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Scientific & Chemical Fundamentals

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Scientific & Chemical Fundamentals

Measurement, Conversions & Calculations

Dr. Ron Rusay

- Quantitative vs. Qualitative
- MASS (Chem: gram; SI: kg)
- LENGTH (Chem: cm & others; SI: m)
- TEMPERATURE (Celsius & Kelvin; SI: K)
- VOLUME (Chem: mL; SI: Liter)
- CHEMICAL AMOUNT: Mole (mol)

Identify the best match between the dimension or quantity and its correct SI base unit.

Dimension or QuantityUnit

A)MassGram

B)LengthKilometer

C)TimeMinute

D)TemperatureCelsius

E)Amount of substanceMole

Identify the best match between the dimension or quantity and its correct SI base unit.

Dimension or QuantityUnit

A)MassGram

B)LengthKilometer

C)TimeMinute

D)TemperatureCelsius

E)Amount of substanceMole

Identify the best match between the dimension or quantity and the unit that is most likely to be measured in Chem 120 lab.

Dimension or QuantityUnit

A)MassKilogram

B)LengthMeter

C)VolumeMilliliter

D)TemperatureFahrenheit

E)Amount of substanceMegamole

Identify the best match between the dimension or quantity and the unit that is most likely to be measured in Chem 120 lab.

Dimension or QuantityUnit

A)MassKilogram

B)LengthMeter

C)VolumeMilliliter

D)TemperatureFahrenheit

E)Amount of substanceMegamole

V = s 3

h

V = l x w x h

Numbers & MeasurementThe Importance of Units

- Measurement - quantitative observation consisting of 2 parts
- Part 1 - number
- Part 2 - unit

- Examples:
- 20grams
- 6.63 joules / second

- Macroscopic vs. Microscopic
- Older IBM financed Video: Powers of Ten (Movie)
- Powers of Ten (Images)
How would you compare your lifespan?.. to that of a dog? ….to the age of the earth?…How about the age of mankind to that of all life?.. ..the age of industrialized mankind to the age of mankind?

for Monday

- Assume that the earth is 4.6 billion years old and that your Chem 120 class’s average lifespan will be 80 years. If the total age of the earth is represented by the face of a clock, how much time will 80 years be represented on the clock?
- 1500 microsecondsB) 0.75 milliseconds
- C) 8 x 10 -4 secondsD) 7.5 megaseconds
- E) 15 gigaseconds

Language describes scale (prefixes)

Hella is a prefix associated with Northern California: UC Davis, UC Berkeley, LBL, LLNL & adopted by Google (2010) & Wolfram Alpha (2011)

"hella-” = 10 27

An array of multilayer mirrors compresses ultrabroadband laser pulses (orange beam). The attosecond x-ray pulses allow the real-time observation of atomic-scale electron motion. The previous spectroscopic method was on a femtosecond scale, which was too slow to capture the movement.

How many times faster is attosecond spectroscopy compared to femtosecond methods?

Science, 317, 765-775, (2007)

“The Electron Stopwatch”

A. 10xB. 100xC. 1,000xD. 1,000,000x

An array of multilayer mirrors compresses ultrabroadband laser pulses (orange beam). The attosecond x-ray pulses allow the real-time observation of atomic-scale electron motion. The previous spectroscopic method was on a femtosecond scale, which was too slow to capture the movement.

How many times faster is attosecond spectroscopy compared to femtosecond methods?

Science, 317, 765-775, (2007)

“The Electron Stopwatch”

10-15 / 10-18 =

A. 10xB. 100xC. 1,000xD. 1,000,000x

These should be known from memory.

Select the correct relationship between these metric units of length or distance.

A) 1 km = 100 mB) 1 mm = 10 cm

C) 1 nm = 109 mD) 103 mm = 1 m

Select the correct relationship between these metric units of length or distance.

A) 1 km = 100 mB) 1 mm = 10 cm

C) 1 nm = 109 mD) 103 mm = 1 m

Coincidentally, a U.S. nickel has a mass of approximately 5 grams. If you had one dollar’s worth of nickels in your jean’s what would be the mass of the nickels in milligrams?

