 Chemistry is where you learn = 10 or something. —Dennis Rodman Chemistry Math With Chemistry-specific graphs

Chemistry = Memorization? FALSE!  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,  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,  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!  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?  ForceHourCisNeigh  KoranFodderCountShun  HeavenBratAn  YeFarthEnt  SagoUponAnew  Figured it out yet?

The 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  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

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 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 / V OMG, 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 cm 3 )

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/cm 3 ”  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  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. m = V x D

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. m = V x D V = m / D

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.  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  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 Formulas for Unit 1  Density  D = m/V  Temperature Conversions  K = °C (note K does not have a ° symbol)  °C = K − 273  °C = (°F − 32) ÷ 1.8 (won’t be on test)  Δ T = T 2 − T 1 or Δ T = T final − T initial

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.

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?

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

Let’s Do Some Math!  Error Analysis  The accepted value for the density of a penny is 7 g/cm 3.  You measure 3 pennies and calculate the density as  7.20 g/cm 3  6.90 g/cm 3  7.40 g/cm 3  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 μ g = 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!

Let’s Do Some Math! You try some!  Convert 345 μ g to kg?  Convert 14.6 mL to L?  Convert 1 hour to seconds?  Convert 100 cm 3 to mL  Convert 500 nm to mm?

Some Other Chemistry Graphs Phase Diagrams Heating Curves Radioactive Decay Reaction Progress

Phase Diagram for H 2 O A phase is a “state” of matter. Solid phase Liquid phase Gas phase We don’t “do” plasma. Critical Point

Phase Diagram for H 2 O 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

Phase Diagram for H 2 O 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

Heating Curve for H 2 O Solid between A&B, liquid between C&D, gas between E&F

Heating Curve for H 2 O 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 Rxn = abbreviation for reaction

Rxn Progress

Significant Figures aka 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 mL?

Sig Fig Rules  1. All digits except for zero are ALWAYS significant.  How many sig figs does have?  How many sig figs does 45.6 have?  2. Zero is SOMETIMES significant.  0’s between other numbers are significant.  has 4 sig figs.  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.  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).  has 4 sig figs (zeros are at the beginning of the number).

Sig Figs  How many sig figs do each of the following have     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 has 2 decimal places has 3 decimal places. Your answer can only have 2 (because 2 is less than 3).  Your answer is  When multiplying/dividing, use the least number of sig figs for the numbers you are working with.  2.00 x 6 =  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   Put the following in regular notation  4.05 x 10 8  2.34 x 10 -4

Let’s Do Some Math! Answer from above.  Answers:  Convert 345 μ g to kg? 3.45 x kg  Convert 14.6 mL to L? L  Convert 1 hour to seconds? 3,600 sec  Convert 100 cm 3 to mL 100 mL  Convert 500 nm to mm? 5 x mm

Homework 1. Stay tuned! Because there will be some.

The End