1. Chapters 3: Unit Systems and Dimensional Analysis
Chemistry 1405
Chapters 3: Unit Systems and Dimensional Analysis
Reference: Intro to Chemical Principles by H. Stephen Stoker

2. Chapters 3: Unit Systems and Dimensional Analysis
The Metric System of units
Metric Units of Length, Mass & Volume
Units in Mathematical Operations
Conversion Factors
Dimensional Analysis
Density
Percentage and Percent Error
Temperature Scales
Graphs

3. Measurement Systems Two measurement systems in US:
English System – used in commerce
Metric System – used in science and some commerce
Quantity
Metric System
English System
Tool for measure
Mass
Length
Volume
Temperature
grams
scale
pounds
in. feet yards
ruler
meters
Graduated cylinder
liters
oz qt gal °C °F
Thermometer

4. SI Units
In 1960, General conference of weights and measures, the international authority proposed a revised metric system called the International System of Units (French, Systeme Internationale d’Units)
The International System (SI) is similar to metric system. SI is more comprehensive and sophisticated.

5. Metric System
In metric system, base or derived units for each type of measurements are multiplied by appropriate powers of ten to form a smaller or larger units.
Metric System is base 10
Prefixes listed in table 3.2, p. 57 of 9th edition; p. 60 of 10th edition.
Uses similar nomenclature for mass (gram), length (meter), time (second) and volume (liter).
1 ml = 1cm3

6. Metric System Mega- M 1,000,000 106 Kilo- k 1,000 103 Hecto- h 100 102
Deca- da
Base units m, g, s, L =1
Deci- d
Centi- c
Milli- m
Micro- m
Nano- n
p. 51 of Chemical Principles by H. S. Stoker, 8th ed
p. 57 of Chemical Principles by H. S. Stoker, 9th ed
p. 60 of Chemical Principles by H. S. Stoker, 10th ed

7. Metric unit of Length
The meter (m) is the SI system base unit of length.
Metre is the preferred international spelling, but it is spelled as meter in US.
kilometer, km (1000 times larger than meter)
centimeter, cm (one-hundredth of a meter)
millimeter, mm (one-thousandth of a meter)

8. Metric Unit of Mass
The kilogram (kg) is the SI system base unit of mass.
The gram, g, is the metric base unit of mass.
Mass is a measure of the total quantity of matter in an object.
Weight is a measure of the force exerted on an object by the gravitational forces.
Mass of the object remains same however weight of the substance varies as per the gravitational force.

9. Metric Unit of Volume
Area is the measure of the extent of the surface. (square inch, in2, square cm, cm2, square feet, ft2 etc.)
Volume is the measure of the amount of space occupied by an object. It’s a three dimensional measure & thus involves units that have been cubed. (in3 cm3 ft3 )
The volume of an object is calculated by multiplying the length (l) by the width (w) by the thickness (t).
volume = l × w × t

10. regular solids: volume = length x width x height
Measuring Volume
regular solids: volume = length x width x height
liquids—use a graduated cylinder. To read the scale correctly, read the volume at the lowest part of the meniscus - the curve of the liquid’s surface in a container.
Your eye should be level with the meniscus when reading the volume
meniscus

11. Metric Unit of Volume
The liter (L) is the basic unit of volume in the metric system.
One liter is defined as the volume occupied by a cube that is 10 cm on each side.
(Refer Figure 3.6, Page 65, 10th Edition)
1 liter is equal to 1000 cubic centimeters
10 cm × 10 cm × 10 cm = cm3
1 L =1000 cm3 = 1000 mL
Therefore, 1 cm3 = 1 mL.

12. Conversion Factors
Conversion factors in the same measurement system are considered exact numbers
English-to-English Conversion factors
Metric-to-Metric Conversion factors
Does this impact significant figures?
Have unlimited number of sig. figs
The number equivalent of prefix (the power of 10) is always associated with the base (unprefixed) unit and the number one is always associated with the prefixed unit. (1km = 103 m or 1cg = 10-2 g))
(Prefixed unit) 1km/ 103 m (unprefixed or base unit)

13. Conversion Factors
Unit equations shows the conversion between different metric units.
The unit equation is 1 km = 1000 m.
1 min = 60 sec
Conversion factors are ratios that specifies how one unit of measure is related to another unit of measure
Each unit equation will have two conversion factors.
1 km or m
1000 m km
1 min or sec
60 sec min

