math and measurement review. chemistry is the science of substances ― their structure, their...
TRANSCRIPT
Math and Measurement Review
Chemistry is the science of substances ― their structure,
their properties, and the reactions that change them into
other substances.
Linus Pauling, “General Chemistry”
Scientific/Exponential Notation
a x 10n
1 ≤ |a| < 10, n is an integer
Negative exponent:
33
110 0.001
10 5
5
110 0.00001
10
Express the following numbers in scientific notation
25
2500
−270000
0.25
−0.0000250
Read Appendix I: A
Units are involved in calculations just as numbers.
Your calculator does not deal with units.You must work on it!
Examples that involve unit calculations
Never drop units!
A physical quantity can be considered asa product of a number and its unit.
a x
number unit
5 m
A B
AB = 15 m
C
AC = 10 m
CB = ?
CB = AB − AC = 15 m − 10 m = (15 − 10) m = 5 m
a x − b x = (a − b) x
H = 3 cm
W = 6 cm
Area = W x H = 6 cm x 3 cm = 18 cm2
a x • b x = ab x2
What is the volume of a cube with edgelength 5 cm?
V = L3 = (5 cm)3 = 53 (cm)3 = 125 cm3
(a x)3 = a3 x3
How many times is AB compared to CD in length?
5.1m10
m15
AC
AB
a a=
b
x
x b
A B15 m
C10 m
D
A B15 m
Time consumed to move from A to B is 5 s.What is the average speed?
m/s3s5
m15
Time
DistanceSpeed
meters per second
a a=
b b
xx/y
y
Chem 1211 and 1212
Mass is a measure of the amount of material in anobject.
Weight is the force that gravity exerts on an object.
F = ma
G = mg
Unit: kg
Unit: N
Mass ≠ Weight
Chemistry is a discipline of science that stronglydepends on experiments.
Experiments Measurements
Some basic concepts related to measurements
Reliability of Measurements
Accuracy refers to the agreement of a particularmeasurement with the true value.
absolute error = experimental value − true value
To quantify accuracy, define:
experimental value (m) absolute error (m)
52 2
50 0
51 1
48 −2
True value = 50 m
sign of error: direction|error|: size
experimental value theoretical value% error = x 100%
theoretical value
relative error = absolute error / true value
= absolute error / theoretical
relative error is often given in percentage:
| |: to make % error a positive number
unknown
experimental value (m) absolute error (m)
52 2
50 0
51 1
48 −2
True value = 50 m
experimental value theoretical value% error = x 100%
theoretical value
What are the percent errors for the measurementslisted in the table?
Error
Random Error: random, cannot avoid. But can take average of multiple measurements to reduce to certain degree.
Systematic Error: same direction, could fix
Based on source
true value
Random error only
true value
Random error and systematic error.
Reliability of Measurements
Accuracy refers to the agreement of a particularmeasurement with the true value.
Precision is the degree of agreement among severalmeasurements.
Accuracy ≠ Precision
The Results of Several Dart Throws Show the Difference Between Precise and Accurate
How to report a measurement?
mL
We report a measurement by recording
ALL the certain digits + ONE uncertain digit
Significant Figures
(except leading zeros)
Or conversions involving prefixes:
Note: Scientific expression does not change the number of sig figs.
a x 10n
1 ≤ |a| < 10, n is an integer
Only need to count sig figs in “a”
Conversion factor # desired unit
# given unit
#: copy from the relation between two units.
= 1
Physical quantity with given unit x Conversion factor
= Physical quantity with desired unit
5.0 in = ? cm
5.000 in = ? cm
19.21 cm = ? in
6.81 cm2 = ? in2
66 km/h = ? m/s
5.000 in = ? m
3.2 m = ? mm
3.2 cm = ? mm
7.8 g/cm3 = ? kg/m3
Three Basic Physical Quantities
Volume
Density
Temperature
1 m = 10 dm = 100 cm
(1 m)3 = (10 dm)3 = (100 cm)3
1 m3 = 103 dm3 = 106 cm3
For liquid, define: 1 L = 1 dm3
Then: 1 mL = ? cm3
= 1 cm3
Volume and its units
How much room an object occupiesin space.
Density: mass of a substance per unit volume of the substance.
V
md ,
Volume
MassDensity
Unit: kg/m3, g/cm3, g/mL
Density is a property of substances. It is determined by thesubstance’s identity and external conditions, not by thesubstance’s mass or volume.
V
md ,
Volume
MassDensity
How to find density?
How to find mass?
How to find volume?
balance
• Liquid: graduated cylinder, beaker, buret, pipet…
• Solid
Regular shape: Measure dimensions, then calculate
Irregular shape: water displacement
Temperature scales
TC, Celsius scale, °C
TF, Fahrenheit scale, °F
TK, Kelvin scale, K (not °K)
Temperature: a measure of hotness or coldness of an object.
Temperature conversions
K C o
KT T 273 K
C
F23C5
F9TT o
o
o
CF
Normal body temperature is 98.6 °F. Convert this temperature tothe Celsius and Kelvin scales.