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 … Power of ten Examples:  6.02 x = 602,000,000,000,000,000,000,000  2.0 x m = m Use calculator to solve problems on p

Accuracy vs Precision  Accuracy- closeness of measurements to the target value Error- difference between measured value and accepted value (absolute value)  Precision- closeness of measurements to each other

Percent Error  %error = (accepted-experimental) x 100 accepted  EX: The measured mass is 5.0g. It was predicted that the accepted value should have been 6.0 g.  % error = 6.0g-5.0g x 100 = 16.7% 6.0g

Significant Figures  Measurements are limited in their sensitivity by the instrument used to measure

Estimating Measurements  Read one place past the instrument  35.0 mL is saying the actual measurement is between 34.9 and 35.1 mL

Why Significant Figures?  Measurements involve rounding  Multiplying/dividing or adding/subtracting measurements can not make them more accurate  Provide a way to tell how sensitive a measurement really is…  5 ≠ 5.0 ≠ 5.00 ≠ 5.000

Recognizing Significant Digits  1. Nonzero digits are always significant meters has 5 significant figures  2. Zeros between nonzeros are significant liters has 5 sig figs  3. Zeros to the right of a decimal and a nonzero are significant 3.10 has 3 sig figs

Recognizing Sig Figs  4. Placeholder zeros are not significant 0.01g has one sig fig 1000g has one sig fig 1000.g has four sig figs g has five sig figs  5. Counting numbers and constants have infinite significant figures 5 people has infinite sig figs

Rule for Multiplying/Dividing Sig Figs  Multiply as usual in calculator  Write answer  Round answer to same number of sig figs as the lowest original operator  EX: 1000 x = =  EX: x = =

Practice Multiplying/Dividing  x  x 230  1.2x10 8 / 2.4 x  / 61321

Rule for Adding/Subtracting  Round answer to least “precise” original operator.  EX:

Practice Adding/Subtracting    1.0 x x 10 4  –

Units of Measure  SI Units- scientifically accepted units of measure: Know:  Length  Volume (m 3 )  Mass  Density (g/mL)  Temperature  Time

The Metric System

Metric Practice  hL = __________ L  1026 mm = ___________cm  kg = ___________mg  Online Powers of 10 Demonstration: enceopticsu/powersof10/

Good Info to Know  Volume- amount of space an object takes up (ex: liters)  V = l x w x h  1 cm 3 = 1 mL by definition

More Good Info to Know  Mass is different from weight  Mass ≠ Weight  Mass= measure of the amount of matter in an object  Weight= force caused by the pull of gravity on an object ***Mass is constant while weight varies depending on the location of an object***

Temperature Scales

Temperature Conversions  Degrees Celsius to Kelvin  T kelvin =T celsius  EX: 25 °C = ? K  T kelvin = =298K  Kelvin to Degrees Celsius  T celsius =T kelvin  EX: 210 K = ? °C  T c = 273–210= -63°C

Derived Quantities- Density  Density- how much matter is in the volume an object takes up.  Density = mass/volume  D= g/mL

Determining Density  Mass- measure in grams with balance  Volume- Regular shaped object: measure sides and use volume formula  EX: rectangle  V= l x w x h Irregular shaped object: water displacement

Density by Water Displacement  Fill graduated cylinder to known initial volume  Add object  Record final volume  Subtract initial volume from final volume  Record volume of object

Graphing Data  General Rules Fit page Even scale Best fit/trendline Informative Title Labeled Axes How Does Volume Impact Temperature?