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