1. Lecture 1.2 –Units of Measurement, Sig Figs, and Uncertainty

2. Every Chef Needs Proper Tools Just like chefs do in the kitchen, chemists use tools to take exact measurements of substances. Sometimes cooking can be an art, but chemistry is a science. We want to be precise and accurate.

3. Precision and Accuracy Precision – Measures how close individual measurements agree with one another o A standard deviation (3.02 +/- 0.01) tells someone how precise you were during a laboratory. Accuracy – How close individual measurements agree with the “true” value. If numbers are precise (3.05, 3.04, 3.04) does that mean they are always accurate? When writing lab reports, include terms like precision and accuracy in your Analysis!

4. Exact Numbers versus Inexact #’s Numbers when MEASURING are inexact or exact #s. There is always uncertainty in the last digit reported for a MEASURED quantity; measured quantities are inexact Numbers that are exact for example 12 in a dozen will always be 12, it’s exact. Ignore exact #s when rounding

5. Quickwrite What do you think is the difference between 4.0 grams and 4.000 grams? 4.0 g implies that 4.0 has more uncertainty and that the true value is closer to 4.0 than it is to 3.9 or 4.1 4.000 has less uncertainty meaning that the true value is closer to 4.000 than it is to 3.999 or 4.001 More accurate!

6. Significant Figures Sig Figs are of critical importance in the lab. They indicate the accuracy of a measurement or a calculation. We don’t want errors based on random ways for rounding or random ways of presenting an answer. The AP FRQ’s will require answers reported to the CORRECT amount of sig figs. 1 mL may be considered wrong, but 1.0mL may be considered right!

7. Determining the Number of Sig Figs The most important rule is that all nonzero digits in any measurement are significant: 1.Zeros between nonzero digits are always significant. For example, 1005 has ______ sig figs. 2.Zeros at the beginning of a number are never significant. For example, 0.005 has _____ sig fig. 3.Zeros at the end of a number are significant only if there is a decimal. For example, 3.0 has ____ sig figs, but 30 has _______ sig fig. 4 2 1 1

8. What about #’s in Scientific Notation? Recall that we can write a number like 10,300 in scientific notation as 1.03 x 10 4 This number would have _____ sig figs 3

9. Scientific Notation 10000 = 1 x 10 4 24327 = 2.4327 x 10 4 1000 = 1 x 10 3 100 = 1 x 10 2 482 = 4.82 x 10 2 10 = 1 x 10 1 89 = 8.9 x 10 1 1 = 10 0 1/10 = 0.1 = 1 x 10 - 1 0.053 = 5.3 x 10 - 2 1/1000 = 0.001 = 1 x 10 - 3 0.0078 = 7.8 x 10 - 3 1/10000 = 0.0001 = 1 x 10 - 4 0.00044 = 4.4 x 10 - 4 Rules: 1.A number other than zero must be at the front followed by a decimal. 2.x10 tell you the number of times you moved the decimal to achieve rule #1 3.If the original number is bigger than 1 then the exponent is positive 4.If the original number is smaller than 1 (decimal) then the exponent is negative. 1.6 x 10 -19 C

10. Sig Figs for Calculations Determine sig figs only after a calculation is complete.

11. Sig Fig for Addition/Subtraction When you add/subtract numbers, the answer has the same number of decimal places as the number with the least decimal places. Round off to one decimal place since 83.1 has the least number of decimal places! Final answer you report is 104.8

12. Another example Three measurements were recorded (inexact or exact number?) below: 0.039 g, 0.4 g, 0.09 grams. A)Accurately show the sum of those measurements. B)Are the three numbers precise? Why or why not?

13. Another example Three measurements were recorded (inexact or exact number?) below: 0.039 g, 0.4 g, 0.09 grams. A)Accurately show the sum of those measurements. 0.529 = 0.5g (least decimal place!) B)Are the three numbers precise? Why or why not?

14. Another example Three measurements were recorded (inexact or exact number?) below: 0.039 g, 0.4 g, 0.09 grams. A)Accurately show the sum of those measurements. B)Are the three numbers precise? Why or why not? None of the 3 are precise to one another. The numbers are not close to one another.

15. Sig Figs for Multiplication/Division When you multiply or divide numbers, the answer has the same number of sig figs as the number with the fewest sig figs. 4 sig figs 2 sig figs, so the answer needs 2 sig figs 32 cm 2

16. Another Example Find the volume of a cylinder whose radius is 5 meters and its height is 1.0 meters. Volume of a cylinder is V = πr 2 h

17. Another Example Find the volume of a cylinder whose radius is 5 meters and its height is 1.0 meters. Volume of a cylinder is V = πr 2 V = π(5m) 2 (1.0m) = 78.5m 3 (how would you turn this into one sig fig?) 8 x 10 1 m 3 convert into scientific notation 80 accepted too. (1 sig fig)

18. What if you have both? Step 1: Use PEMDAS. Step 2: You either multiply/divide or add/subtract Step 3: At the end of each step, you must ask yourself, What is the next operation that I will perform on the number that I just calculated? If the next operation is in the same group of operations that you just used (example: multiply/divide) then do NOT round yet If the next operation is from the other group (add/subtract), then you must round off that number before moving on to the next operation.

19. Example: Compute: [(3.5 x 3.333)] / [(3.04 x 3.0)] Since it’s all multiply/divide, don’t round until the very end! The lowest sig fig is two, so your answer must be rounded to one sig fig 1.279 (did you get this?) Now round to 2 sig figs: 1.3

20. Example 2: Compute: [(3.5 + 3.333)] / [(3.04 - 3.0)] 1 dec place 1 dec place Do what’s in parenthesis first (PEMDAS) and immediately round to appropriate sig figs since you’ll be dividing soon! (see rules) [6.8/0.04] =[6.8/4.0x10 -2 ]= 170 = 1.7 x 10 2 1 sig fig 2 sig figs

21. SI Units: Metric System The metric system is based on the power of 10. These powers of 10 will convert you back to the base unit. Once you are at the base, you can convert to the desired unit. This makes no sense to me! It will later… First, know these 6 Base Units o Grams is for mass o Meters for length o Seconds for time o Kelvin for temperature o Moles for amount of substance o Ampere for current Base units don’t have prefixes!!!

22. Water Measurements Temperature measures how cold or hot some object is. In chemistry, we use Kelvin as units. o 0 Kelvin is the lowest temperature that exist (absolute zero) Know this about Water The freezing point of water is 0 0 C. The boiling point of water is 100 0 C Density is in mass/volume Density of water is 1g/cm 3 or 1g/mL

23. Memorize these prefixes and conversion!

24. PrefixFactor Milli- (m)10 -3 Centi- (c)10 -2 Deci- (d)10 -1 Base10 0 Deka- (D)10 1 Hecto- (H)10 2 Kilo- (k)10 3 Ends in –i you know it’s small Ends in –a or –o you know it’s big

25. How to read this: (a lot of the small stuff!) 1 kg (big) = 1,000 grams 1 m = 100 cm (small) 1 L = 1000 mL (small) 10 9 nanometers (small) = 1 meter This is one way you can remember what equals what.

26. The second way is to use base units

27. Sig. Fig Practice Complete Problem Set 1.2 Be sure to use the appropriate units!