Applying Mathematical Concepts to Chemistry

DATA ANALYSIS

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

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.

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.

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

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

MEASUREMENT PRECISION

Measurements are limited in by the precision of the instrument used to measure

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

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

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

50.20 x 1.500

0.412 x 230

1.2x108 / 2.4 x 10-7

50400 / 61321

PRACTICE MULTIPLYING/DIVIDING

Round answer to least “precise” original operator.

Example

RULE FOR ADDING/SUBTRACTING

1001.2345 =1000

990- 12

978 = 980

100.23 + 56.1

.000954 + 5.0542

1.0 x 103 + 5.02 x 104

1.0045 – 0.0250

PRACTICE ADDING/SUBTRACTING

If you haven’t already done so, you should begin to read Section 3.1 Measurements and Their Uncertainty (pg.63-72)

Based on the reading, the notes, and practice work you have done in your packet, you should be able to complete the following:

Supplemental Questions 1 and 2Written work Questions 57-62 on page 96

80 on page 97

BENCHMARK

UNITS OF MEASURE

SI Units- scientifically accepted units of measure: Know:

Length Mass Temperature Time

THE METRIC SYSTEM

G M K h da (base unit) d c m n p

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

Degrees Celsius to Kelvin

Tkelvin=Tcelsius + 273

Kelvin to Degrees Celsius

Tcelsius=Tkelvin - 273

TEMPERATURE CONVERSIONS

If you haven’t already done so, you should begin to read Section 3.2 The International System of Units (pg. 73-79)

Based on the reading, the notes, and practice work you have done in your packet, you should be able to complete the following:

Supplemental Questions 3-5Written work Questions 64-66 on page 96

82 on page 97

BENCHMARK

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

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

DENSITY BY WATER DISPLACEMENT

Fill graduated cylinder to known initial volume

Add objectRecord final volumeSubtract initial

volume from final volume

Record volume of object

GRAPHING DATA

General Rules Fit page Even scale Best fit/trendline Informative Title Labeled Axes with

units

The Affect of Temperature on Volume

If you haven’t already done so, you should begin to read Section 3.4 Density (pg. 89-93)

Based on the reading, the notes, and practice work you have done in your packet, you should be able to complete the following:

Supplemental Questions 6-9

Written work Questions 74-77 on page 96 86 ,87, 92 on page 97 102 on page 98 2-14 even on page 99

(Also do 90 on page 97)

BENCHMARK