Scientific & Chemical Fundamentals

Measurement, Conversions & Calculations

Dr. Ron Rusay

Spring 2008

© Copyright 2003-2008 R.J. Rusay© Copyright 2003-2008 R.J. Rusay

Measurement & UnitsSI units & common units in General Chemistry

(Lab Manual pp. 139-142)

•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)

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© Copyright 1998-2008 R.J. Rusay

Units U.S. SI Chemistry

Mass (weight) Pound (lb) Kilogram (kg) “Gram”(g, mg)

Volume Gallon (gal) Liter (L) “Liter” (mL, L)

Temperature Fahrenheit(oF)

Kelvin (K) K & Celsius (oC)

Length Mile (mi),Feet(ft), Inches

(in)

Meter (m) “Meter” (cm, mm, nm)

Time Second (s) Second (s)Mole (mol)

Units of Measure

u

Mass and Volume Measurements:Mass and Volume Measurements: Refer to pp. 5-8Refer to pp. 5-8

Mass Determination(Weighing Devices: Balances)

Volumes of regular shapes

hh

V = l x w x hV = l x w x h

V = s V = s 33

Volume

01_05

1dm3= 1 L

1 cm

1 cm

1m3

1cm3= 1 mL

Liquid Measurement Tools

Numbers & MeasurementThe Importance of Units

Measurement - quantitative observation consisting of 2 partsMeasurement - quantitative observation consisting of 2 parts

• Part 1 - Part 1 - numbernumber• Part 2 - Part 2 - unitunit

Examples:Examples:• 2020 gramsgrams• 6.63 6.63 joules / secondjoules / second

Scale: Size & Comparison

Macroscopic vs. Microscopic IBM financed Video: http://www.wordwizz.com/imagendx.htm

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?

Graphic Comparisons

Powers of Ten:Scale

Shorthand PrefixesLanguage describes scale (prefixes)

How many zeroes does yotta yotta yotta have? How many zeroes does yotta yotta yotta have?

Commonly used prefixes in Chemistry

These should be known from memory.These should be known from memory.

Commonly used prefixes in Chemistry

Attosecond spectroscopy = 10Attosecond spectroscopy = 10 -15 -15 x 10 x 10 -3 -3 secondssecondsScience, Science, 317317, 765-775, (2007), 765-775, (2007)

““The Electron Stopwatch”The Electron Stopwatch”

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

1. 100 milligrams2. 50 milligrams3. 1,000 milligrams4. 100,000 milligrams

1000 milligrams (mg) = 1 gram (g)1000 milligrams (mg) = 1 gram (g)

ANSWERChoice 4 shows the correct conversion. After determining that 20 nickels make up one dollar, then one dollar’s worth of nickels would have a mass of 100 grams. Next, the conversion between grams and milligrams can be performed by multiplying by 1,000 (because there are 1,000 milligrams per gram.)

Section 1.3: Units of Measurement

Scientific Notation &Significant Digits

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

Examples: 2,345 mL and 0.002340 g Examples: 2,345 mL and 0.002340 g

2,345 mL = 2,345 mL = 2.345 x 10 2.345 x 10 33mLmL 0.002340 g = 0.002340 g = 2.3402.340 x 10x 10 -3 -3 g g

Numbers

• 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

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What is the length of the rod?

Different measurement tools give different numbers:Different measurement tools give different numbers:Which ruler is better?Which ruler is better?

? cm? cm

? cm? cm

4.2 - 4.3cm4.2 - 4.3cm

4.24 - 4.25cm4.24 - 4.25cm

What is the diameter of a circle?All measuring devices are not the same, and the values All measuring devices are not the same, and the values

(numbers) that come from them indicate their (numbers) that come from them indicate their limitations.limitations.

Is there a better instrument to use other than a ruler? Is there a better instrument to use other than a ruler?

01_08

0

10

20

30

40

50

mL

Buret

22.2 mL

What does each line represent? What does each line represent?

1 mL1 mL

What can be estimated? What can be estimated?

O.O.1 1 mLmL

Measurement Assignmenthttp://chemconnections.llnl.gov/General/Chem120/volume1.htm

Temperature ScalesRelative to Water

“Normal” Body Temperature

QUESTIONDr. 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?

1. I agree, that would be 31°C.2. I agree, that would be – 31°C.3. I do not agree, that would be 31°C.4. I agree, that would be –31.15°C.

