Notes: Measurement (text Ch. 2)

Transcription

1 Name Per Notes: Measurement (text Ch. 2) NOTE: This set of class notes is not complete. We will be filling in information in class. If you are absent, it is your responsibility to get missing information from a fellow classmate or the chemistry website : http ://othschem.weeb!y.com/ Scientific Measurement Metric System: based on powers of ten, so it's easy to convert between units. You need to memorize the order and meaning of the prefixes from kilo- to milli-. If you need to use the other units, they will be given to you. KING HENRY DANCED BEFORE DRINKING CHOCOLATE MILK giga mega kilo hecto deka BASE deci centi milli micro nano G M k h da --- d c m p n or 1 "Decimal-hopping" method for converting metric units: 45 cm = ujsÿ mm 750 ml = O, "ÿ5 L 3200 g = km = 5000 m 58 cl = '5 ÿ0 ml 4 dg = Ul O0 66 mm = O.o[o(D m 7 kl = L 4 dag = ÿ10 kg mg g Sl (Systeme Internationale) base units useful in chemistry: Quantity Base Unit Time second Length meter Mass kilogram Temperature Kelvin Amount of a substance mole Symbol S m kg K mol Sl derived units useful in chemistr1: (derived units are calculated from base units) Quantity Derived Unit Volume: various formulas, such as cubic centimeters or milliliters LxWXH liters Density: mass divided by volume grams per milliliter or grams per cubic centimeter Specific Heat: energy divided by Joules per gram per C (mass x AT) Symbol cm3 or ml L g/ml g/cm3 J / (g C) ***NOTE THAT 1 cm3 IS EQUAL TO 1 ml!!! And a cc also is the same as a cm3.

2 Scientific Notation You will encounter very small and very large numbers in chemistry. Scientific notation is useful for expressing these numbers. Rules for expressing numbers in scientific notation: a. Move the decimal so that there is only ONE nonzero digit to the left of the decimal. b. Express that number times 10. (x 10) c. Count the number of times you moved the decimal and that is your power of ten. d. If the decimal was moved to the left, the power of ten is expressed as a positive number. e. If the decimal was moved to the right, the power (exponent) is expressed as a negative number. Examples: Convert to scientific notation: 56, ÿ X I(]u X: 10- z. 4,500,000 H.5 ÿ( %7 ;ÿ I[') -ÿ ÿ ÿ I0ÿ ÿ,ÿ X IO -1 Convert to standard notation: 6.67 x 10 5 (p ÿ-'/ x x10 ÿ ' 9.114x x ÿ 000ÿ x oozz5 O. Ool I1ÿ.1 ( Precision: Accuracy: Measurement Vocabulary how close a measurement is to other values in a set of repeated measurements how close a measurement is to the true value (the "correct answer") + Precise (but not accurate) Accurate (and somewhat precise) Accurate and precise Are the followinq.qroups of measurements accurate, precise, both, or neither? 1) Given: true volume of sample of water is 33.3 ml ÿrtÿci,ÿp,., Measurements made: 22.4 ml, 22.2 ml, 22.4 ml, 22.3 ml 2) Given: true length of copper wire is 58.5 cm Measurements made: 58.4 cm, 58.5 cm, 58.5 cm, 58.4 cm Precis accuro+ 3) Given: true mass of sample of zinc is 14.5 g Measurements made: 13.2 g, 15.6 g, 17.9 g, 12.0 g n i44ntr"

3 Qualitative: a descriptive measurement (quality); does not involve numbers Examples: (ÿolowr OdOV'l Sh04>?_. Quantitative: a numerical measurement (quantity) Examples: V'OIUV3q. ) V'(ÿ5ÿ) "ÿ'rvÿpcr(ÿtl"lj 'ÿ Siqnificant Fiqures (siq ficls) Scientific measurements are limited by the degree of "exactness" or precision* that the measuring instrument gives us. For example, if we wish to measure the length of a kernel of corn with a centimeter ruler, we can estimate the length to the hundredths place, estimatinq one digit beyond what we can see marked on the ruler. The digits we obtain in our measurements are called si,qnificant fiqures. What is an appropriate measure for the length of this kernel of corn? How many sig figs? ) Certain instruments can give us more significant figures than others. For example, if we were to find the mass of a sample of metal using a simple bathroom scale, we could obtain a reading to the nearest pound (eg. 14 Ibs). But with a digital balance, we could measure it to the nearest tenth or hundredth of a pound (eg or Ibs). The digital balance gives more significant figures and therefore more precision. The number of significant figures in a measurement is important, because when we use measured numbers in a calculation, we have to round our answers to reflect the precision of the original measurements. The least precise measurement (the one with the fewest significant figures) will limit the precision of the final answer. Before we can learn to round answers to our calculations, we need to know how to count significant figures in a measurement. ***Note that the term "precision"in this context refers to the # of measured digits Rules for counting significant figures in a measurement: a. Nonzero digits and zeros between nonzero digits are always significant. Examples: 235, 88, 808, 109 (all digits are significant) b. Leading zeros are not significant. Examples: 0.5 or 0.05 or (all have 1 SF) c. Zeros to the right of all non-zero digits are only significant if a decimal point is shown. Examples: (3 SF), (5 SF), (6 SF), 5000 (1 SF) d. For values written in scientific notation, the digits in the coefficient (big # in front) are all significant. Examples: x 10s (4 SF), 3.4 x 103 (2 SF)

