Lecture 1: chemistry, measurement, conversions Topic Brown Chapter 1 Science and Chemistry What is science? The scientific method What is chemistry? 1.1 What is matter? 1.2 States of matter Pure substances vs. mixtures Physical vs. chemical change 1.3 Measurement, metric units & prefixes 1.4 Derived units and density Exact & inexact numbers Uncertainty, precision & accuracy 1.5 Significant figures & use in calculation Scientific notation Dimensional analysis = conversions 1.6 With multiple conversion factors Conversions with unit prefixes With cubed unit volumes Each week we’ll start with an outline of the material to be covered that week. These lists should help you prepare for quizzes and tests.

Measurement is an essential part of chemistry. Quantitation uses the metric system. Chemistry uses scientific notation & unit prefixes. Amounts are usually very small. The general process of advancing scientific knowledge by making experimental observations and by formulating hypotheses, theories, and laws. It’s a systematic problems solving process AND it’s hands-on….. Experiments must be done, data generated, conclusions made. This method is “iterative”; it requires looping back and starting over if needed. [Why do you think they call it REsearch?] Often years, decades or more of experiments are required to prove a theory. While it’s possible to prove a hypothesis wrong, it’s actually NOT possible to absolutely prove a hypothesis correct as the outcome may have had a cause that the scientist hasn’t considered.

Measurement: metric base units Like the rest of the world, chemistry uses the metric system. Notes: Chemists tend to use grams, rather than kg, for mass. Chemists tend to use Celsius for most temperature data, but use Kelvin for gas temperatures. I’ll always give you English-metric conversion factors on quizzes & exams. Get to know them! p.14

Metric prefixes! Prefixes are used to more easily describe fractions or multiples of base metric units. Deci is rarely used & chemists are more concered with the smaller units. However, you’ll need to learn the rest! When doing conversions it’s quite useful to know how to easily multiply and divide exponents - might want to review this: Multiplying numbers with exponential notation? Multiply the numbers Add the exponents 2. Dividing? Divide the numbers Subtract the exponents An easier way? Don’t worry about the sign of the exponent, just the number. And know whether the prefix is larger or smaller than the base unit. p.14

What’s a derived SI unit? A derived unit is a “complex” unit created by multiplying or or dividing one unit by another. Speed has units of meters/second (m/s) Density has units of mass per volume (g/mL = g/cm3 = g/cc) Questions for you: Is density an intensive or extensive property? What’s the difference between density and mass? 3. How can you easily measure the density of an odd-shaped object? p.17 & 20

Calculating density It’s essential that you have the ability to rearrange equations in order to solve for the chosen variable. And ALWAYS show units! = m/v Calculate the density of beer if a keg has a mass of 7.71x104 g & a volume of 58.7 L.  = m = 7.71x104 g = 1.31 g/mL (Known value ~1.050 g/mL) v 5.87x104 mL What’s the mass of 3 mL of gold if its density is 19.3 g/cm3? You may need to review this issue of rearranging equations - think carefully and follow through with that if necessary. Why have I rounded the answers to the second and third answers? Because of significant digits - more to come on this soon! m = v --> 3 mL 19.3 g = 57.9 g --> 60 g  1 mL What volume is occupied by 2 kg of peanuts if their density is 0.272 g/mL? v = m --> 2 kg = 2000 g --> v = 2000 g = 7352.9 --> 7 L  0.272 g/mL

Exact, inexact and uncertainty Numbers or values can be described as either exact or inexact: Exact Values are known precisely; or values given as references. Conversion factors are exact. Results of most counting are exact. Inexact Values measured by humans & their instruments; some uncertainty. Uncertainty Some level of uncertainty exists in all inexact numbers (or all measured values) The last digit is generally the most uncertain, since it represents the technical limits of the instrument used. Instruments are least accurate at the ends of their ranges. 2.2405  0.0001 g The ten thousandth place is the least certain as it’s the smallest calibration on the instrument. The  notation also shows this by saying that that 5 could easily be a 4 or a 6. Examples of exact numbers? Twelve donuts to a dozen 24 bottles in a case 32 students in a class 2.54 cm/inch Examples of inexact numbers? Your weight this morning The width of this room The number of popular votes in presidential elections - because this number is too large to count precisely or accurately p.20-1

