Every measurement we make includes some uncertainty. We can never measure something exactly or know...

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Transcript of Every measurement we make includes some uncertainty. We can never measure something exactly or know...

Page 1: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.
Page 2: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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

Page 3: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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.

Page 4: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

In general, all digits are significant, except zeros that are not measured but are used to position the decimal point (place holders).

Page 5: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

• 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.

Page 6: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

How many sig. figs are in… Answer12.35 g 4 (count all non-zero digits, not

just decimal places)

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 mL 1 (trailing zeroes do NOT count if no decimal is showing –– but don’t leave them out, or it looks like 5 mL!)

0.0250 L 3 (leading zeroes never count, but trailing zero counts if decimal is showing)

Page 7: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

Sig. Figs

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 mL l. 0.000200 kg

e. 1000 mL/L m. 144

f. 100. Lbs n. 1001 tons

g. 85 boxes o. 340. lbs

Page 8: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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

Page 9: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

When adding or subtracting, round off to the fewest number of decimal places.

22.9898 g 1.00794 g12.011 g47.9982 g84.00694 g, round to 5 sig. figs 84.007

g

Page 10: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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

Page 11: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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)

Page 12: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

6.9 g7.3 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/s2.44 kg·m2/s2

Page 13: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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)

Page 14: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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

Page 15: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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.

Page 16: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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.

Page 17: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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.

Page 18: Every measurement we make includes some uncertainty.  We can never measure something exactly or know a quantity with absolute certainty.  The numbers.

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?