Lecture 1: chemistry, measurement, conversions TopicBrown Chapter 1 1.Science and Chemistry What is science? The scientific method What is chemistry?1.1 2.What is matter?1.2 States of matter Pure substances vs. mixtures Physical vs. chemical change1.3 3.Measurement, metric units & prefixes1.4 Derived units and density Exact & inexact numbers Uncertainty, precision & accuracy1.5 Significant figures & use in calculation Scientific notation 4.Dimensional analysis = conversions1.6 With multiple conversion factors Conversions with unit prefixes With cubed unit volumes

Unit conversion is a fundamental & critical skill Railroad tracks work well. You must master conversions - by any method.

“Dimensional analysis” p.24-8 This is just another term for unit conversion and it’s a cornerstone of chemistry, other sciences and engineering. Conversion factors Are fractions with different units for the numerator & denominator. All conversion factors are exact numbers with true values of one. Conversion factors can be “flipped” either way cmor1 inch 1 inch2.54 cm I teach the “railroad track” method. You are welcome to use any method you wish if your answer is correct and you show the work! 1.Start with the value with one unit. 2.Operate on it with the conversion factor to change units. 3.Units cancel out diagonally. unit given new unit = new unit unit given

Examples: dimensional analysis 1. Convert the height of a 8.5 inch beer bottle into centimeters. 8.5 in 2.54 cm = cm --> 22 cm 1 in 2. If a woman has a mass of 115 lb, what is her mass in grams? (Sanity check: Is she going to feel better or worse when she sees this new value?) Worse! There are lots of grams one pound, so the result is going to be big! The back cover of the text gives: g/1 lb, or 1 lb/ g. But you know that g is the new unit, & lb is the old unit, so: 115 lb g = g --> 5.22x10 4 g (3 sf) 1 lb 3. Convert 0.5o lb to grams. (Again, are there going to be more grams or fewer grams?) 0.50 lb g = g -> 230 g 1 lb Remember to place the new unit on top and the old unit below. When in doubt FOLLOW THE UNITS !!!!!!

190 pg Conversions with unit prefixes When converting prefixes only, students tend to become confused about whether their factors are “right-side-up” or “upside-down” x 10 3 km 10 3 m = x 10 6 m 1 km = 1.90 x g Convert 190 pg to grams. This method helps me: 1.Start with the value given. (190 pg) g pg 2.Set up the units of the conversion factor to cancel old units. 3.Ask which conversion factor unit is larger. (grams) 4.Assign that larger unit a value of one.(1 gram) 5.Assign the smaller unit 10 raised to a positive exponent. (pico = 12) 6.Do the math, ignoring the one.(Here divide 190 by ) Convert x 10 3 km into meters.

Keys to problem solving If you find conversion problems challenging think about using these steps when trying to solve a problem. 1. Read the problem. Read it again. 2. Stop – think – try to visualize the amounts involved… … and or the process you’ll use to solve the problem. 3. Start setting up the solution and show the units. 4. In many cases, asking yourself if the answer makes sense can provide a helpful ‘sanity check.’

Using more than one conversion factor Again, it’s all about choosing the proper conversion factors & setting up the problem to solve for desired UNIT! The average speed of a nitrogen molecule in air at 25°C is 515 m/s. Convert this speed to miles/hour. 515 m1 km 1 mile 60 s 60 min = 1.15x10 3 miles 1 s 10 3 m km 1 min 1 hour hour 2-part strategy: 1) meters ----> km ----> miles 2) seconds ----> minutes ----> hours 100 cm/1 m1 in/2.54 cm 8 m 100 cm 1 in = in --> 300 in 1 m 2.54 cm miles hour It also helps to have a STRATEGY. You’re asked to convert 8 meters to inches. Think setup & strategy! 8 mcm in

Conversions with cubed-length volumes This sort of problem requires the same strategies & set-ups as you’ve seen before, but adds a new twist involving cubing. Why? Because volumes can be calculated by cubing lengths. What is the mass (g) of a piece of gold that’s 2 inches on each side? STRATEGY: in > in > cm > g The Earth’s oceans contain 1.36x10 9 km 3 of water. Convert to liters! STRATEGY: km > m > L Remember! Cube both the value and the unit. cube! cm 3 g 1 3 in 3 cm in cm g = 633 g --> 600 g 1 3 in 3 1 cm m 3 1 L 1 3 km m x10 9 km m 3 1 L = 1.36x10 21 L 1 3 km m 3

Dimensional analysis FAQs 1. What’s the numerical value of a conversion factor? 3. What are the most common mistakes students make? 4. Is there a quick check to tell me whether my answer is right? Because the values of the numerator & denominator are actually equal. Conversions go wrong when students a) use the wrong conversion factors, or b) use the factor upside down. So, chose the factor that has both old and new units. Place the old unit on the bottom & the new unit on top. Don’t start playing with the numbers until you’ve successfully cancelled units. And don’t forget to cube lengths & units when converting lengths to volumes!!!!!!! Yes, it’s called an order of magnitude sanity check. If you know, very roughly, the size of your answer you’ll be able to quickly recognize & correct any errors. Know whether you expect more or fewer numbers in your answer than in the value you start with. More or much more? Less, or way, way less? 2. Do conversion factors have significant digits? Technically, the non-1 value does have sig figs. However, the number of sig figs given is often dependent on the reference; you’ll find a range of values when looking up the number of quarts in a liter. In science, we limit the number of sig figs in a result by the number of sig figs in the data.