1. Mathematical Relationships in Chemistry
CP Chemistry

2. What You’ll Learn in this Unit
Measurement
Dimensional Analysis
Scientific Notation
Significant Figures
Error
Density

3. Measurement Every measurement has two parts
Number with the correct sig - figs
Scale (unit)
SI system (le Systeme International) based on the metric system
Prefix + base unit
Prefix tells you the power of 10 to multiply by - decimal system -easy conversions

4. Measurement
COMMON SI UNITS
Symbol  
Unit Name  
Quantity  
Definition
   m
meter
length
base unit
   kg
kilogram
mass
   s
second
time
   K
kelvin
temperature   
   °C
degree Celsius**  
temperature
   m3
cubic meter
volume m3
   L
liter**
dm3 = m3
   N
newton
force
kg·m/s2
   J
joule
energy
N·m
   W
watt
power
J/s
   Pa
pascal
pressure
N/m2
   Hz
hertz
frequency
1/s
We use the SI (not the Sports Illustrated) It is called the Systeme Internationale.

5. Metric SI Units Mass - kilogram (kg) Length- meter (m)
Time - second (s)
Temperature - Kelvin (K)
Electric current - ampere (amp, A)
Amount of substance - mole (mol)

6. Prefix
Symbol
Magnitude
Giga G
1,000,000,000 (109)
Mega M
1,000,000 (106)
Kilo K
1,000(103)
Hecto H
100 (102)
Deca da
10 (101)
base unit
g, L, m
1 (100)
Deci d
0.1 (10-1)
Centi c
0.01 (10-2)
Milli m
0.001 (10-3)
Micro μ
(10-6)
Nano n
(10-9)
Pico p
(10-12)

7. Using Units to solve problems
Dimensional Analysis
Using Units to solve problems

8. Dimensional Analysis Use conversion factors to change the units
1 foot = 12 inches (equivalence statement)
12 in = = 1 ft ft in
2 conversion factors
multiply by the one that will give you the correct units in your answer.

9. Example Problem There are 2.2 lb in 1 kg
If you weigh 158 lbs, how many kg do you weigh?

10. Example Problems 11 yards = 2 rod 40 rods = 1 furlong
8 furlongs = 1 mile
1 mile = 1.6 km
The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?

11. Example Problems
Convert:
475m to km
35daL to mm

12. Scientific Notation 100 = 1.0 x 102 0.001 = 1.0 x 10-3
-- This provides a way to show significant figures.

13. TOO QUICK FOR YOU! So here are the rules.. slowly!
Place decimal point after 1st real non-zero integer. (ex) 1.0 NOT 10.0
Raise 10 to the exponential which equals the number of places you moved.

14. Sample Problems
2387

15. Answers
2.387 x 103
7.031 X 10-5
2.9 x 109
8.900 X 10-3
9.01 X 107
2.10 X 10-6

16. Uncertainty Basis for significant figures
All measurements are uncertain to some degree
Precision- how repeatable
Accuracy- how correct - closeness to true value.
Random error - equal chance of being high or low- addressed by averaging measurements - expected

17. Uncertainty Systematic error- same direction each time
Want to avoid this
Better precision implies better accuracy
You can have precision without accuracy, and vice versa

18. Precision vs. Accuracy
Precision- the degree of agreement among several measurements of the same quantity.
Accuracy- the agreement of a particular value with the true value

20. Significant Figures Meaningful digits in a MEASUREMENT
The number of significant figures in your measurement will tell the reader how exact the instrumentation is
If it is measured or estimated, it has sig figs.
If not, it is exact.

21. Significant Figures All numbers except zero are significant.
Some zeros are, some aren’t

22. Which Zeros Count? In between other sig figs does
Before the first number doesn’t
After the last number counts if it is after the decimal point
the decimal point is written in
sig figs
sig figs

23. Doing the Math
Multiplication and division, same number of sig figs in answer as the least in the problem
Addition and subtraction, same number of decimal places in answer as least in problem.

24. Volume The space occupied by any sample of matter
Calculated for a solid by multiplying the length x width x height
SI derived unit = cubic meter (m3)
Everyday unit = Liter (L), which is non-SI

25. Units of Mass Mass is a measure of the quantity of matter
Weight is a force that measures the pull by gravity- it changes with location
Mass is constant, regardless of location

26. Working with Mass
The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gram
Measuring instrument is the balance scale

27. Density Which is heavier- lead or feathers?
It depends upon the amount of the material
A truckload of feathers is heavier than a small pellet of lead
The relationship here is between mass and volume- called Density

28. Density The formula for density is: mass volume
Common units are g/mL, or possibly g/cm3, (or g/L for gas)
Density =

29. Density Useful for identifying a compound Useful for predicting weight
An intrinsic property- does not depend on what the material is
Intensive Property
Density is a physical property, and does not depend upon sample size

30. Things related to density
Corn oil density – 0.921g/mL
Water density – 1.000g/mL
What happens when corn oil and water are mixed?
Why?
Will lead float in water?

31. Example Problem
An empty container weighs g. Filled with carbon tetrachloride (density=1.53 g/cm3), the full container weighs g. What is the volume of the container?

32. Density and Temperature
What happens to density as the temperature increases?
Mass remains the same
Most substances increase in volume as temperature increases
Thus, density generally decreases as the temperature increases

33. Density and water Water is an important exception
Over certain temperatures, the volume of water increases as the temperature decreases
Does ice float in liquid water?
Why?

34. Specific Gravity
A comparison of the density of an object to a reference standard (which is usually water) at the same temperature
Water density at 4 oC = 1 g/cm3

35. Specific Gravity Formula
D of substance (g/cm3)
D of water (g/cm3)
Note there are no units left, since they cancel each other
Measured with a hydrometer
Uses? Tests urine, antifreeze, battery
SG =

36. Temperature A measure of the average kinetic energy
Different temperature scales, all are talking about the same height of mercury.
In lab take the reading in ºC then convert to our SI unit Kelvin
ºC = K

37. Temperature Heat moves from warmer object to the cooler object
Glass of iced tea gets colder?
Remember that most substances expand with a temp. increase?
Basis for thermometers

38. Temperature scales Celsius scale- named after a Swedish astronomer
Uses the freezing point(0 oC) and boiling point (100 oC) of water as references
Divided into 100 equal intervals, or degrees Celsius

39. Temperature scales Kelvin scale (or absolute scale)
Named after Lord Kelvin
K = oC + 273
A change of one degree Kelvin is the same as a change of one degree Celsius
No degree sign is used

40. Temperature scales Water freezes at 273 K Water boils at 373 K
0 K is called absolute zero, and equals –273 oC

41. 100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF 1ºC = (180/100)ºF 1ºC = 9/5ºF
For Calculations:
°F = 9/5 (°C) + 32
°C = 5/9 (°F - 32)

42. Error Calculations X 100 accepted value
Error = Experimental value - accepted value
% error = [error]
accepted value
X 100