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Handout 1 – Chem 1A Fall 2014

Part 1: Metrics, Measurements and Sig Figs

1.3 Units of Measurement (important for quantitative measurements)

A. Units of Measurements Table 1.1: The SI Units (be able to recognize):

Table 1.2: Common Metric Prefixes (know pico through Mega):

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Intensive vs. Extensive Properties of Matter

• Extensive properties depend upon the amount of substance present.– Examples?

• Intensive properties do not depend upon the amount of substance present.– Examples?

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Units of Measurement

• Be able to recognize the SI units.

• Memorize the common metric prefixes!(pico through Mega)

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B. Derived Units – formed using SI base units (example: velocity is distance travelled per unit time, thus m/s)

1. Volume

2. Density              

Example: Give the derived SI units for each of the following quantities in base SI units:

a. acceleration = distance/time2

b. force = mass × acceleration

c. work = force×distance

d. pressure = force/area

e. power = work/time.

f. energy = mass x (velocity)2

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Derived Units of Measurement

Formed using the SI base units. For example, velocity is distance traveled per unit time, thus m/s.

• Volume

• Density

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Uncertainty and Errors in Measurements: Covered in detail in lab. It is essential that you have a complete understanding of these!

• AccuracySystematic ErrorPercent Error (MEMORIZE FORMULA!)

• Precision Random ErrorSignificant FiguresRange (MEMORIZE FORMULA)

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1.4 Uncertainty in Measurement When we make a measurement in the laboratory we need to know how good it is. To this end, we introduce two concepts: Precision and Accuracy.

A. Precision and Accuracy

B. Numbers

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Derived Units of Measurement

Formed using the SI base units. For example, velocity is distance traveled per unit time, thus m/s.

• Volume

• Density

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Uncertainty and Errors in Measurements: Covered in detail in lab. It is essential that you have a complete understanding of these!

• AccuracySystematic ErrorPercent Error (MEMORIZE FORMULA!)

• Precision Random ErrorSignificant FiguresRange (MEMORIZE FORMULA)

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C. Uncertainty in Measurement

Glassware Picture Notes Beaker

50-mL Graduated Cylinder

Buret

Pipette

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1.5 Significant Figures

A. Rules for Sig Figs in Inexact Numbers

Lecture Example: How many significant digits do the following measured quantities have?

a) 2.83 cm b) 14.0 g c) 0.02 mL d) 3 fingers e) 36.77 mm f) 0.0033 kg g) 0.2410 km h) 1.00009 L i) 0.0056040 g j) 3600. m k) 1.30x10-3

g

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B. Sig Figs in Calculated Numbers Practice: Round each of the following to 3 significant digits. (a) 6.167 (b) 0.002245 (c) 2.135 (d) 3136 Practice: Round the following calculations to the proper number of significant digits using the rules above. (a) 6.19 x 2.8 (b) 3.18/1.702 (c) (4.10 x 302 – 1100)/1.56x10–4 (d) 6.82 – 2.111 (e) 213 – 0.01 (f) 5.19x10–2 + 1.83 + 219

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1.6 Dimensional Analysis (Factor Label Method) – English ⇔ Metric (i.e. inches to cm; conversions provided)

Metric ⇔ Metric (i.e. micrograms to kilograms; must know pico through Mega)  

Table 1.3: Selected Metric to English Conversion Factors

Lecture Examples:

a. Donuts cost $4.79 a dozen. How much do 3 dozen donuts cost? b. Convert 0.34 cm to µm

c. What volume will 50.0g of ether occupy if the density of ether is 0.71g/mL?

2.54 cm = 1 in Defined

€

2.54 cm1 in

or 1 in2.54 cm

1760 yd = 1 mi Defined

€

1760 yd1 mi

or 1 mi1760 yd

5280 ft = 1 mi Defined

€

5280 ft1 mi

or 1 mi5280 ft

12 in = 1 ft Defined

€

12 in1 ft

or 1 ft12 in

0.9144 m = 1 yd

€

0.9144 m1 yd

or 1 yd0.9144 cm

1.6093 km = 1 mi

€

1.6093 km1 mi

or 1 mi1.6093 km

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Unit Conversions-Dimensional Analysis• English <—> Metric (Conversion factors provided)

• Metric <—> Metric (Must know pico through Mega)

• Ratios• Sequential• Converting squared and cubed units

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Questions and Problems

Text Problem 1.63: Give the derived SI units for each of the following quantities in base SI units:

a) acceleration = distance/time2

b) force = mass × acceleration

c) work = force × distance

d) pressure = force/area

e) power = work/time.

f) velocity = distance/time

g) energy = mass x (velocity)2

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d. Suppose you build a planter box for growing vegetables in your back yard and you want to determine the amount of soil needed to fill the box. You measure the box to be 3.10 m long, 1.52 m wide and 50.0 cm high. When you go to Orchard Supply to order the soil, you discover that garden soil is sold by the cubic yard at a cost of $35.00 per cubic yard. Being highly skilled in unit conversions, you confidently calculate the amount of soil needed in cubic yards. How many cubic yards do you decide to order and what will be the total cost?

e. In the 2012 London Olympics, Michael Phelps won a gold medal in the

100 m butterfly with a time of 51.21 seconds. What was his average speed in miles per hour? (Assume that the uncertainty in the distance is ±0.01 m.)

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f. Gold can be hammered into extremely thin sheets called gold leaf. If a 200-mg piece of gold (density = 19.32 g/cm3) is hammered into a sheet measuring 2.4 ft × 1.0 ft, what is the average thickness of the sheet in meters? How might the thickness be expressed without exponential notation, using an appropriate metric prefix?

1.7 Temperature A. Three common temp units:

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Lecture Example: You’re in Australia and the current temperature is 28°C.

What is this in Farenheit?

Lecture Example: Helium boils at 4 K. What is this temperature in oC?

Lecture Example: The melting point of silicon is 2572oF. What is the equivalent temperature on the Celsius scale?