ANSWERChoice 2 provides a correct (very) cold temperature. The formula to use is K = °C + 273.15. However this must be rearranged slightly to yield K – 273.15 = °C. Since this is a subtraction, the correct value would have no numbers beyond the decimal point because 242 does not have numbers beyond the decimal point.

Section 1.7: Temperature

Temperature

Reporting NumbersRules for Significant Digits (Figures)

Nonzero integersNonzero integers always count always count as significant figures.as significant figures.

3456 g3456 g has how many sig figs? has how many sig figs? 44 sig figs. sig figs.

• Expressed in scientific notation?Expressed in scientific notation?

3.456 x 10 3.456 x 10 33 g g

Reporting NumbersRules for Significant (Digits) Figures

Exact numbers (unit, conversion or Exact numbers (unit, conversion or scale factors)scale factors) can can have an infinite have an infinite number of significant figures.number of significant figures.

11 liter = liter = 1,000.1,000. ml, exactlyml, exactly

11 inch = inch = 2.542.54 cm, exactlycm, exactly

ZerosZeros

Leading zerosLeading zeros do not count as do not count as significant figures.significant figures.

0.0486 mL0.0486 mL has how many sig figs? has how many sig figs? 33 sig figs. sig figs.

• Number expressed in scientific Number expressed in scientific notation?notation? 4.86 x 10 4.86 x 10 -2 -2 mLmL

ZerosZeros

Captive zeros Captive zeros always count asalways count assignificant figures.significant figures.

16.16.007 cm 7 cm has how many sig figs?has how many sig figs? 44 sig figs. sig figs.

Number expressed in scientific Number expressed in scientific notation?notation? 1.607 x 10 1.607 x 10 11 cm cm

ZerosZeros

Trailing zerosTrailing zeros are significant onlyare significant only if if the number contains a decimal the number contains a decimal point.point.

9.300 kg9.300 kg has how many sig figs? has how many sig figs? 44 sig figs. sig figs.

• Number expressed in scientific Number expressed in scientific notation?notation? 9.3009.300 kgkg

QUESTIONWhich one of the following does NOT represent a result with four significant digits?

1. 0.071002. 0.71003. 0.70104. 0.0710

ANSWERChoice 4 only has three significant digits. Note that the lone zero in front of the decimal point is not based on any measurement and the next zero serves only as a place holder not as a measurement.

Section 1.5: Significant Figures and Calculations

Mathematics & Arithmetic

• 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:dbhs.wvusd.k12.ca.us/SigFigsFable.html

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Systematic Problem SolvingDimensional/Unit Analysis: Conversions

Workshop pp. 145-149

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

? mL? mL0.500.50 gal gal

11 gal = gal = 44 qt qt 11 qt = qt = 946946 mL mL

0.500.50 gal gal | | 4 4 qt qt || 946946 mL mL | | 1 1 gal gal | | 11 qtqt

= ? mL= ? mL

Complete the followingUnits & Conversions

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

NumberNumber Scientific Notation Scientific Notation Named unit Named unit 1.3 x 1010 yrs

___________ mL ___________ mL ______________ mL ______________ mL 0.546 Liters0.546 Liters

____________ kg____________ kg ____8.45 x 10 8.45 x 10 -1-1 kg kg___ ____ _? grams? grams____

5.46 X 10 5.46 X 10 22 546 546

0.8450.845

845845 g g

0.546 L0.546 L

Computational Rules

• 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

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Addition

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

Report the result correctly:0.05 cm

12.01 cm1.9 cm

+ 2.386 cm_______

16.346 cm16.346 cm

QUESTIONIf 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?

1. 23.98 kg2. 24.464 kg3. 24.46 kg4. 24.5 kg

ANSWERChoice 3 provides both the conversion and proper number of significant digits. Consider that the 482 grams of mass must be doubled (to include both books) and that 482 grams is 0.482 kg. When adding two measurements always report your answer to the same number of decimal places as the least precise measurement used in the calculation. In this case the answer should be reported to the hundredths place.

Section 1.5: Significant Figures and Calculations

Mathematical Processes:

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

12.01 x 1.90_______ _______ _______=

2.386

12.01 x 1.90_______ _______ _______+ 0.05 =

2.386

9.56370 9.56370

9.613709.61370

QUESTIONThe 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?

1. 0.760 grams2. 0.759 grams3. 0.7590 grams4. 0.253 grams

ANSWERChoice 2 provides three significant digits (and accurate math work). 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.

Section 1.5: Significant Figures and Calculations

Conversion Factor Method (Dimensional Analysis)

• 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

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