Wisdom is not measured by age, Intelligence is not measured by grades, Personality is not measured by what others say. O.Z "Osama Alzoubi" I. What you should already know Exact Numbers counting numbers; no degree of uncertainty; used by mathematicians. Measured Numbers are inexact; have a degree of uncertainty. These have units (e.g. cm, ml, etc.); used by science geeks. Use metric only; it s from the International System of Units (abbreviated SI from the French Système International d Unités). II. What you should know 1. length -- basic unit = A = B = C = D = E = 5 cm ruler F = 2. mass -- basic unit = mass = triple beam balance scale 3. volume -- basic unit = a. b. c. d. ml volume = volume = volume = volume = various sizes of graduated cylinders
4. temperature -- science unit = a. b. temp. = temp. = thermometers Let s practice. 1. 3. (graduated cylinder) (thermometer) 2. 4. (centimeter ruler) (voltmeter) Back to Notes. III. Significant figures (definition, counting, and rounding) this is old stuff, right????? Try this (yes, you may use your calculator). 88.6 g 2.9 cm 3 (don t forget the unit)
A. What do they mean? Consider the picture below. 3.67cm uncertain digit A significant digit is one that can be measured; all marked digits and ONE guessed (or eyeballed or uncertain) digit. B. Determining Sig Figs 1. Examples 500 g has sig figs. 0.340 L has sig figs. 1.0120 kg has sig figs. 123Ō ml has sig figs. 1.230 X 10 3 ml has sig figs (scientific notation or exponential notation) 2. Scientific Notation & sig figs a. What is scientific notation; when and why do we use it? Short cut way to represent very large (>10 3 or very small <10-3 ) numbers AND still maintain sig figs. b. YOUR non-graphing, non-programmable calculator input and display
c. Examples of switching from scientific notation to positional notation and vice versa; number of sig. figs in each method a. 3.080 X 10-3 mg = ; # sig figs = b. 4.0 X 10 4 cm = ; # sig figs = c. 6.200 X 10 1 mg = ; # sig figs = d. 5.80 X 10 34 ml = ; # sig figs = is this difficult? e. 32.09 X 10-2 mg = ; # sig figs = notice anything? d. Rounding measured values You know the rules for greater than 5 and less than 5, but the perfect 5 is different in science than it is in math: In science, perfect fives round to an even digit. Examples Round each of the following so that it only has two significant figures (don t let the decimal point move!!) 986 m 982 mg 985 ml 975 g 995 o C 0.00125 L 0.001255 kg 13,789 mm 1,450,020 mg IV. Significant figures (in calculations) If you are multiplying or dividing, count the sig figs in each measurement, and round to keep the least amount of sig figs you counted in your answer. Do you remember how to multiply and divide units? A. Examples 0.5431 cm (12.003 cm) = (42.385 mm 3 ) (6.10 mm) = (5.02 X 10 4 g) (3.0 X 10-12 ml) = 22(156 cm) =
B. If you are adding or subtracting, line the measurements up vertically; going from left to right, cut off the answer in the place that the first one runs out of sig figs. In other words, round the answer to the least precise place that is in the actual problem. A word of caution: when adding and subtracting measured values, the units must be identical. C. Examples 0.12 cm + 0.979 cm = 1,200 cm 2 + 1,106,987 cm 2 = D. But what if both rules are in the same problem? In this class, we use sub-answers, then a final answer. Do each operation separately, keeping ONE more digit (this is not a sig fig) than necessary (mark the actual place of the last true sig fig with a check mark). We only round one time and that is for our FINAL answer. E. Examples 981.47 m 2 + 0.01 m (25 m) = (672.8 cm 2 2.0 cm) 121 cm =
G. Let s practice a little (don t forget sub-answers you must always show them): 1. 10.21 g + 0.2 g + 256 g 2. 1,000 kg + 10,100 kg 7. 45.6789 o C + 0.7 (98 o C) SA = 3. 295 mi (1.609 km/mi) 8. 12.3 m + 0.092 m SA = 8.3 m 4. 36.2 cm (0.11 cm) 5. 17.3 g + 2.785 g SA = 30.20 ml 6. 236.45 g 1.3 g SA = (2.4561 cm )(32.675 cm 2 ) 9. 32 (0.125 cm + 5.43 cm) SA = 23.18 10. 3887.6 cm X 3.1416 cm 2 25.4 g 11. (6.23 m) 2 H. A little more practice 1. (81.4 mm + 1.628 mm) 0.00400 mm SA = 2. (1.062 X 10 4 g) [(3.8 cm X.02 cm X 3.70 cm) + 10.72 cm 3 ] SA = SA =
Homework The procedure for homework is always write them in your black composition book; USE PENCIL, INK WILL GIVE YOU A 0 GRADE no need to write the questions answers without work to support them are meaningless and will not be given any credit do not write answers in columns always use my question numbers (don t renumber them 1,2,3, etc.), You may wonder about the question numbers they re different! Well, question 1-4 means that this is the fourth question in chapter 1 of your textbook. I may have tweaked the textbook questions them just a bit. always start on a new page in your composition book (be sure to use the back of pages if you don t, you will run out of pages). By the way, remember that Homework is due the next class day at the beginning of the period before the bell rings. This may be subject to change, so listen to verbal instructions from the teacher. 