data analysis
DESCRIPTION
Data Analysis. Applying Mathematical Concepts to Chemistry. Scientific Notation. concise format for representing extremely large or small numbers Requires 2 parts: Number between 1 and 9.99999999 … (coefficient) Power of ten (exponent) Examples: - PowerPoint PPT PresentationTRANSCRIPT
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Applying Mathematical Concepts to Chemistry
DATA ANALYSIS
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concise format for representing extremely large or small numbers
Requires 2 parts: Number between 1 and 9.99999999…(coefficient) Power of ten (exponent) Examples:
6.02 x 1023 = 602,000,000,000,000,000,000,000 2.0 x 10 -7 m = 0.0000002 m
See Appendix C R63 for instructions on how to properly calculate numbers in scientific notation with a calculator
SCIENTIFIC NOTATION
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Additional and Subtraction In order to add or subtract numbers that are expressed in scientific
notation, the exponents must be the same. If the exponents are different, it always helps to convert the number
with the smaller exponent to a number with the larger exponent. Don’t worry about having a proper coefficient – you won’t
Once the exponents are equal, add or subtract the coefficients and attach the larger exponent.
SCIENTIFIC NOTATION CALCULATIONSAddition and Subtraction
Being able to perform scientific notation calculations without a calculator is a great skill to have. It gives you’re the power to evaluate if you made a computational mistake.
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Multiplication. Multiply the coefficients and
add the exponents If the calculated coefficient
is 10 or greater, move the decimal to the left and increase the exponent.
SCIENTIFIC NOTATION CALCULATIONSMultiplication and Division
In order to multiply or divide numbers that are expressed in scientific notation, the exponents DO NOT have to be the same.
Division Divide the coefficients and
add the exponents If the calculated coefficient
is less than 10, move the decimal to the right and increase the exponent.
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Accuracy- closeness of measurements to the target value
Error - difference between measured value and accepted value
Precision- closeness of measurements to each other
ACCURACY VS PRECISION
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PERCENT ERROR
Example:In order to calibrate a balance a 5.0g mass standard (accepted) was placed on the balance. The output registered 4.8g
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MEASUREMENT PRECISION
Measurements are limited in by the precision of the instrument used to measure
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SIGNIFICANT DIGITS IN MEASUREMENT
Read one place past the instrument
52.7
If a measurement is observed on one of the graduated lines, you must add a zero at the end of the number to indicate that degree of precision 50.0
Always read the volume of a liquid in a graduated cylinder from the bottom of the meniscus
Significant digits in measurement include all of the digits that are known and plus one measure (the last digit) of uncertainty
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1. Nonzero digits are always significant (543.21 5SF)2. Zeros between non-zeros are significant (1003 4SF)3. Zeros to the right of a decimal and a nonzero are significant (32.06200 7SF)4. Placeholder zeros are not significant
0.01g 1 SF 1000.g 4 SF1000g 1 SF 1000.0g 5 SF
5. Counting numbers and constants have infinite significant figures 5 people (infinite SF)
Relax There are only two situations where zeros are not significant. Evaluate the zeros in any number first. If they are all significant then every digit in your number is significant.
RECOGNIZING SIGNIFICANT DIGITS
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Multiply as usual in calculatorWrite answerRound answer to same number of sig figs as the lowest
original operator
EX: 1000 x 123.456 = 123456 = 100000EX: 1000. x 123.456 = 123456 = 123500
RULE FOR MULTIPLYING/DIVIDING SIG FIGS
A CALCULATED ANSWER CANNOT BE MORE PRECISE THAN THE LEAST PRECISE MEASUREMENT FROM WHICH IT WAS CALCULATED
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50.20 x 1.500
0.412 x 230
1.2x108 / 2.4 x 10-7
50400 / 61321
PRACTICE MULTIPLYING/DIVIDING
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Round answer to least “precise” original operator.
Example
RULE FOR ADDING/SUBTRACTING
1001.2345 =1000
990- 12978 = 980
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100.23 + 56.1
.000954 + 5.0542
1.0 x 103 + 5.02 x 104
1.0045 – 0.0250
PRACTICE ADDING/SUBTRACTING
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UNITS OF MEASURE
SI Units- scientifically accepted units of measure: Know:
Length Mass Temperature Time
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THE METRIC SYSTEM
G M K h da (base unit) d c m n p
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623.19 hL = __________ L
102600 nm = ___________cm
0.025 kg = ___________mg
Online Powers of 10 Demonstration:http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
METRIC PRACTICE
G M K h da (base unit) d c m n p
62319
0.01026
25000
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Degrees Celsius to Kelvin
Tkelvin=Tcelsius + 273
Kelvin to Degrees Celsius
Tcelsius=Tkelvin - 273
TEMPERATURE CONVERSIONS
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DERIVED QUANTITIES - VOLUME
Volume- amount of space an object takes up (ex: liters)V = l x w x h 1 cm3 = 1 mL by definition
The volume of an irregularly shaped object can be determined by displacing its volume
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DERIVED QUANTITIES- DENSITY
Density- ratio of the mass of an object to its volume
Density = mass/volumeD= g/mLDensity depends on the composition of
matter, no the amount of matter
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DENSITY BY WATER DISPLACEMENT
Fill graduated cylinder to known initial volume
Add objectRecord final volumeSubtract initial
volume from final volume
Record volume of object
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GRAPHING DATA
General Rules Fit page Even scale Best fit/trendline Informative Title Labeled Axes with
units
The Affect of Temperature on Volume