100 milligrams

50 milligrams

1,000 milligrams

100,000 milligrams

1000 milligrams (mg) = 1 gram (g)

Coincidentally, a U.S. nickel has a mass of approximately 5 grams. If you had one dollar’s worth of nickels in your jean’s what would be the mass of the nickels in milligrams?

100 milligrams

50 milligrams

1,000 milligrams

100,000 milligrams

20 nickels make up one dollar, then one dollar’s worth of nickels would have a mass of 5g x 20=100 grams. Next, the conversion between grams and milligrams is done by multiplying by 1,000 (because there are 1,000 milligrams per 1 gram.)

Would the weight of the nickels pull your jean’s down off of your waist?

Coincidentally, a U.S. nickel has a mass of approximately 5 grams. If you had one dollar’s worth of nickels in your jean’s what would be the mass of the nickels in milligrams?

100 milligrams

50 milligrams

1,000 milligrams

100,000 milligrams

20 nickels make up one dollar, then one dollar’s worth of nickels would have a mass of 5g x 20=100 grams. Next, the conversion between grams and milligrams is done by multiplying by 1,000 (because there are 1,000 milligrams per 1 gram.)

Would the weight of the nickels pull your jean’s down off of your waist?

Likely not. 100g = 100g/454 g/lb equals 0.22lb ~ the weight of a quarter pounder

Scientific Notation: A single digit followed by a decimal and a power of ten.

Examples: 2,345 mL and 0.002340 g

2,345 mL = 2.345 x 10 3mL

0.002340 g = 2.340x 10 -3g

- Expressing a number correctly is determined by the method used in the measurement!
- How many numbers should I include?
Significant Digits (Figures)

Consider: the exactness of the measured value

- Short Hand expression translates the number: Scientific Notation

Different measurement tools give different numbers:

Which ruler is better?

? cm

4.2 - 4.3cm

? cm

4.24 - 4.25cm

All measuring devices are not the same, and the values (numbers) that come from them indicate their limitations.

Is there a better instrument to use other than a ruler to measure the diameter of the sphere?

What does each line represent?

1 mL

What can be estimated?

O.1 mL

Dr. R. walks into class and claims, “It is very cold in here today. It feels like 242 K.” If that were the temperature, would you agree that you would feel cold? What would that be in Celsius degrees?

I agree, that would be 31°C.

I agree, that would be – 31°C.

I do not agree, that would be 31°C.

I do not agree, that would be 515°C.

Dr. R. walks into class and claims, “It is very cold in here today. It feels like 242 K.” If that were the temperature, would you agree that you would feel cold? What would that be in Celsius degrees?

I agree, that would be 31°C.

I agree, that would be – 31°C.

I do not agree, that would be 31°C.

I do not agree, that would be 515°C.

The formula to use is K = °C + 273.15. Rearranged to yield K – 273.15 = °C.

Reporting NumbersRules for Significant Digits (Figures)

- Nonzero integersalways count as significant figures.
- 3456 g has how many sig figs?
- 4 sig figs.
- Expressed in scientific notation?

3.456 x 10 3g

Reporting NumbersRules for Significant (Digits) Figures

- Exact numbers (unit, conversion or scale factors) can have an infinite number of significant figures.
- 1 liter = 1,000.ml, exactly
- 1 inch = 2.54cm, exactly

Zeros

- Leading zeros do not count as significant figures.
- 0.0486 mL has how many sig figs?
- 3 sig figs.
- Number expressed in scientific notation?

4.86 x 10 -2 mL

Zeros

- Captive zeros always count as significant figures.
- 16.07 cm has how many sig figs?
- 4 sig figs.
- Number expressed in scientific notation?

1.607 x 10 1cm

Zeros

- Trailing zerosare significant onlyif the number contains a decimal point.
- 9.300 kg has how many sig figs?
- 4 sig figs.
- Number expressed in scientific notation?

