Presentation on theme: "Unit 1: Introduction to Chemistry Measurement and Significant Figures."— Presentation transcript:
Unit 1: Introduction to Chemistry Measurement and Significant Figures
Precision and Accuracy What is the difference between precision and accuracy in your measurements? Accuracy refers to how close you are to the true value. It can be improved by making better measurements. Precision refers to how close several measurements are to each other, or how many significant digits are allowed in a measurement. It can be improved by repeating the measurements, or by using a better instrument.
Precision and Measurements Why must reported values show the correct number of “significant digits?” Because your measurement will only be as good as the instrument you use! Precision is limited by the gradations -or markings -on your instrument. We can typically estimate to one-tenth of a gradation mark when using graduated instruments in chemistry.
Measurement Practice Not accurate Not accurate Accurate ( avg. is falsely accurate ), but is precise and precise not precise BEAKER CYLINDER BURET 47 +/- 1 mL 36.5 +/- 0.1 mL20.38 +/- 0.01 mL
How good are your measurements? For example, if you are 1.6 meters tall, we know that you are exactly ONE meter tall (not 0 or 2) but the second digit is an estimate, and contains some uncertainty (it could be 0.58 rounded up, or 0.62 rounded down…) Scientific measurements are rounded off so that the last digit is the only one that is uncertain. Preceding digits are known with certainty, and unnecessary digits are not included. Any measurement will have some degree of uncertainty associated with it…. 1.57865467 m?
What is meant by “significant figures”? What is the difference between the measurements 25.00 mL and 25 mL? The first measurement is known more precisely and contains more significant figures –it could be 25.01 or 24.99, whereas the second measurement lies between 24 and 26. The number of significant figures tells us how well we know a measurement, and depends on how good the instrument used to measure it was. The known numbers PLUS the last uncertain number in a measurement are significant.
20.15 mL three certain digits one uncertain digit four significant digits!
Middle zeros always count. Beginning zeros never count. Ending zeros count IF a decimal point is anywhere in the number. 0.0700600 round to least # of decimal places round to least # of significant digits six sig figs
Examples of each rule: Any non-zero number is ALWAYS significant. example: 762 has 3, and 2500 has 2 Zeros: (a) beginning zeros are not significant, they are just place holders. Ex: 006471 has 4, and 0.00284 has 3 (b) Middle zeros between nonzeros are significant. Ex: 1.008 has 4 and 12046 has 5 (c) Ending zeros are significant ONLY if the number contains a decimal point. Ex: 1.0 x10 2 has 2, and 3000. has 4 Note: Exact numbers are numbers that are determined by counting (not measurement), or by definition are assumed to have an infinite number of significant figures. example: 1 minute equals 60 seconds 15 students are in class today
Lets Practice (notes): (4) How many sig figs are in each? a) 2.07 mL b) 0.057010 g c) 0.0026700 m d) 19.0550 kg e) 3500 V f) 1809000 L three five six two four
More Practice: How many sig figs are in each? 4.5090 0.00607 6.7 x10 3 200. 250 698,000.1 2.0000 x10 6 five three two three two seven five
Converting to Sci. Not. The following rule can be used to convert numbers into scientific notation: The exponent in scientific notation is equal to the number of times the decimal point must be moved to produce a number between 1 and 10. Example: In 1990 the population of Chicago was 6,070,000. To convert this number to scientific notation we move the decimal point to the left six times. 6,070,000 = 6.07 x 10 6 To convert numbers smaller than 1 into scientific notation, we have to move the decimal point to the right. The decimal point in 0.000985, for example, must be moved to the right four times. 0.000985 = 9.85 x 10 -4
Scientific Notation The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant, as shown by the following examples: 2.4 x 10 22 has 2 significant figures 9.80 x 10 -4 has 3 significant figures 1.055 x 10 -22 has 4 significant figures
How is density calculated? Density is defined as the mass per unit volume of a substance. Equation:
Ex: How many mL are occupied by 112 g of a liquid with a density of 0.97 g/mL?