Precision vs. accuracy Both terms are used to discuss how certain, or uncertain, data, results or other types of information are. But the terms are often confused. Precision How closely do individual measurements agree with each other? Accuracy How close is the measurement to a truth or known value? Precision is easier in the lab. Accuracy is always quite difficult to achieve and requires great training, experience and instrumentation. Precision is possible for most of us to achieve with practice and care. Determining precision requires that we perform multiple tests or trials and then calculate means and standard deviations to see how much variation there is within data. More on that in the lab next week. Determining accuracy requires that we know the “truth” or reference value that we’re investigating, and how precise our data is. Without precision you’ll never achieve accuracy. Questions for you? Which is easier to achieve in the lab? How can we know if we are precise? How can we know if we’re accurate? p.21

Significant figures - ZEROs All digits of a measured value are significant, thought the last value is usually least certain. So why is this such a pain in the #@&!? 1. Zeros 2. Calculations Zeros in a value may or may not be significant. Here are the rules: 1. Trapped zeros - between non-zero digits are ALWAYS significant 1005 kg, 1.03 seconds 2. Leading zeros - before any non-zeros are NEVER significant 0.0039 g, 0.2 cm This requires some practice. It will be tested for on quizzes and exams. 3. Trailing zeros - may be significant IF WITH A DECIMAL 3500 NO, only 2 sf 3500.0 YES, all five are sf p.21-2

Significant figures in calculations There are two simple rules that are OFTEN ignored… to the peril of chemistry grades. You want calculated answers to reflect the degree of calibration of the instruments used to gather the data. 1. Multiplication & division: least sf rules! The answer has only as many sf as the value with the lowest sf. (6.221 cm)(5.2 cm) = 32.3492 cm2 -> 32 cm2 2. Addition & subtraction: limit number of sf after the decimal So the number of digits following the decimal is limited by the value in the calc with fewest sf after the decimal. Number before the decimal is not limited. 20.4 + 1.322 + 83 = So you can’t depend on a calculator to tell you how many sf should be in your answer. Calculators lie! You can use them to do the calculation, but you’ve got to decide how many of the digits spat back at you are significant (sfs). I’ll grade based on sfs through the first exam, and less so later. However, I focus on sf in lab, so do learn the rules and practice them. What about rounding? It’s most important that you’re consistent and don’t round to improve your results. Generally, round up at five an over. 104.722 -> 105 There are 1609.344 m in a mile. How many meters are there in 1.35 miles? 1.35 miles 1609.344 m = 2172.6144 m --> 2.17x103 m 1 mile 64.2 + 7.9 220.3 71.2 = 0.327 220.3 p.23

Scientific notation Allows rapid & clear expression of very large, or very small numbers with the correct number of significant figures. Exponent tells you how many zeros (or places) should follow the first digit, or how many places to move the decimal. + right; - left 101 = 102 = 103 = 104 = 106 = 2 X 101 = 2 X 102 = 2.5 X 102 = 3.9 X 106 = 0.8 X 1012 = Translate from scientific nontation 1.03 X 104 1.030 X 104 1.0300 X 104 0.0300 X 104 How many sig figs? 10 20 3 100 200 4 1000 250 5 10000 3.9 million So you can’t depend on a calculator to tell you how many sf should be in your answer. Calculators lie! You can use them to do the calculation, but you’ve got to decide how many of the digits spat back at you are significant (sfs). I’ll grade based on sfs through the first exam, and less so later. However, I focus on sf in lab, so do learn the rules and practice them. What about rounding? It’s most important that you’re consistent and don’t round to improve your results. Generally, round up at five an over. 1 million 8 w/ 11 zeros 3 Calculate the volume of the box with width, length & height of 15.5, 27.3 x 5.4 cm. volume of a cube = w x l x h = (15.5 cm)(27.3 cm)(5.4 cm) = 2285.01 cm3 The height, 5.4 cm, limits the number of sfs in the answer to 2. So, 2285.01 cm3 = 2.3x103 cm3