chemistry is where you learn 2 + 2 = 10 or something. —dennis rodman chemistry math with...

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Chemistry is where you learn 2 + 2 = 10

or something.

—Dennis Rodman

Chemistry Math With Chemistry-specific graphs

Chemistry = Memorization?FALSE!

http://www.magazine-agent.com/officials-logic-problems/magazine

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?

1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845 Pretty hard? Pretty Easy?

Why?

Easy huh? OK, what’s the next number in

the sequence? How about the next 5 numbers?

1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461,

10923, 21845http://www.antiqueradiomuseum.org/RR%20Rule%20Book%20for%20CMSP&P%20RR.jpg

The numbers don’t seem to follow any kind of pattern.

But, what if you knew a rule? It wouldn’t just be memorization then.

OK, good point! The rule is: Start with 1. Double and add 1. Double and subtract 1. And so on.

You just wish it was that EASY!

Learn HOW to do the problem; don’t just memorize the steps!

http://familyfun.go.com/Resources/printable-previews/previews/beaver_memorygame_august2.jpg

Doesn’t “knowing the rule” make the list easier to memorize?

You don’t have to memorize a bunch of unrelated numbers.

IF YOU KNOW the rule, you can generate the number list on the test easily. Anytime! Anywhere!

Don’t

Can you make sense out of NONSENSE?

Force Hour Cis Neigh

Koran Fodder Count Shun

Heaven Brat An

Ye Farth Ent

Sago Upon Anew

Figured it out yet?

The Gettysburg Addresshttp://www.old-picture.com/defining-moments/pictures/Abraham-Lincoln-Antietam-Battlefield.jpg

http://en.wikipedia.org/wiki/Gettysburg_Address

“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.”

Being able to look at something new, and make sense of it is an important skill for the rest of this course.

You have to be able to DO chemistry in your mind.

Yes, Ms Rackley, I know this was Antietam, but it’s a nice picture.

Unfortunately (for you) I’m not Bill Nye

http://www.tvgasm.com/newsgasm/Bill-nye.jpg

In Chemistry, when we have numbers, most of the time we do one of three things: Multiple 2 x 3 Divide 2 / 3 Divide 3 / 2

If you can figure out which operation to do when, you can actually solve the problem.

That’s our goal.

What would Bill Nye do?

Units TELL you the right ANSWER

If your units don’t work out right, your answer is wrong.

Don’t just ignore wrong units. It is a big clue for you.

LISTEN to the units!

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. Like density!

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 + b To graph without your calculator,

you need 2 points to define a line. Use the y-intercept for the first

point (x = 0 so y = b) Set y = 0 to find the second point

(x = − b/m when y = 0). Use a RULER to draw your lines!

Accuracy & Precision

Accuracy is how close you are to the true value. Think of a “bullseye” in darts.

Precision is how close all your measurements are to each other.

Can you be accurate but not precise? Can you be precise but not accurate?

Density Anyone remember the formula for density?

Anyone remember the “density heart?”

D = m / VOMG, we just zoomed into Chapter 3

We don’t use x to solve Chem problems.

We use real variables that mean something D = density m = mass (units of grams) V = volume (units of mL or L or cm3)

D = m / V

OMG, we just zoomed into Chapter 3

Density equals mass divided by volume. That’s what the formula is telling you. (Most of you probably already knew that).

Density has units of “g/mL” or “g/cm3”

But what does density really mean? Density tells you how much 1 milliliter (volume) is going to weigh.

One mL of water weighs 1 g. One mL of gold weighs 19.3 g.

Write this down and learn it!

D = m / V

If you know 2 of those 3 variables, you can solve for (calculate) the remaining one. This is basic, basic algebra 1.

Rearrange the formula so that mass is by itself.

Rearrange the formula so that volume is by itself.

D = m / V




m = V x D

D = m / V




m = V x D

V = m / D

D = m / V




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!

m = V x D

V = m / D

K = °C + 273

This formula converts Celcius temperature into Kelvin temperature.

This will be on the SOL.

For some problems in Chemistry, we need to use Kelvin temperature.

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).

What is the formula if you want °C by itself?

Answer: °C = K − 273

Helpful Formulasfor 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 (won’t be on test) 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 (sometimes a curve 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.


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?

Helpful Formulas

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

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


Error Analysis The accepted value for the density of a penny is 7

g/cm3. You measure 3 pennies and calculate the density

as 7.20 g/cm3

6.90 g/cm3

7.40 g/cm3

What is the average density? What is the error? What is the percent error?

Helpful Formulas

Unit 1 SI Units and Conversions

Need to know what these prefixes mean Kilo (k) ex 1 kg = 1000 g Centi (c) ex 100 cm = 1 m Milli (m) ex 1,000 mL = 1 L Micro (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 thing 1,000 mm = 1 m 1,000 mg = 1 g 1,000 mL = 1 L Milli- ALWAYS means that there are 1,000

divisions of the base unit.

Let’s Do Some Math!: First,

plan! 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! Then, use

the calculator. Convert 45 cm to mm? 45 cm × 1 m × 1,000 mm = ? 100 cm 1 m 45 cm × 1 m × 1,000 mm = 450 mm 100 cm 1 m

The framework works!


You try some! 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?

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


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


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.

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 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).

Significant Figuresaka Sig figs

If you didn’t know the exact amount of coffee, is adding one more drop significant?

In other words, by adding one more drop, do you now know that it’s exactly 200.05mL?

Sig Fig Rules 1. All digits except for zero are ALWAYS significant.

How many sig figs does 12.34 have? How many sig figs does 45.6 have?

2. Zero is SOMETIMES significant. 0’s between other numbers are significant.

100.3 has 4 sig figs. 10101010101 is totally significant. Every one of the digits is

significant. Make sense? 0’s at the end of a number are significant IF they are also to the

right of the decimal point. BOTH things must be true. End of the number. AND, to the right of

the decimal point.

Zeros are the beginning of a number are never significant

Sig Fig Rules

Therefore. 14.50 has 4 sig figs (end of the

number AND right of the decimal point).

1,450 has 3 sig figs (zero is at end of the number BUT to the LEFT of the decimal point).

0.02345 has 4 sig figs (zeros are at the beginning of the number).

Sig Figs How many sig figs do each of the following have

1234.0 0.000000000000000000001 0.000100 50 50.0 60 min = 1 hour

How many sig figs does 60 have? How many sig figs does 1 have?

Rules for Sig Figs if you take the

measurement yourself. All of the digits you can read directly off the measuring

instrument are significant.

The first digit you can ESTIMATE is also significant.

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?

Suppose the meniscus was between 20 and 20.1 mL. What then?

Rules for Sig Figs when doing math

problems. When adding/subtracting, use the number of decimal places to

decide. 2.22 + 3.333 = 5.553.

2.22 has 2 decimal places. 3.333 has 3 decimal places. Your answer can only have 2 (because 2 is less than 3).

Your answer is 5.55.

When multiplying/dividing, use the least number of sig figs for the numbers you are working with. 2.00 x 6 = 12.00

2.00 has 3 sig figs. 6 has only 1 sig fig. Your answer can only have 1 (because 1 is less than 3).

What is your answer? The answer CANNOT be 12, since that has 2 sig figs!!

Scientific Notation

Put the following in scientific notation. 150,000 0.000045

Put the following in regular notation 4.05 x 108

2.34 x 10-4


Answer from above. Answers:

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

Homework1. Stay tuned! Because there will be some.

The End

chemistry is where you learn 2 + 2 = 10 or something. —dennis rodman chemistry math with...

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