What does temperature measure? Temperature is a measure of the average kinetic energy of molecules. A thermometer bulb’s view of a hot liquid…
How do we convert between temperature scales? °C(9/5) + 32 K - 273
Addition and Subtraction Using Significant Figures The answer must have the same number of decimal places as the least precise measurement used in the calculation. For example, consider the sum 12.11 18.0 + 1.013 31.123 The answer is 31.1 since 18.0 only has one decimal place. Final answer must match leftmost decimal place of combined measurements
Multiplication and division using sig. figs. The number of significant figures in the answer is the same as the least precise measurement (lowest number of sig. figs.) used in the calculation. For example, consider the calculation 4.56 x 1.4 = 6.38 The correct answer is 6.4 (it should only have two sig figs since 1.4 has only two)
(5) 3.052 m + 2.10 m - 0.75 m = (6) 6.15 m x 4.026 m = (7) (13.7 g + 0.03 g) 8.2 mL = Notes: Get a calculator! 4.40 m 24.8 m 2 13.7 g 1.7 g/mL
four three two three 6.384 31.123 190.08 190 More practice: 6.4 31.1 1.90 x 10 2 35.2 x 5.4
How do we know if our results are GOOD? One way to tell how “far off you are” is to compare your results to the “true” or “accepted” value. To determine the percent error of your results, use the following formula: % Error = accepted value – (YOUR) measured value x 100% accepted value
% Error calculation % Error = accepted value – meas. value x 100% accepted value What is the percent error of a measurement that is 2.51 cm if the accepted value is 2.54 cm? ANSWER: (2.54 – 2.51) x 100% = 0.03 x 100% 2.54 = 1.18% = 1% error Activity: Find the density of Zn metal and calculate your % error when compared to known density. Use sig figs in measurements and calculations.
Common Unit Conversions We will often need to convert from one unit to another when solving problems in chemistry. These “conversion factors” allow us to change the unit without changing the value of the measurement. 60 2.54 12 5,280 60 454 4.18 1 1,000
Review: metric unit prefixes Prefix Symbol Factor Numerically Name Giga G 10 9 1 000 000 000 billion Mega M 10 6 1 000 000 million kilo k 10 3 1 000 thousand Deca D 10 1 10 ten deci d 10 -1 0.1 tenth centi c 10 -2 0.01 hundredth milli m 10 -3 0.001 thousandth micro μ 10 -6 0.000 001 millionth nano n 10 -9 0.000 000 001 billionth The metric system (a.k.a. SI system) is based on powers of ten and Greek prefixes.
Dimensional Analysis The best way to convert between units is by a method called dimensional analysis (a.k.a. factor-label method). Always remember this: For example, consider a pin measuring 2.85 cm in length. Given that one inch is equal to 2.54 cm, what is its length in inches? ? in = 2.85 cm x 1 in = 1.12 in 2.54 cm
Some Examples: Convert 50.0 mL to liters: How many seconds are in two years? Linking conversion factors
More examples A Japanese car is advertised as having a gas mileage of 15 km/L. Convert this rating to mi/gal. (Given conversion factors 1 mi = 1.609 km, 1L=1.06 qt and 4 qt = 1 gal) ANSWER: 15 km x 1mi x 1 L x 4 qt = 35.18 mi/gal L 1.609 km 1.06 qt 1 gal With correct sig figs this rounds to 35 mi/gal
Tips for using the method… In math you use numbers, in chemistry we use quantities. A quantity is described by a number and a unit. 100 is a number: 100 Kg is a quantity (notice that in chemistry we give meaning to the numbers). In science we solve a lot of the "math" by watching the units of the quantities There are two main rules to solving science problems with the factor-label method: 1. Always carry along your units with any measurement you use. Cancel units when appropriate. 2. You need to form the appropriate labeled ratios, (which means conversion factors have equal numerators and denominators). NO NAKED NUMBERS!
Conversions (notes) 1.How many ms are in 45 min? 2. How many in 3 are in 86.3 cm 3 ? 3. How fast is 65 mi/h in ft/sec? 4. How many cm 3 are in 7.5 gal? 5. How many lb/ft 2 are in 75 g/cm 2 ? 6. How many km are in 1500 mm?
Extra Credit Gas prices from Italy trip summer 2014. Can you convert the advertised values to dollars per gallon? What conversion factors will you need? How do these prices compare to American prices?
More Unit Conversion Practice A pencil is 7.00 inches long. How long is it in cm? ANSWER: 17.8 cm A student has entered a 10.0 km race. How long is this in miles? ANSWER: 6.22 mi The speed limit on many highways in the U.S. is 55 mi/hr. What is this in km/hr? ANSWER: 89 km/hr
Exponent Review Some of the basics of exponential mathematics are given below: –Any number raised to the zero power is equal to 1. ex: 1 0 = 1 and 10 0 = 1 –Any number raised to the first power is equal to itself. ex: 1 1 = 1 and 10 1 = 10 –Any number raised to the nth power is equal to the product of that number times itself n-1 times. ex: 2 2 = 2 x 2 = 4 and 10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 –Dividing by a number raised to an exponent is the same as multiplying by that number raised to an exponent of the opposite sign. ex: 5 ÷ 10 2 = 5 x 10 -2 = 0.05