Chapter 1 Matter and Measurement
Description of Matter
• Properties
Mass, Volume (Dimensions),
Colour, Charge,
Heat capacity,
Thermal and electrical conductivity
etc, etc…
• State of Matter
“Environment”
Pressure, Temperature, External fields,
“Change”
Time, Velocity
• Composition of matter
Pure or mixture
Particles: atoms, molecules, and ions
• In any science one compares the state of a
system, at one time, to it, at some other time, or
to another state.
• States are therefore described in terms of its
properties, environments (influences) and
composition, which are defined by the measured
values.
• Need a mathematically based language of
description:
“Units”
Universal - “Like is compared with like”
Meaningful –related to common experience
Useful - Easy to work with
Example: Universal
1) One case of beer?
Europe vs Canada
How many in the case?
6, 8, 12, 24,
Count Universal
Size of bottle?
12 ounces
500 ml
“not universal”
2) Money
Roman System “Universal” based on weights
1£
= 1 pound of silver
1 shilling = 1 troy ounce of silver
1 d (penny) = 1/12 of an troy ounce
20 shillings = 1 £
12 d = 1 shilling
240 d = £
Florine (fl)
= 2 shillings
Thaller/Mark (dollar) = 3 shillings
Crown
= 5 shillings
2) How much do you weigh?
Canada
U.K.
Europe
200 pounds
14 stone
90 Kg
“Easy”
9*1010 µg
“not easy”
3) How much does a hydrogen atom weigh?
1.67*10-27 Kg, 3.68*10-27 pounds, 2.63-28stone
“not easy”
1.0079 atomic mass units
“easy”
4) How tall are you ?
6 ft,
180 cm = 1.8 m
1.9*10-16 light year
How large is an hydrogen atom?
1*10-10 m = 1 Å or 0.1 nm
Scientific Notation
Number become too large too write conveniently
Ex. 231,000,000,000
Write number as a product between a number
between 1 to 10 and a power of 10.
Ex.
2.31*1011
The power ten term can often be abbreviated into the
units used as a prefix.
Ex
2.31*1011 Units = 2.31*102*109 Units
= 2.31*102 Giga Units.
Ex)
1 nano gram = 1*10-9 grams
1 mega gram =1*109 grams = 1*106 Kilo grams
Dimensional Analysis
Units themselves obey certain mathematical relationships.
Velocity = distance/time
Units = meters/seconds = m/s
Acceleration = 0.5*distance/(time)2
Units = meters/seconds2 = m/s2
Compound units themselves have special names:
Force = mass* acceleration
Units = kilo gram*meter/seconds2 = kg m/s2
1 Newton = 1 kg m/s2
Consider energy:
Kinetic energy = 0.5*Mass * velocity2
Units = kg*(m/s)2 = kg m2/s2
Work = Force*distance
Units = Newton*meter = (1 kg m/s2)*m = kg m2/s2
1 Joule = 1 kg.m2/s2
Dimensional analysis of units give physical insights.
Consider Volume:
3-D units
units = meter*meter*meter = m3
Ex ) How many litres are in a pool of water that is 2
meters long, 2 meters wide and 1 meter deep?
Volume = L*W*H = 2 m * 2 m * 1 m = 4 m3
1 liter = 1 dm3 = 1 dm3 * (0.1 m/dm)3 = 0.001 m3
i.e. 1000 l/ m3
4 m3* 1000 l/m3 = 4000 l.
Ex) how many molecules are in a 10. ml sample taken
from a 3.2 Molar solution?
# of moles = N = C*V = (3.2 mol/l)*(10 ml) ???
10 ml = 10 cm3 = 10 cm3 * (0.10 dm/cm)3 = 0.010 dm3
= 0.010 l
# of moles = N = C*V = (3.2 mol/l)* (0.010 l)
= 0.032 mol
A = 6.02*1023 molecules/mol
Therefore #
of molecules = A*N
= (6.02*1023 molecules/mol)* (0.032 mol)
= 1.9 * 10 22 moles
Why? 1.9 Why not 1.9264 ?
Significant Figures
What doe sit mean that you measured something to:
105.9 units
Its is not 106.0 nor 105.8 units
i.e its certainty is 0.1/105.9 = 0.00094/1
= 0.001
i.e we know with certainty of 4 orders of
magnitude.
Consider
0.0001059 units
0.0000001/0.0001059 = 0.00094/1
= 0.001
4 orders of magnitude i.e 4 significant digits.
General rule: # of significant figures, is the number of
digits known with certainty.
0.1057 has 4 sig figs
0.1
has 1 sig fig. as does 1, 100 , 1000, etc
100.
has 3 sig figs
How do the number of significant figure propagate
through a calculation?
Ex) I have 5.0 ml of 0.100 M solution of A how many
moles are there?
5.0 ml has 2 sig. figs. 0.100 M has 3 sig. fig.
Which one limits the accuracy of the result?
The one with the lowest number of sig. figs.
Therefore the result can only be known to 2 sig. figs.
N
= 0.100 (mol/l)*(5.0 ml)*(0.001000.. l/ml)
= 0.00050 mol
n.b. conversion factors are considered to be exact and
therefore have infinite sig. figs. In other words they do
not affect the result.
Ex) A sample of 0.5398 g was added to a container
weighing of a container is 25.21 g. What is the total
weight.
0.5398 g and 25.21 g both have 4 sig. figs.
25.21g is the least accurately known.
0.54 g + 25.21 g = 25.75 g
Precision and Accuracy
Accuracy
Degree of closeness of the measurement to the correct (true)
value.
Precision
Degree of consistency in the measurement.
Ex) Measuring Atmospheric Pressure
You are told that the atmospheric pressure in the room 100 kPa.
You make the following tw sets of measurements:
1) 92, 91, 89, 94, 86 kPa
2) 50, 70, 130, 150 kPa
Comment on the precession and accuracy of each set.
Concepts
Units:
Universal - “Like is compared with like”
Meaningful – related to common experience
Useful - Easy to work with
SI System
Mathematical Language
Dimensional Analysis
Scientific notation
Prefixes and suffixes
Significant figures
Propagation through addition and multiplication
Precision
Degree of reproducibility
Accuracy
Degree of correctness