1. Plan Unit systems (base units / derived units)
CHM 121
T 1/22/08 (Wk2)
Plan
Unit systems (base units / derived units)
Mass, Weight, Volume, Density
Calculations with units (dimensional analysis)

2. *
*Current would seem to be a derived quantity: charge / time (C/s)

3. CHM 121
T 1/22/08 (Wk2)
All other quantities are related to (derived from) these “fundamental” ones
Volume = length3  cm3 (= mL)
Density = mass/volume  g/mL
Concentration = amount/volume  mol/L

4. Mass, Weight, Volume, Density
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density
Mass is basically:
the amount of “fundamental stuff” (i.e., protons, neutrons, etc.) present in an object or sample.
Mass is independent of where the object/sample is located.
Mass is also the quantity that determines how hard it is to change the motion of an object.
It is harder to accelerate [or decelerate!!] a truck than it is a subcompact because there is more mass in the truck than in the car.

5. Mass, Weight, Volume, Density (continued)
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density (continued)
Weight, on the other hand, is a reflection of
the gravitational force or “pull” (of a planet or moon, for example) on something that has mass.
A bowling ball will weigh less on the moon than it does on the earth, even though the object’s mass is the same.
This is because the force of gravity depends on the mass of both objects. The moon has less mass than the earth, so its "pull" is less strong on a given object.

6. Mass, Weight, Volume, Density (continued)
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density (continued)
Volume (of a sample) is
the amount of space occupied by the “stuff” (in that sample).
Volume is not a measure of an "amount of matter". It is a measure of "space“.
1000 cm3 of Styrofoam has a lot less mass in it than does 1000 cm3 of lead, but these two samples occupy the same amount of space.

7. Mass, Weight, Volume, Density (continued)
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density (continued)
Density (of an object or sample) reflects
how much mass is present in a given volume (of the object or sample)
Density is a measure of the "compactness" of matter.
A high value of density means "very compact" matter (a lot of mass in a given amount of space). A low value means "very spread out" matter.
Popcorn kernel before popping is more dense than the “fluffy” piece of popcorn that remains afterwards (mass gets “spread out” upon popping).

8. Mass, Weight, Volume, Density (continued)
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density (continued)
Density determines whether a substance “sinks” or “floats” in a liquid (once it is submerged)
If dsub > dliq  substance sinks
If dsub < dliq  substance floats
Velocity of object doesn’t matter
Neither does surface area or surface tension (that can affect something whether something on the surface of a liquid submerges; discussed later)

9. Mass, Weight, Volume, Density (final qualitative comments)
CHM 121
T 1/22/08 (Wk2)
Mass, Weight, Volume, Density (final qualitative comments)
“amount of matter”  “amount of space”
(mass)
(volume)
How do you experimentally assess?
Volume can be determined by “liquid displacement”
& can be estimated [roughly] by sight
Mass can be determined with a balance.
& can be estimated [roughly] by “feel”
Density is usually calculated rather than measured directly
& can be estimated [roughly] by “sight” and “feel”

10. Demo/Exercise(s) Can’t assess mass “visually”
CHM 121
T 1/22/08 (Wk2)
Demo/Exercise(s)
Can’t assess mass “visually”
Try “feeling”, but sometimes brain is fooled!
Can (if shapes same) assess volume visually
Water displacement can be used to measure volume (if non-absorbent, and substance sinks in water!)
(Try PS1b Q’s now!)

11. CHM 121
T 1/22/08 (Wk2)
Basic Calculations involving Physical Quantities (& Dimensional Analysis [DA])
Unit conversion calculations
What is the mass of a 154 lb person expressed in grams?
1 kg = 1000 g (this is an exact qty; discussed later)
2.205 lb = 1 kg (this is not an exact qty)
Many approaches. How would you do it?
(Some use explicit proportions; in US, most use DA)
Online resource with examples:
(NOTE: I have some issues with some the work on this site, but overall, the examples themselves are good ones)

12. *Can be used with any
SI unit of measurement
**Prefixes with an arrow indicate those you are responsible for on Exam 1b

13. CHM 121
T 1/22/08 (Wk2)
Assertions
Units are treated like a algebraic variables during calculations
It is often useful to turn “equivalences” into “conversion factors” (fractions) to do many calculations.
“this for that” concept
Procedure called “Dimensional Analysis” (or “factor label”)

14. Dimensional Analysis uses “conversion factors”
CHM 121
T 1/22/08 (Wk2)
Dimensional Analysis uses “conversion factors”
1 kg = 1000 g 
Note: You can do the math with the numbers and combine the units, without loss of info:
1000 g/kg or (1/1000) kg/g = kg/g
lb = 1 kg 
/ means “per”

15. See board (redo earlier problem)
CHM 121
T 1/22/08 (Wk2)
Conversions can be done by starting with one qty and multiplying by one or more “factors”
If you are looking for an “amount”, start with an “amount”; if you are looking for a “this for that”, start with a “this for that”
See board (redo earlier problem)
Be careful to construct factors properly
Can’t just “make them up” to fit your needs!!!
The factors are “what they are” (determined by equivalences)

16. → (See Table at the front of Tro for more equivalences)
CHM 121
T 1/22/08 (Wk2)
Equivalences within a system are typically exact (defined) (e.g., 1 L = 1000 mL).
Those between systems are usually NOT exact. Exceptions should be indicated as here, with “exact”.
The “1” in any equivalence is always exact; any uncertainty in an inexact equivalence is found in the quantity that is not “1”.
→ (See Table at the front of Tro for more equivalences)

17. Example Convert 45 pm into km
CHM 121
T 1/22/08 (Wk2)
Example
Convert 45 pm into km
One way (not shortest, but generalizable!)
Write equivalences:
1 pm = m; 1 km = 1000 m
Convert from pm to m (the “base” unit) first
Use/create appropriate conversion factor
Then convert from m to km
SEE BOARD
(Try PS1b, more Q’s now!)

18. 2nd Example (w/ squares and cubes)
CHM 121
T 1/22/08 (Wk2)
2nd Example (w/ squares and cubes)
For long (multistep) conversion calculations, use the “dimensional analysis” approach to guide you, BUT NEVER STOP THINKING!
Be careful with squares and cubes:
Instructions for a fertilizer suggest applying kg/m2. Convert into lb/ft2
2.205 lb = 1 kg; cm = 1 in (exact)
See board and/or next slide for setup and solution

19. Convert 0.206 kg/m2 into lb/ft2
CHM 121
T 1/22/08 (Wk2)
Convert kg/m2 into lb/ft2
2.205 lb = 1 kg; cm = 1 in (exact)
I’ll convert kg to lb in the numerator first; then convert m2 to ft2 in denom.
Note: lb/ft2 is a “this for that”, so started with a “this for that” (kg/m2)
(Try PS1b, more Q’s now!)

20. CHM 121
T 1/22/08 (Wk2)
Dimensional Analysis
Useful tool, but very easy to stop thinking…DON’T!
See Ppt03 slide; you already know about “amounts” and “this for thats”!
For single step calculations in particular, think about the “big guys” and “little guys” and reason first (use DA to check work)
See board, next Ppt for idea and examples