4 Using Significant Figures in Calculations: Addition and Subtraction: Round the answer so that it has the same number of DECIMAL PLACES as the measurement with the least number of DECIMAL PLACES (the least precise measurement). Example: = before rounding. After rounding, the result should be 56.5 (.one decimal place), since the limiting term (2.5) has only one decimal place. Calculate and round to the correct # of SF: * = ÿ1ÿ. II round to ÿjÿ. I +ÿn+h 5 1ctc _ = Iÿ_.-ÿ roundto Iÿ Otq'e.4 IÿiÿxC.ÿ. "k_) Multiplication and Division: Round the answer so that it has the same number of TOTAL significant figures as the measurement with the least number of TOTAL significant figures (the least precise measurement). Example: 4.28 x 8.3 = before rounding. After rounding to the proper # of SF, the result should be 36 2(2_.ÿE), since the limiting term (8.3) has only 2 SF. Calculate and round to the correct # of SF: 52.3x8.8= ÿ0.2.ÿ -) roundto I'J(ÿO 2 Si.ÿ ÿiod5 5/2.2= 2.ÿ roundto Z I 5iÿ ÿ:iÿ Dimensional Analysis Dimensional Analysis is an important method of solving mathematical problems requiring unit conversions (changing from one unit to another). DO NOT attempt to do these problems using your own method. We are in training, and you will have to be able to solve problems using this technique, so start learning now! Conversion Factors: ratios relating two amounts that are equal. a. Example: if eggs cost $1.44 per dozen, this is the same as saying that $1.44 = 1 dozen. They are not literally equal, but equivalent in the sense that if you have 1 dozen eggs, then you have spent $1.44. To write this expression as a conversion factor, just write one amount over the other: $1.44 OR 1 doz. 1 doz. $1.44 The statement "$1.44 per dozen" allows us to RELATE or CONNECT one amount ($1.44) to another amount (1 dozen). _$1.44 and 1 doz. 1 doz. $1.44 Both make the same connection, which is that $1.44 = 1 dozen. In this statement, the equal sign tells us these 2 amounts are equivalent. 4

5 Practice writing conversion factors: STATEMENT EQUALITY CONVERSION FACTORS There are 60 seconds in a minute. 1 min = 60 s There are 100 pennies in a dollar. $1 = 100 There are 16 cups in a gallon. There are 1000 milliliters in a liter. I ÿo,i = I[#CUPÿ; 1000 m L = I L 1 min and 60s 60 s 1 rain $1 and 100 _ loo $1 a, a llÿ CuPS I 0j,ÿl IL IOOOmL Otn o!, , I L looo ÿl. b. C, d, There are 5280 feet in a mile. 5 Z8(3 F-F : I nni 280 F o.ÿ& I m_._ÿ 5Z80ÿ" In a conversion factor, the top part equals the bottom part. In other words, a conversion factor is ALWAYS equal to one (because when you divide something by another quantity that is equal to it, it is like dividing that number by itself, which always equals ONE) We use conversion factors as a way of converting between different units of measurement. Since conversion factors have a value of 1, when you multiply by them, although the number (and units) may change, the value stays the same, since you're just multiplying by 1. In order to use a conversion factor, we need to align the units so that the units were are trying to get rid of cancel out and we are left with the units we are looking for. In order to cancel spmething out, you do the opposite operation (ie. If the unit is on the top, we put it on the bottom in the conversion factor, so that that unit cancels out and the new unit will be on the top.) Example: How many minutes are there in 3480 seconds? x 60\ 1. Both "60 s" and "1 min" are the same length of time (multiplying by the conversion factor didn't change the VALUE of the time). 2. However, the units are different after using the conversion factor. 3. CROSS OUT THE SECONDS BECAUSE THEY CANCEL. 4. YOU ARE LEFT WITH MINUTES FOR THE UNIT OF YOUR ANSWER. ***The question started with a large number of SMALL time units and ended with a small number of LARGE time units. e, Every dimensional analysis problem contains three major parts: i. The unknown and its UNIT, ii. The given amount and its UNIT, iii. A conversion factor or factors which relate(s) or connect(s) the given UNIT to the UNIT of the unknown. Examples: one-step problems unknown Cifn &/ C.F. 1. What is the c'ÿost of 2 clz'o"ÿz, eggs if eggs are $1.44/doz.? Cy wÿ* is or, Given C.F. 5 lh' Uni..ÿ_ÿ (,&ocel cliagonqllÿ'

6 . If a car can go 80. km in 1 h, how far in km can the car go in 8.5 h? [- 8o 3. If a chemical costs $50.00 per gram, what is the cost of 100. g of the chemical? fÿ We can use these same principles for metric conversions that we learned earlier. These conversion factors will have a few special properties: i. The conversion factors will always contain a "1" ii. The "1" will always go with the larger unit of the two in the conversion factor iii. One of the units in the conversion factor(s) always needs to be the base unit (no prefix). Always go through the base unit! For example, when converting from milligrams to kilograms, you will need to go through grams in the middle. See example 6 below. Examples: Metrics ÿ. Jrhtÿ;e C.F. PÿO Iqt'ÿ'Cl 4"0 b4t rylcrÿoriz. ÿ!). How many kilometers are in meters? IO _- 581, ooo" -Iooo'.. How many milliliters are in 4.56 liters of solution?, How many kilograms are in milligrams? ***As you saw in #6 above, some dimensional analysis problems require more than one conversion factor to solve. The same basic principles apply; you will just have more steps and more unit cancellations in your problem. Try this one! 7. An astronaut needed some more hydrogen for his fuel cell. He asked a space alien for 48.0 grams of hydrogen. The alien could only measure the hydrogen in "zooms." 5 zings = 4 grams, 2 warps = 3 zings, and 9 zooms = 5 warps. How many zooms does the astronaut need? '72.0 z.oom