s Do Some
Math!
 Convert 45 cm to mm?
 To do this you need to know the conversion factors
 100 cm = 1 m
 1,000 mm = 1 m.
 First step: convert cm to meters.
 Second step: convert meters to mm.
 To find the answer: cancel out units until you have the
units you are looking for.
Let’s Do Some
Math!
 Convert 45 cm to mm?
 45 cm ×
1m
100 cm
 45 cm ×
1m
100 cm
× 1,000 mm =
?
1m
× 1,000 mm =
1m
450 mm
Let’s Do Some
Math!
 Convert 345 μg to kg?
 Convert 14.6 mL to L?
 Convert 1 hour to seconds?
 Convert 100 cm3 to mL
 Convert 500 nm to mm?
Let’s Do Some
Math!
 Convert 345 μg to kg? 3.45 x 10-7 kg
 Convert 14.6 mL to L? 0.0146 L
 Convert 1 hour to seconds? 3,600 sec
 Convert 100 cm3 to mL 100 mL
 Convert 500 nm to mm? 5 x 10-4 mm
Let’s Do Some
Math!
 Convert 345 μg to kg? 3.45 x 10-7 kg
 Convert 14.6 mL to L? 0.0146 L
 Convert 1 hour to seconds? 3,600 sec
 Convert 100 cm3 to mL 100 mL
 Convert 500 nm to mm? 5 x 10-4 mm
Some Other Chemistry
Graphs
Phase Diagrams
Heating Curves
Reaction Progress
Not all chemistry graphs will be straight lines. But most
will. Let’s see some distinctive ones which aren’t.
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
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
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
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?
After 1 half life, 50% remains. After 2 half lives, 25% remains.
HALF of whatever is left decays during each half life.
Rxn =
abbreviation
for reaction
Rxn Progress
The reaction is exothermic (products have less energy
than reactants). Enzyme = biological catalyst.
Rxn Progress
This reaction is endothermic. Products are higher than
reactants (have more potential energy).
The End
```