Unit 1 Uncertainty in Measurement Significant Figures Significant

Significant Figures in Measurement Every measurement we make includes some uncertainty. We can never

Significant Figures in Measurement The digits we record in a measurement (certain and uncertain)

Determining Which Digits Are Significant In general, all digits are significant, except zeros that

Which zeroes count as sig. figs and which do not? • Leading zeroes never

Here are some examples: How many sig. figs are in… 12. 35 g Answer

Now for some practice… Sig. Figs a. 0. 103 cm i. 2, 300 g

Significant Figures in Calculations Answers to calculation cannot be more accurate than the information

Addition and Subtraction When adding or subtracting, round off to the fewest number of

Division and Multiplication Keep the same number of sig. figs. as the measurement with

Now for some practice… 1. 234 g + 2. 2 g + 3. 45

Answers 6. 9 g 7. 3 X 102 -You have to change the number

A little review… You’ve observed the changes that occur when you place a piece

A model for gas pressure Boyle’s Law describes what gases do, but not why.

A model for gas pressure Every time a molecule hits the syringe wall or

Kinetic Molecular Theory of Gases Model Now, let’s say we decrease the volume of

Does the KMT of Gases explain other observations about gas pressure? You bet! Here

But, are all gas molecules the same? Absolutely not! Think gas splint test. Example:

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Unit 1: Uncertainty in Measurement: Significant Figures

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

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.

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).

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 m. L has 4 sig. figs, but the quantity 250 m. L has only 2 sig. figs.

Here are some examples: How many sig. figs are in… 12. 35 g Answer 0. 00568 L 3 (leading zeroes never count) 3. 007 g 4 (internal zeroes always count) 21. 0 °C 3 (trailing zeroes count if decimal is showing) 500 m. L 1 (trailing zeroes do NOT count if no decimal is showing –– but don’t leave them out, or it looks like 5 m. L!) 3 (leading zeroes never count, but trailing zero counts if decimal is showing) 0. 0250 L 4 (count all non-zero digits, not just decimal places)

Now for some practice… Sig. Figs a. 0. 103 cm i. 2, 300 g b. 2. 306 in j. 8. 10 L c. 21 k. 2. 40603 x 105 µm d. 0. 032 m. L l. 0. 000200 kg e. 1000 m. L/L m. 144 f. 100. Lbs n. 1001 tons g. 85 boxes o. 340. lbs

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

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

Division and Multiplication Keep the same number of sig. figs. as the measurement with the least number of sig. figs Example : 1. 2 m X 2. 00 m = 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

Now for some practice… 1. 234 g + 2. 2 g + 3. 45 g = 2. 2 m X 333 m = 47. 0 m 2. 2 s = 4. 257 kg x (1019 m 2 – 40 m 2) (54. 5 s x 31. 3 s)

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·m 2/s 2

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 H 2 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)

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

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.

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.

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.

But, are all gas molecules the same? Absolutely not! Think gas splint test. Example: CO 2 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?