9.300kg

- In which of these measured values are the zeros
- not significant figures?
- I) 0.0591 cm
- II) 504 g
- III) 2.70 m
- IV) 5300 L

- In which of these measured values are the zeros
- not significant figures?
- I) 0.0591 cm
- II) 504 g
- III) 2.70 m
- IV) 5300 L

- Which one of the following does NOT represent four significant digits?
- 0.07100 mg
- 0.7100 mg
- 0.7010 mg
- 0.0710 mg

- Which one of the following does NOT represent four significant digits?
- 0.07100 mg
- 0.7100 mg
- 0.7010 mg
- 0.0710 mg

The zero in front of the decimal point is not a part of any measurement, the next zero is a place holder, and the last zero is part of the measurement and significant. Therefore 3 sig figs.

- Relative to method(s) of measurement
- Short Hand expression: Scientific Notation
- Numbers : How many to include?
Quantitative vs. Qualitative

- Addition/Subtraction......
- Multiplication/Division.....
- What is “significant”?.....Rounding Off
- http://www.chemteam.info/SigFigs/SigFigsFable.html

How many mL of milk are in a1/2 gallon carton?

0.50 gal

? mL

1 gal = 4 qt

1 qt = 946 mL

0.50 gal | 4 qt |946 mL

| 1 gal | 1qt

= ? mL

Number Scientific Notation Named unit

1.3 x 1010 yrs

13,000,000,000 yrs.________________ __? gigayears

13 Gyrs

546

5.46 X 10 2

___________ mL ______________ mL 0.546 Liters

0.546 L

0.845

____________ kg__8.45 x 10 -1 kg___ _? grams__

845g

- Addition/Subtraction: Answer expressed to the least number of decimal places of the figures in the process
- Multiplication/Division: Answer expressed to the least number of significant figures

- Four students were each asked to measure a piece of wire and provide a total length for the four pieces.
- Report the result correctly:

16.346 cm

If you were unloading a 23.50 kg box of books from your car and a “friend” added two more 482 gram chemistry books, how much in kg and using the rules for significant digits, would you be lifting?

23.98 kg

24.464 kg

24.46 kg

24.5 kg

If you were unloading a 23.50 kg box of books from your car and a “friend” added two more 482 gram chemistry books, how much in kg and using the rules for significant digits, would you be lifting?

23.98 kg

24.464 kg

24.46 kg

24.5 kg

The 482 grams of mass must be doubled (to include both books) and 482 grams is 0.482 kg. When adding measurements the answer has the same number of decimal places as the fewest decimal places in the calculation. Therefore the answer has 2 decimal places.

- Provide correct answers assuming each value (unit omitted) is written with the correct number of sig figs:

9.56370

9.61370

The average mass of a certain brand of vitamin C tablets is 253 mg. What is the mass of three such tablets rounded to the proper number of significant digits?

0.760 grams

0.759 grams

0.7590 grams

0.253 grams

The average mass of a certain brand of vitamin C tablets is 253 mg. What is the mass of three such tablets rounded to the proper number of significant digits?

0.760 grams

0.759 grams

0.7590 grams

0.253 grams

3 tablets 253 milligrams = 759 milligrams, then dividing by 1,000 converts the milligrams to grams. Note the three is a count of the number of objects, not a measured quantity and 759 retains the same number of significant digits as the least found in related measurements.

- Qualitative Descriptions vs. Quantitative
- Use exact numbers / “scale factor” UNITS
- A Bookkeeping Method: Example Short”
___ ft___in --------> ? m

- (1 ft = 12 in; 2.54 cm = 1 in; 100 cm = 1 m)
- ___ft x 12 in/ft + ___in = ___in
- ___in x 2.54 cm/in x 1 m/100cm = ___m

5

4

5

4

64

1.626

64

162.6 cm

for Monday

- Assume that the earth is 4.6 billion years old and that your Chem 120 class’s average lifespan will be 80 years. If the total age of the earth is represented by the face of a clock, how much time will 80 years be represented on the clock?
- 1500 microsecondsB) 0.75 milliseconds
- C) 8 x 10 -4 secondsD) 7.5 megaseconds
- E) 15 gigaseconds

- Assume that the earth is 4.6 billion years old and that your Chem 120 class’s average lifespan will be 80 years. If the total age of the earth is represented by the face of a clock, how much time will 80 years be represented on the clock?
- 1500 microsecondsB) 0.75 milliseconds
- C) 8 x 10 -4 secondsD) 7.5 megaseconds
- E) 15 gigaseconds