In chemistry we use metric units (called SI units after the French term for Systeme internationale.

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1 Metric system / SI units: In chemistry we use metric units (called SI units after the French term for Systeme internationale. SI units: The SI units we ll be primarily concerned with are shown here: Base units are bold. Unit second (s) meter (m) kilogram (kg) Pascal (Pa) kelvin (K) Celsius( o C) mole (mol) Newton (N) g/cm 3 Joule (J) J/g x o C What it measures time (t) length (l) mass (m) pressure (p) temperature (T) temperature (T) quantity of substance force/weight density (d) energy (e) specific heat capacity Note: The unit degrees Celsius (ºC) is frequently used in place of kelvin. Though it is not a metric unit, per se, it is used often enough that it might as well be. To convert between kelvin and ºC, use the equation: K = ºC Prefix What it means Tera (T) trillion Giga (G) billion 10 9 mega (M) million 10 6 kilo (k) 1000, 10 3 deci (d).10, 10-1 centi (c) 0.01, 10-2 milli (m) 0.001, 10-3 micro (µ) , 10-6 nano (n) ,10-9 pico (p)

2 o How to convert between the units without prefixes and units containing prefixes. We ll solve this using a sample problem: How many milligrams are there in 439 grams? Step 1: Make a t Step 2: Put whatever value (with units) that the question has given you to convert in the top left. Step 3: Put the units of whatever is in the top left in the bottom right. This causes them to cancel each other out. Step 4: Put the units of whatever you re trying to find in the top right. Step 5: Put 1 in front of whatever unit has the prefix in it. Step 6: Put whatever the prefix means in front of the unit without the prefix. Step 7: Multiply the stuff on the top together and divide by the stuff on the bottom. This gives you, in our case, an answer of 439,000 g. o Do some more examples, including examples in which you have to convert between two units with prefixes in them (for example, mg to kg).

3 Derived units: These are units that are derived in some fashion from the base units and are used to measure everything else that the base units don t cover. Some examples: Unit What it measures liter (L) volume (1 L = 1 dm 3 ) g/cm 3 or g/ml density joule (J) energy o Density: Density is calculated using the equation: density = mass volume The units of density that result from this will depend on how mass and volume are measured. Typically, mass is measured in grams and volume in cubic centimeters (cm 3 ) = ml. Sample problem: What is the density of a brick that weighs 4500 grams and has a volume of 650 cm 3? 6.52 g/cm 3 Water has a density of 1.00 g/ml under standard conditions. As a result, 1 ml = 1 g for water. How good are data? Not surprisingly, it s important for us, as scientists, to use the best data possible when doing an experiment. Let s talk about how we can see how good our data are: Some background: Accuracy and precision. Though the terms are frequently used interchangeably, accuracy and precision are two different things.

4 o Accuracy: How close a measured value is to the true value. o Precision: How close a series of measurements are to each other. Let s see what this means: Accurate and precise: The knife thrower is precise (the knives are closely placed to one another) and accurate (the knives are where he wants it). Neither accurate nor precise: The knife thrower has neither placed the knives close to each other (making it imprecise) nor placed them where he wanted them (making them inaccurate). Precise, but not accurate: The knife thrower is precise (the knives are closely grouped) but not accurate (they are presumably not where he wanted them). How can we tell if data are accurate? In order to determine if data are accurate, we must first know what the actual value of the thing being measured is. The accuracy of a measurement is expressed by the measurement s percent error :

5 A high percent error means that the data were not very accurate, while a low percent error means that they were. Example: The mass of a sample of a compound was found to be 45.0 grams. If the actual mass of the compound was 55.0 grams, what is the percent error of this calculation? 18.2% How can we tell if data are precise? The number of decimal places that are shown in a measured value give us an idea of how precise they are. For example, the measurement 18.0 grams is assumed to be precise to the nearest 0.1 grams because if it wasn t, we wouldn t have gone to the trouble of writing the.0 at the end of the value. The digits in a measured value that give us this kind of information are referred to as significant digits or significant figures. Any digit that gives us useful information is said to be significant. Determining the number of significant figures in a measured value. The rules: o Nonzero numbers in measurements are always significant. The number 35 grams has two significant figures and is precise to the nearest whole gram. o Zeros between nonzero numbers are always significant. The number 202 grams has three significant figures and is precise to the nearest whole gram.

