Scientific Measurement

Objectives

• Understand how to calculate percentage error.

• Understand the concepts of accuracy and precision.

• Explain how precision lead to accuracy.

Accuracy

100A

EAE %

accuracy: closeness to accepted value (true, actual)percentage error: represents accuracy

Sample Problems

• An automobile scale is used to measure the weight of a car. The true weight of the car is 3245 lbs, but the scale says 3238 lbs. What is the percentage error?• The same scale is used to measure the weight of a cat. The cat actually weighs 12 lbs, but the scale says 5 lbs. What is the % E?

100A

EAE %

Precisionprecision: consistency of results

precise results: 45.9 mL, 45.8 mL, 45.9 mL, 45.9 mLnot as precise: 46 mL, 48 mL, 51 mL, 45 mL

precision: number of significant figures in a measurement; depends on the quality of the measuring tool

more precise: 3.584 cm less precise: 3.6 cm

Accuracy and Precision

• A tool with better precision usually results in greater accuracy…1. less estimation is required, so…2. greater certainty = more accurate

Objectives

• Be able to determine the number of significant figures in a measurement.

• Be able to report the correct number of significant figures for a calculation.

Significant Figures

What is the world’s population?

7,052,000,000 people = not as precise7,052,155,751 people = very precise value

significant figures: measured values that imply precision

Which zeros are significant andwhich ones are not?

50 mL or 50.0 mL?

Sig Fig Rules

• Non-zero digits are always significant: 25.6 m = 3 SF• Zeros between SF are significant: 1026 g = 4 SF• Left-most zeros are not significant: 0.0042 mL = 2 SF• Ending zeros after decimal are significant: 45.30 g = 4 SF• Placeholder zeros are not significant: 44000 people = 2 SF• Easily counted whole items, defined values, and whole #s

in equations have unlimited significant figures: 13 cats 1 min = 60 sec C = 2r (all are exact!)

How many significant figures?

a. 49.4 cmb. 0.023 sc. 7000 bisond. 22 studentse. 9.08 gf. 1.030 mLg. 0.40 mh. 0.0007 kgi. 1 ft = 12 in

321unlimited3421unlimited

Calculations with Sig Figs

Multiplication and division: the reported answer should have the same number of SFs as the least precise measurement

13.4 m x 2.7 m = 36.18 m2 = 36 m2 45.67 g / 12.8 mL = 3.56796875 g/mL = 3.57 g/mL

You can use the removed digits to round if necessary.

Calculations with Sig Figs

Addition and subtraction: the answer should be rounded to the least precise decimal position

4.5 m + 9.18 m = ?

14.832 g – 9.25 g = ?

4.5+9.1813.68 = 13.7 m

14.832-9.25 5.582 = 5.58 g

Objectives

• Be able to define commonly used types of measurements used in chemistry.

• Be able to identify the units used in chemistry.• Be able to identify the types of instruments

used to make measurements.

Common Metric Measurements

• mass: amount of matter• grams (g)• use a balance • nearest 0.01 g

• length: measure of distance• centimeters (cm)• nearest 0.1 cm with ruler

42.3 cm

MASS IS NOT WEIGHT!weight is the force of gravity

measurement: includes value and unitWhich of the following are measurements?a. 12 grams b. pounds c. 4.5 mLd. 3.1415

Volume

# mL water = # g water ONLY TRUE FOR WATER!

• volume: amount of 3-D space• cubic centimeters (cm3) for solids• milliliters (mL) for liquids• # cm3 = # mL

volume = 52.7 mL

1.00 L water = 1.00 kg water

• use a graduated cylinder or graduated flask• +/- 0.1 mL (using meniscus)

Temperature

• temperature: measures particle vibrational motion (faster = hotter)• degrees Celsius (oC) or Kelvin (K)• measure to nearest 1oC

absolute zero: coldesttemperature, all particle motion stops0 K = -273oC

• # oC + 273 = # K• # K - 273 = # oC

Objectives

• Be familiar with Celsius and Kelvin temperature.

• Be able to make conversions between common prefixes used in the metric system.

• Understand the meaning of accuracy.• Be able to calculate percentage error.

Metric Prefixes

Use the prefix scale to move the decimal point…M ● ● k ● ● unit ● c m ● ●

M mega = 106 k kilo = 103

c centi = 10-2

m milli = 10-3

micro = 10-6

14.5 cm = ? mm 145 mm

4.57 kg = ? g 4570 g

34.6 mL = ? L 0.0346 L

Objectives

• Understand the concept of density in terms of a physical property.

• Be able to use the density equation to calculate density, mass, or volume.

Density

Vm

ddensity: mass per volume (g/cm3 or g/mL)

All samples of a substance (at sameconditions) will have an identical density.

If 3.00 cm3 of lead has a mass of 34.0 g, then 6.00 cm3 will have a mass of 68.0 g. What are their densities?

3cm

g3 11.3

3.00cm34.0g

d

3cm

g3 11.3

6.00cm68.0g

d

Density

Vm

d

If the density and either the mass or volume is known, then the other variable can be calculated.

What is the volume of a 45.8 g piece of copper? d = 8.96 g/cm3

dm

V

3cm

g8.9645.8g

V V = 5.11 cm3

Density

Vm

d Vdm

What is the mass of a 12.5 cm3 piece of iron? Look up the density on your periodic table!

3

cm

g 12.5cm7.86m 3 m = 98.3 g

Thickness of Aluminum Foil Lab

Vm

d hwlV

Question: How much thicker is “heavy duty” aluminum foil than “regular” aluminum foil?

We can use density to help answer this question.

hwlm

d

Measure the mass, length, and width of a sheet ofeach type of foil. The density will be the same for each.The thickness (h) can be calculated and compared.

Vernier Calipers

= 1.23 cm

The 3rd line on vernier scale aligns with scale above

This line showsthat the lengthis a little more than 1.2 cm