14. Conversion Factors
Conversion factors are used to convert between English system and Metric system
These conversion factors are considered measured (inexact) numbers and have a specific number of significant figures.
Conversion factors are always rounded to fewer specific number of significant digits.
1.00lb = 454 g (three sig. figs)
1.000lb = g (four sig. figs)
1.0000lb = g (five sig. figs)

15. Applying what you have learned:
Dimensional Analysis
Applying what you have learned:
Dimensional analysis is a general problem solving method in which the units associated with numbers are used as a guide in setting up the calculations.
These can be used for simple or complex calculations.
Also know as the Factor-Label method.
You will use this type of analysis all semester.

16. Dimensional Analysis
Step 1: Identify the given quantity (numerical value and the unit) and the units of unknown or new quantity.
Step 2: Multiply the given quantity by one or more conversion factors so that undesired units are cancelled leaving desired units.
Step 3: Perform the mathematical operations indicated by the conversion factor setup.
Check number of significant figures.

17. Dimensional Analysis Simple Example: Complex Example:
Convert hours to seconds
(0.598 hr) x (60 min/1 hr) x (60 sec/1 min) = 2.15x103 sec
Complex Example:
Express 60.0 Kilometers per hour in centimeters per second
(60.0km/1hr)x(1000m/1km)x(100cm/1m)x(1hr/60min)x(1min/60sec)
=1670 cm/sec
Other Examples?

18. Metric-metric Conversion
What is the mass in grams of a 453 mg aspirin tablet?
Step 1: We want grams.
Step 2: We write down the given: 453 mg.
Step 3: We apply a unit factor (1 mg = g) and round to three significant figures.
453 mg ×
= g
1 mg
0.001 g

19. Conversions with two unit factors
A hospital has 135 deciliters of blood plasma. What is the volume in milliliters?
Step 1: We want the answer in mL.
Step 2: We have 135 dL.
Step 3: We need to first convert dL to L and then convert L to mL:
0.1 L and mL
1 dL L

20. Conversions with two unit factors
Apply both unit factors, and round the answer to 3 significant digits.
Notice that both dL and L units cancel, leaving us with units of mL.
135 dL ×
= 13,500 mL ×
1 dL
0.1 L
1 mL
0.001 L

21. Conversions with two unit factors
The mass of the Earth’s moon is 8.35 × 1022 kg. What is the mass expressed in megagrams, Mg?
We want Mg; we have 8.35 × 1022 kg.
Convert kilograms to grams, and then grams to megagrams.
8.35 × 1022 kg ×
= 8.35 × 1019 Mg ×
1 kg
1000 g
1 Mg g

22. English-Metric Conversion
The length of an American football field, including the end zones, is 150 yards. What is the length in meters?
Convert 150 yd to meters given that yd = m.
150 yd ×
= m = 140 m
1 yd
0.914 m

23. English-Metric Conversion
A half-gallon carton contains 65.0 fl oz of milk. How many milliliters of milk are in a carton?
We want mL; we have 65.0 fl oz.
Use 1 qt = 32 fl oz, and 1 qt = 946 mL.
65.0 fl oz ×
= ml
= 1,920 mL ×
32 fl oz
1 qt
946 mL

24. Conversions Using Two Types of Units
Some measurements have a ratio of units.
For example, the speed limit on many highways is 55 miles per hour. How would you convert this to meters per second?
Convert one unit at a time using unit factors.
first, miles → meters
second, hours → seconds

25. Conversions Using Two Types of Units
A motorcycle is traveling at 65 km/hour. What is the speed in meters per second?
We have km/h; we want m/s.
Use 1 km = 1000 m and 1 h = 3600 s.
= 18 m/s ×
1 km
1000 m
1 hr
3600 s
65 km hr

26. Density
Density (d) is the ratio of the mass (m) of an object to the volume (v) occupied by that object.
D = m/v
Units of density are grams (g) per cubic centimeter (cm3) or g/cm3
Also g/ml since 1ml = 1 cm3
Using density as a conversion factor to relate mass and volume. E.g.1.54g = 1mL

27. Density
Knowing volume and mass you can find the density. If you know the mass and density can you find the volume?
v = m/D
If you know the volume and the density, can you find the mass?
m = D x v
If you have a cylinder with a known mass, diameter and height, can you find the density?
D = m/[p(d/2)2h ]
If you have a formula for volume, know the mass, you can calculate density.

