Unit 1: Uncertainty in Measurement: Significant Figures

1. Unit 1: Uncertainty in Measurement: Significant Figures

2. Significant Figures in Measurement • Every measurement we make includes some uncertainty. • We can never measure something exactly or know a quantity with absolute certainty. • The numbers (quantity) we use must tell us two things: • 1. How large or small • 2. How well were you able to measure it

3. Significant Figures in Measurement • The digits we record in a measurement (certain and uncertain) are called, significant figures (sig. figs). • The greater the # of sig. figs in a measurement, the greater the certainty.

4. Determining Which Digits Are Significant • In general, all digits are significant, except zeros that are not measured but are used to position the decimal point (place holders).

5. Which zeroes count as sig. figs and which do not? • Leading zeroes never count as sig. figs • There are only 3 sig. figs in the quantity 0.00275 kg. • Internal zeroes always count as sig. figs • The quantity 1.004 g has 4 sig. figs • Trailing zeroes count as sig. figs only if the decimal point is written. • The quantity 12.40 mL has 4 sig. figs, but the quantity 250 mL has only 2 sig. figs.

6. Here are some examples:

7. Now for some practice…

8. Significant Figures in Calculations • Answers to calculation cannot be more accurate than the information you entered in calculation- but calculators don’t know that. • 2 rules when reporting the uncertainty in calculations. • Addition and Subtraction • Division and Multiplication

9. Addition and Subtraction • When adding or subtracting, round off to the fewest number of decimal places. 22.9898 g 1.00794 g 12.011 g 47.9982 g 84.00694 g, round to 5 sig. figs 84.007 g

10. Division and Multiplication • Keep the same number of sig. figs. as the measurement with the least number of sig. figs Example : 1.2m X 2.00m = 2.4 m The first measurement 1.2 has 2 sig. figs The second measurement has 3 sig. figs. So your answer may only have 2 sig. figs

11. Now for some practice… • 1.234g + 2.2g + 3.45g = • 2.2m X 333m = • 47.0 m  2.2 s = • 4.257 kg x (1019 m2 – 40 m2)  (54.5 s x 31.3 s)

12. Answers • 6.9 g • 7.3 X 102 -You have to change the number to scientific notation because that is the only way you can have two sig. figs • 21 m/s • 2.44 kg·m2/s2

13. A little review… • You’ve observed the changes that occur when you place a piece of Al foil into a blue solution. • Lots of observations (avoid jumping to conclusions) • Bubbles form (gas behaves like H2 gas) • You’ve observed the relationship between P and V • Best to quantify observations (measured volumes while applying pressure) • PV = constant (1662 Robert Boyle- Boyle’s Law)

14. A model for gas pressure • Boyle’s Law describes what gases do, but not why. To answer the “why” we need a model. • Imagine air as a collection of particles (tiny-ping pong balls) bouncing around inside syringe. • Tiny particles = molecules

15. A model for gas pressure • Every time a molecule hits the syringe wall or plunger, it pushes against surface. • The surface pushes back and molecule bounces off in another direction. • This process is called gas pressure.

16. Kinetic Molecular Theory of Gases Model • Now, let’s say we decrease the volume of the syringe. What happens to the molecules inside the syringe ? They move! • Smaller volume = more collisions = more gas pressure • This moving-particles model of gases is called the kinetic molecular theory of gases.

17. Does the KMT of Gases explain other observations about gas pressure? • You bet! • Here are some examples: • Inflating a bike tire • Inflating a balloon • All gases obey Boyle’s Law and KMT of gases seems to explain gas pressure behavior for all gases.

18. But, are all gas molecules the same? • Absolutely not! Think gas splint test. • Example: CO2 extinguishes flame • Different gases= different molecules (particles are always moving and bouncing around, PV relationship is the same) • Now, the question is what happens when different kinds of gases are combined?