1-5 How many sig figs are in each of the following measurements? a) 0.045 in d) 21.0 m g) 0.0080 in b) 405 ft e) 7.060 qt h) 2200 lb c) 0.340 cm f) 2.0010 yd 1-9 Round each of the following measurements so that they have TWO significant figures a) 115 m d) 0.47322 L g) 1,557,000 ml b) 27.678 cm e) 55.6 ml h) 321 m 3 c) 37,500 o C f) 0.0396 cm ******more on next column****** 1-15,21 Carry out the following operations and sig fig the answer. a) 0.013 m + 0.7217 m + 0.04 m b) 243 m 2 / 0.5 m c) 15.3 o C + 1.12 o C - 3.377 o C d) 35.48 L 4 L + 0.04 L e) 3.0 ft(472 ft) f) (1.84 yd)(42.8 yd) / 0.8 yd g) 337 in + 0.8 in 12.0 in h) 0.0575 in (21.0 in) 1-23 These are the both rule problems; review how that s done remember, you must show subanswers. a) 67.43 (0.44 in) 23.456 in b) (0.22 in + 12.451 in + 1.782 in)(0.876) c) 1.20 m(0.8842) + 7.332(0.0580 m) Reading at Home pages 18 28; sections 1-2 thru 1-4 This section, Reading at Home, is used to introduce and reinforce the items learned in class. Every person learns a little more the second time they hear something. You may or may not have a quiz over the reading. Web Site http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html https://www.khanacademy.org (search significant figures) Web Site will list one or two web sites that are current (as of the date of printing of this handout) and helpful. These sites may provide additional help with the current topic. When you are finding a topic difficult, you may want to explore these sites for a variety of examples and questions. There are usually many web sites that can be found. Feel free to search for more. Note: Once in a while, a web site may give conflicting information with what was learned in class. In this event, please ask me for guidance.
Reading at Home pages 15 18; section 1-1 V. Error in measurements A. In words. 1. Accuracy is the agreement of a value with the correct answer. 2. Precision is agreement with other values; it may or may not be the correct answer. Another way to say it is precision is consistency of values. B. In pictures VI. Using sig figs to calculate error A. Absolute Error, aka accuracy B. Relative error, aka precision
C. Example: You will be calculating relative error in your labs. Sometimes you will be asked to calculate the absolute error. In one of your labs this year, you will need to calculate the mass of copper produced in the lab. Let s assume that three individuals obtained the following data in that lab. person (no units) mass (g) Kay Mart 4.87 Ceil Ling Bob Bing 5.632 4.9 Calculate the relative error of the mass watch your sig figs! Mean: Deviations: Mean Deviation: %RE: (average of values) ( mean value ) (average of deviations) mean deviation mean X 100 What does the RE value actually convey? shows an average variation among values > RE means < precision; likewise, <RE indicates >precision Even though each lab is independent and interpretation of the RE depends on variables in each lab, we will say for all of chemistry that RE< 5% is good precision and RE> 20% is poor precision.
Now let s calculate the absolute error. The actual mass of the copper for the previous example is 5.02g. Knowing that the lower the absolute error, the greater the accuracy, would you say that our accuracy for this example is good? Mini-lab: You Guessed It! Safety: no gum, food, drink Precise and accurate measurements are essential in chemistry experiments. You will be given a handout from your teacher. Complete the top portion (name, etc.) of the handout first. You will place your answers to various questions in this lab on the handout. Remember, use pencil only; use of ink = 0. Length 1. Use a ruler to draw a line exactly 5 inches long in the rectangular box on your handout. 2. Measure the line with the metric side of your ruler. Write the answer (don t forget the units) in the appropriate place on your handout. Mass 3. Zero a triple beam balance using the small, silver-colored knob under the balance pan. This simply means that when nothing is on the balance and all the masses (including the dial) is at 0, you will make sure that the pointer (on the right of the balance) is pointing to the 0 on the right side of the balance. 4. Place a massing dish (AKA weighing boat) on the balance; record the mass (don t forget the units). 5. Place 10 paper clips in the massing dish; record the mass. 6. Showing your work, determine the mass of the 10 paper clips without the massing dish; record (this is a sub-answer ). Remember, a sub-answer has the correct number of sig figs with a check mark on the last sig fig. It includes one extra digit (that extra digit isn t a sig fig). Then determine the mass of a single paper clip using math NOT the balance! Again, show work! Record your answer. 7. Return the paper clips to their proper place and remove the massing dish from the balance.
