Chemistry is where youlearn 2 + 2 = 10 or something. —Dennis Rodman

Chemistry Math With Chemistry-specific graphs

VariablesIndependent

Variable “I” changeGraphed on “x” axis

DependentVariable which “Depends” on independent variableTested during experimentGraphed on “y” axis

ControlVariables you control so they do not change and mess

up your experimentNever 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 FitReal 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 + bTo 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!

Helpful Formulas

Unit 1DensityD = m/V

Temperature ConversionsK = °C + 273 (note K does not have a °

symbol) °C = K − 273°C = (°F − 32) ÷ 1.8ΔT = 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!

DensityIf 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!

TemperatureIf 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?

Helpful Formulas

Unit 1How to Figure out your Quiz Grade:Your Grade ÷ 25 × 100 = SCORE

Calculating ErrorError = |Your Number − True Number|% Error = Error ÷ True Number × 100

Let’s Do Some Math!

Error AnalysisThe 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

You should record your final answer as 2.6% after rounding.

Helpful Formulas

Unit 1SI Units and Conversions

Need to know what these prefixes meanKilo (k) ex 1 kg = 1000 gCenti (c) ex 100 cm = 1 mMilli (m) ex 1,000 mL = 1 LMicro (μ) ex 1,000,000 μg = 1 g Nano (n) ex 1,000,000,000 nm = 1 m

Dimensional Analysis

The base unit can change, but the prefix means the same thing100 cm = 1 m100 cg = 1 g100 cL = 1 LCenti 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 factors100 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 × 1 m × 1,000 mm

= ? 100 cm 1 m45 cm × 1 m × 1,000 mm =

450 mm 100 cm 1 m

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 mLConvert 500 nm to mm?

Let’s Do Some Math!

Answers:Convert 345 μg to kg? 3.45 x 10-7 kgConvert 14.6 mL to L? 0.0146 L Convert 1 hour to seconds? 3,600 secConvert 100 cm3 to mL 100 mLConvert 500 nm to mm? 5 x 10-4 mm

Let’s Do Some Math!

Answers:Convert 345 μg to kg? 3.45 x 10-7 kgConvert 14.6 mL to L? 0.0146 L Convert 1 hour to seconds? 3,600 secConvert 100 cm3 to mL 100 mLConvert 500 nm to mm? 5 x 10-4 mm

Some Other Chemistry Graphs

Phase Diagrams

Heating Curves

Radioactive Decay

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

A phase is a “state” of matter.

Solid phaseLiquid phaseGas phase

We don’t “do” plasma.

Critical Point

Triple Point

Phase Diagram

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.

Critical Point

Triple Point

Phase Diagram

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.

Boiling Point

MeltingPoint

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.

Rxn Progress

The reaction is exothermic (products have less energy than reactants). Enzyme = biological catalyst.

Rxn = abbreviation for reaction

Rxn Progress

This reaction is endothermic. Products are higher than reactants (have more potential energy).

The End