6 o Zeros to the left of all nonzero digits are never significant. They re just placeholders. The number 0.02 grams has one significant figure and is assumed to be precise to the nearest 0.01 gram. This rule is set up so that we get the same number of significant figures whether or not we use scientific notation. o Zeros to the right of all nonzero digits are only significant if there s a decimal place explicitly shown. The number 2.00 grams has three significant figures and is assumed to be precise to the nearest 0.01 gram. The number grams has two significant figures and is assumed to be precise to the nearest gram. o When using scientific notation, only pay attention to the part of the value before the x. The number 2.0 x 10 2 grams has two significant figures and is precise to the nearest 0.1 x 10 2 grams. Do some more significant figure examples until they seem to get it. When we do calculations using data, we need to make sure that our answers also reflect the value of the data that went into making them. o For example, if we found the mass of a car to be 1000 kg using a truck scale (this is precise to the nearest 1000 kg) and the volume of the truck to be 9 m 3 using a rule (this is precise to the nearest 10 m 3 ), it wouldn t make any sense to insist that the density of the car was (infinite) kg/m 3, because our data weren t good enough to say that.

7 o Rules for finding significant figures in calculations: When adding and subtracting, the answer should be rounded to the last significant figure of the least precise value. When multiplying and dividing, the answer should have the same number of significant figures as the value with the least number of significant figures grams / ml = 3.29 g/ml 34.0 grams has three significant figures and ml has four significant figures. Our answer, then, will be rounded to three significant figures. More examples of this kind.

8 How to record data using the right number of significant figures: Because significant figures give you important information about how good the data you re using are, it s important that you write the correct number of significant figures when taking measurements in the lab. The rules for correctly writing significant figures in measurements: Record the number of digits that can be directly measured by the equipment that you re using and estimate one digit past that. o For example, if you re using a ruler that has markings for centimeters, you should record the length of an object down to the nearest 0.1 cm: For digital equipment, simply record whatever digits the equipment gives you (no estimation!)

9 Making Graphs The following guidelines should be used at all times when making graphs in chemistry class: Always make a line graph! o Bar graphs are used to show how a single quantity varies with time this isn t usually something we see. o Pie charts are used to subdivide something into smaller pieces. This is more common in economics than in chemistry. o Line graphs show the dependence of one variable on another. This is what we re all about! The x-axis is always the independent variable (what you change) and the y-axis is always the dependent variable (which happened). o In other words, y changes as a result of x changing, not the other way around (example of age and height height changes as a result of increasing age, not the other way around). o The x-axis is usually time in chemistry. Abrupt changes in a graph tell you that something significant has happened. o Whenever you see a discontinuity, always examine this point to see what has happened.

10 Graphs should always be shown as lines or curves, NEVER as connect the dots! o When you take data, there is always some experimental error that comes in making the measurement. o If you connect the dots, you re saying that there was absolutely ZERO error in any measurement and that everything you saw can be EXACTLY reproduced. o Sometimes you just have to guess about whether a line or curve does a better job of describing the data. Graphs are often open to interpretation! The line that you draw in a graph doesn t need to go through the origin. o Example: If you make a chart of the affect of a baby s weight on age, you wouldn t say that a baby weighs zero pounds when it was born! The title of a graph should always be The Dependence of [dependent variable y-axis] on [independent variable x- axis]. Units should be drawn on both axes of the graph. o If the units aren t made explicitly clear, it won t be clear what you re looking at. The data in the graph should fill the space allowed for it. Use a ruler when drawing straight lines!

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