data analysis applying mathematical concepts to chemistry

Data Analysis

Applying Mathematical Concepts to Chemistry

Units of Measure SI Units- scientifically

accepted units of measure:

The Metric System

Metric Practice

623.19 hL = __________ L 1026 mm = ___________cm 0.025 kg = ___________mg

Online Powers of 10 Demonstration:

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Derived Quantities- Volume

Volume- amount of space an object takes up.

V = l x w x h (all in meters)

V= m3 m3 is too large so cm3 are

used 1 cm3 = 1 mL by

definition

Temperature Scales

Temperature Conversions

Degrees Celsius to Kelvin

Tkelvin=Tcelsius + 273

EX: 25 °C = ? K

Tkelvin=25 +273=298K

Kelvin to Degrees Celsius

Tcelsius=Tkelvin - 273

EX: 210 K = ? °C

Tc= 273–210= -63°C

Scientific Notation

A method of expressing very large or small numbers in a concise manner

Requires 2 parts:– Number between 1 and 9.99999999…– Power of ten

– EX: 5432.1 meters 5.4321 x 103 meters

Factor Labeling (Dimensional Analysis)

Any number divided by itself is equal to 1– 6/6 = 1– 6 meters/6 meters = 1

Any number can be multiplied by one without changing its value– 5 x (6/6) = 5– 5 x (6 meters/6 meters) = 5

Converting Units Through Dimensional Analysis

Equal units divided by one another are equal to 1

1m/100 cm = 1 m/cm 100 cm/1m = 1 cm/m

50 cm x (1m/100cm) = 0.5 m 50 m x (100cm/1m) = 5000 cm

Practice Problems

12.5 eggs = ? Dozen

13.69 m = ? cm

13.69 km = ? cm

1.25 x 103 ft = ? yd

Multiple Step Factor Labeling

5.2 x103 yd = ? In

45 mph = ? ft/min

3.1 g/mL = ? Kg/L

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?

Accuracy vs Precision

Accuracy- closeness of measurements to the target 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– 543.21 meters has 5 significant figures

2. Zeros between nonzeros are significant– 505.05 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– 1000.0g has five sig figs

5. Counting numbers and constants have infinite significant figures– 5 people has infinite sig figs

Practice Identifying Sig Figs

A) Clearly circle the significant digits in each of the following numbers:

0.540 30 m 46.93 L 0.004 79 g 56.00 s

B) Rewrite each of the following numbers to the number of significant digits which is specified in the parenthesis:

0.012 70 (2) 2,190,050 L (2) 0.005 23 g (1) 3.079 s (2)

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 123.456 = 123456 = 100000 EX: 1000. x 123.456 = 123456 = 123500

Practice Multiplying/Dividing

50.20 x 1.500

0.412 x 230

1.2x108 / 2.4 x 10-7

50400 / 61321

Rule for Adding/Subtracting

Only place values where all measurements being added/subtracted have sig figs are utilized

EX: 1002

+ 1.2345

1003

Practice Adding/Subtracting

100.23 + 56.1

.000954 + 5.0542

1.2 x 104 – 5.02 x 103

1.0045 + 0.0250