28. Examples
Calculate the density, in grams per ml, for 15.0 g of seawater having a volume of 14.6 mL.
Calculate the mass, in grams, of 33.3 cm3 of bone with a density of 1.8 g/mL.
Calculate the volume of 244 g of milk given the density is 1.03 g/mL.
Knowing there are 29.6 ml in one ounce, state the volume in ounces.

29. Estimating Density What floats?
If all the liquids listed below are added to a graduated cylinder, what floats on top and what is on the bottom?
Glycerol g/mL
Corn syrup 1.38 g/mL
Corn oil g/mL
Water ??

30. This Galileo thermometer combines art with science
This Galileo thermometer combines art with science. It provides an accurate reading of current weather conditions. Temperature is indicated by the lowest "floating" sphere in the top grouping. As accurate as laboratory thermometers. Predict changes in the weather by referencing fluid rise and fall in the barometric tube. The hygrometer measures humidity.
How the thermometer works:
The colored floating spheres are "pushed" either up or down depending on the changing density of the clear fluid inside the glass thermometer body. When the temperature goes up, the clear fluid becomes less dense and rises - forcing the spheres down one by one. When the temperature goes down, the clear fluid becomes denser - forcing the spheres upward.
How the barometer works:
While not as accurate as modern day aneroid barometers, the principle of the early "Water Barometer" is sound. When atmospheric pressure decreases, the fluid is pulled upward toward the top of the barometer tube (low pressure). As atmospheric pressure increases, the fluid is "pushed down" (high pressure). Standard atmospheric pressure at sea level is 29.92".
How the hygrometer works:
The Hygrometer Gauge measures % of relative humidity in the air. Humidity is determined by reading the number at the end of the indicator pointer.

31. Percentage
Percent is the number of items of a specified type in a group of 100 total items.
A percent is a ratio of parts per 100 parts.
The formula for calculating percent is shown below:

32. Percentage Calculations
Sterling silver contains silver and copper. If a sterling silver chain contains 17.5 g of silver and 2.5 g of copper, what is the percent of silver in sterling silver?

33. Percent Unit Factors
A percent can be expressed as parts per 100 parts.
25% can be expressed as 25/100 and 10% can be expressed as 10/100.
We can use a percent expressed as a ratio as a unit factor.
A rock is 5.70% iron, so

34. Percent Unit Factors
The Earth and Moon have a similar composition; each contains 5.70% iron. What is the mass of iron in a lunar sample that weighs 230 g?
Step 1: We want g iron.
Step 2: We write down the given: 230 g sample.
Step 3: We apply a unit factor (5.70 g iron = 100 g sample) and round to three significant figures.

35. Percent error = measured value - accepted value x 100
Percent error is the ratio of the absolute value of the difference between the measured value and the accepted value for the measurement and the accepted value itself, multiplied by 100
Percent error = measured value - accepted value x 100
accepted value

36. Example for Percent Error
The accepted length of an aluminum rod is 34.7 cm. Three students were asked to determine the length of a rod experimentally. Their results are:
Student
Student
Student
Calculate the percent error with each result.

37. Percent error = measured value - accepted value x 100
34.4 cm – 34.7 cm
x 100
Percent error =
34.7 cm
-0.3 cm =
x 100
34.7 cm =
0.9%

38. Temperature Scales Fahrenheit Celsius Kelvin, also know as Absolute
Water freezes at 32°F and boils at 212°F
Celsius
water freezes at 0°C and boils at 100°C
Kelvin, also know as Absolute
Water freezes at K and boils at K

39. Temperature Conversions9 5
Converting between °F
and °C requires adjusting for the ice point. °F =
(°C) + 32 5 9 °C =
(°F - 32)
K = °C

40. Conversions:
K = oC
273 K = 0 oC
373 K = 100 oC
oC = (oF – 32) 9 5
oF = (9/5 xoC) + 32
32 oF = 0 oC
212 oF = 100 oC

41. Graphing
Independent variable: Controlled or manipulated by the experimenter.
Plot on X-axis
Dependent variable: magnitude is dependent on the change in the independent variable.
Plot on Y-axis
Label graph and axis; include legend.

42. Title 20
Label (units) 10 10 20
Label (units)

43. Graphing

44. Graphing