Volume Part I 8. Fill a test tube, a 50 ml beaker, and a 100 ml beaker about 3/4 th full (that means an approximate amount, nothing exact don t waste time trying to get it that way). However, don t let it overflow. 9. Pour the water from each item into an appropriately sized graduated cylinder. Record each volume (don t forget units). 10. Pour the water in the sink and dry the beakers. Part II 11. Add approximately 50 ml of water (again, not an exact amount) to a 100 ml graduated cylinder. Record the volume. 12. Carefully, add five dice to the 100 ml graduated cylinder. Record the volume. 13. Showing your work, calculate the volume of the three dice without the water; record (this is a sub-answer.. Then, calculate the volume of a single die (the plural is dice) without using a ruler. Keep this as a subanswer as we are going to use this number in more calculations. Again, show your work! Relative Error 14. Record the last sub-answer from number 13 above in the first values column of the relative error table. You may need to know that 1mL = 1cm 3. 15. Legally trespass to two other groups and obtain their values. Do NOT mention whether you think their values are correct or not. Record their volumes in the second and third spaces in the values column in the relative error table. 16. Now, complete the relative error table. Usually, we do not show our work for the answers obtained in this table however, for this lab only, show your work (for each of the remaining columns) on your handout in the space indicated. 17. For most of our labs, a low relative error would be < 5%. What does a high relative error (usually > 20%) indicate? Use the word precision in your answer which should be written in a complete sentence(s). Be concise; don t ramble. 18. Using complete sentences (as stated above, be concise; don t ramble), state your relative error and suggest a reason for its value, i.e. why it is so high or so low. Wrap it Up 19. Check your partners work. Stack em according to the teacher s directions. 20. Turn em in. Back to notes..
VII. Unit conversions Chemistry calculations that involve formulas REQUIRE a five-box, format. However, when we are simply doing conversions from one unit to another, we will use dominoes, which are nothing more than ratios. To get the hang of it, we ll practice on some conversion factors that you used in physics. A. Example How many inches are in 345.7 ft? 1. You need an equality (a domino) that relates the two units. 2. You start with their number. You rotate the domino so that diagonals cancel. This is a list of dominoes. It s not complete. Notice the ones that affect sig figs. bold = measured (these are the only ones from this sheet that affect sig figs.) length 1 nm = 1 X 10-9 m = 10 Å 1 in = 2.54 cm 1 mi = 1.609 km = 5280 ft 1 m = 100 cm = 1000 mm = 10 dm = 0.001 km = 1 X 10 9 nm = 1 X 10 6 μ m 1 ft = 12 in mass & weight 1000 g = 1 kg 1000 mg = g 1 lb = 0.4546 kg volume 1000 L = 1 kl 1 dm 3 = 1 L = 1.057 qt = 1000 ml = 10 dl 1 cm 3 = 1 ml 4 qt = 1 gal temperature temperature ( o F) = [temperature ( o C) X 1.8] + 32 temperature ( o C) = [temperature ( o F) 32] 1.8 metric prefixes (applies to basic metric units; e.g. meter, gram, etc) 1 base unit = 10 18 exa = 10 15 peta = 10 12 tera = 10 9 giga = 10 6 mega = 10 3 kilo = 10 2 hecto = 10 1 deca 1 base unit = 10-18 atto = 10-15 femto = 10-12 pico = 10-9 nano = 10-6 micro = 10-3 milli = 10-2 centi = 10-1 deci B. Example How many millimeters are in 0.0007890 meters?
C. Example How many km/hr is.022mi / min? (HINT: Start your domino with 0.022 mi ) min D. Example Change 1,520 cm 3 to gallons. (HINT: Look at the volume section of your conversion chart.) E. A volume of a cylinder is calculated using the formula: h π r 2. Calculate the volume of a cylinder in m 3 that has the following dimensions: h = 4.00 ft r = 0.005 km. The use of formulas requires a 5-box. F. A few pictures for perspective. 1. 1 ml = 1 cm 3 2. 1000 cm 3 = 1 L 3. 1 ml of water = 1 g (at 3.98 o C you ll 3. 1 L of water = 1 kg at 3.98 o C See later why temperature is mentioned)
Homework math answers are in bold at the end of the problem. (Remember the rules for doing homework and when it s due? Don t forget to use pencil; ink = 0. ) 1. Change 25.4 mg to kg. [2.54 X 10-5 kg] 2. Change 32.4 yd to cm. [2,960 cm] 3. Change 62 m/s to mi/hr. HINT: Change the top unit, then the bottom unit. Use only one domino. [140 mi/hr] 4. What is the volume of a rectangular solid in μm 3 that has h = 0.0023 mm, w = 0.0006 in, and l = 0.000200 ft? [ 2,000 μ m 3 ] Reading at Home pages 24-34; section 1-4 thru 1-5 Web Site http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html https://www.khanacademy.org (search convert units)