Transcript Chapter 2 ppt


Quantity - number + unit
UNITS MATTER!!
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Quantitative- use numbers to describe
 Qualitative- use description without
numbers
 4 feet
 extra large
 Hot
 100ºF

Quantitative - easy to check
 Easy to agree upon, no personal bias
 The measuring instrument limits how
good the measurement is.

Scientists use two word to describe
how good the measurements are
 Accuracy- how close the
measurement is to the actual value
 Precision- how well can the
measurement be repeated

Good accuracy
Good precision
Poor accuracy
Good precision
Poor accuracy
Poor precision
Random errors:
Systematic errors:
reduce accuracy reduce precision
(instrument)
(person)
Accuracy can be true of an individual
measurement or the average of
several
 Precision requires several
measurements before anything can
be said about it
 examples

Let’s use a golf anaolgy
Accurate? No
Precise? Yes
10
Accurate?Yes
Precise? Yes
12
Precise?
No
Accurate? Maybe?
13
Accurate?Yes
Precise? We cant say!
18

Accuracy - how close a measurement is to
the accepted value

Precision - how close a series of
measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
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65,000 kg  6.5 × 104 kg

Converting into Scientific Notation:
› Move decimal until there’s 1 digit to its
left. Places moved = exponent.
› Large # (>1)  positive exponent
Small # (<1)  negative exponent
› Only include sig figs.
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0.00002205
1
2
3
4
2.205 x
-5
10
5
In scientific notation, a number is separated into two parts.
The first part is a number between 1 and 10.
The second part is a power of ten.
Form:
(# from 1 to 9.999) x 10exponent
800
2531
= 8 x 10 x 10
= 8 x 102
= 2.531 x 10 x 10 x 10
= 2.531 x 103
0.0014 = 1.4 / 10 / 10 / 10
= 1.4 x 10-3
Practice Problems
1. 2,400,000 g
2.4  106 g
2. 0.00256 kg
2.56  10-3 kg
3. 7  10-5 km
0.00007 km
4. 6.2  104 mm
62,000 mm
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EE
EXP
EE or EXP means “times 10 to the…”
23::
How
out 6.02
6.02 xx 10
1023
How to
to type out
6
0
.
2
EE
EE
2
3
Don’t do it like this…
6
WRONG!
0
.
2
yx
2
3
WRONG!
…or like this…
6
.
0
2
x
1
.
EE
2
3
TOO MUCH WORK.
…or like this:
6
0
0
2
x
1
0
yx
2
3
Example:
1.2 x 105

2.8 x 1013
Type this calculation in like this:
1
.
2
EE
5
2
.
8
EE
1

3
Calculator gives…4.2857143 –09
or… 4.2857143 E–09
This is NOT written…
4.3–9
But instead is written… 4.3 x 10–9
=

Calculating with Scientific Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
= 671.6049383
7
÷
8.1
= 670 g/mol
EXP
EE
4
EXE
ENTER
= 6.7 × 102 g/mol
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Divide: (5.44 x 107) / (8.1 x 104)
671.604938
5.44
8.1
54400000.
07
04
00
How to enter this on a calculator:
5.44
EE 7
.
.
8.1
EE 4
ENTER
OR
5.44
EXP7
.
.
8.1
671.6049383
rounded to 6.7 x 102
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52
EXP 4
=

How do you make a measurement?
› With most measuring devices, you should be
able to estimate to one decimal place more
than the smallest division on the device.
The smallest division is a tenth
_____ of a centimeter, so
hundredth (or ___
you can guess to the _____________
2 decimal
places like 1.24).
= 1.94 cm
= 3.00 cm
= 1.5 cm
1
1=
5.73
2=
3.0
3 = .35
2
3

Indicate precision of a measurement.

Recording Sig. Figs.
› Sig. figs. in a measurement include the known
digits plus a final estimated digit
1.19 cm
0
1
2
3
4
Centimeters
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5

Significant Figures
› All of the known digits plus the estimated digit
are significant – they are not placeholders.
› When we measured the volume of cylinder 1
on the last slide we got:
5.73 mL
known
estimated
› This would mean 3 significant figures.
300
300
200
200
100
100
120 mL
120 mL
What is the smallest 300
mark on a graduated
cylinder that measures
142.15 cm?
200
 242 mL?
 240 mL?
 Here there’s a
problem… does the 100
zero count or not?

300
200
100
Significant Figure Rules
Every nonzero is significant.
1.
•
4 sig figs
Zeros between nonzero digits are significant.
2.
•
3.
123.2 g
1004 m
4 sig figs
Zeros to left of nonzero are NOT significant.
•
0.01 g
1 sig fig
Zeros to the right of a nonzero number if there
is no decimal point are NOT significant
4.
•
1200 g
2 sig figs







How many sig figs in the following
measurements?
458 g
4085 g
4850 g
0.0485 g
0.004085 g
40.004085 g

Counting Sig Figs REVIEW
› Count all numbers EXCEPT:
 Leading zeros -- 0.0025
 Trailing zeros without
a decimal point -- 2,500
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Counting Sig. Figs. Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
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405.0 g
 4050 g
 0.450 g
 4050.05 g
 0.0500060 g
 Next we learn the rules for calculations

Look at the number behind the one
you’re rounding.
 If it is 0 to 4 don’t change it
 If it is 5 to 9 make it one bigger
 Round 45.462 to four sig figs
 to three sig figs
 to two sig figs
 to one sig fig


Round the following to 3 significant
figures
› 55.8954 m
› 527,254 g
› 4.998 mL
› 959,600 m
Write in Standard form
 1. 6.32 x 105
2. 5.05682 x 103

Write in Scientific Notation
 3) 9384000 g
4) 0.00000034623 m

Calculate~ Answers need to be in scientific
notation!
 5. (6.02 X 1023) X (9.54 x 10-13)
 6. (5.23 X 10-21) / (1.23 X 1023)

An answer can’t have more significance
than the measurements upon which it is
based.
 YOUR ANSWER IS ONLY AS GOOD AS
YOUR WORST MEASUREMENT!


Calculating with Sig Figs
› Multiply/Divide - The # with the fewest sig
figs determines the # of sig figs in the
answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
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Same rules for division
Practice
 4.5 / 6.245
 4.5 x 6.245
 9.8764 x .043
 3.876 / 1983
 16547 / 714


Calculating with Sig Figs (con’t)
› Add/Subtract - The # with the lowest decimal
value determines the place of the last sig fig in
the answer.
224 g
3.75 mL
+ 130 g
+ 4.1 mL
7.85 mL  7.9 mL 354 g  350
g
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For example
27.93 + 6.4
27.93
+ 6.4
34.33
First line up the
decimal places
Then do the adding
Find the estimated
numbers in the
problem
This answer must be
rounded to the tenths
place
Practice Problems
1. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2. 18.9 g
- 0.84 g
18.06 g  18.1 g
2 SF
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500 is only 1 significant figure
 If it really has two, how can I write it?
 A zero at the end only counts after the
decimal place
 Scientific notation
 5.0 x 102
 Now the zero counts.

1. 4.8 + 6.8765
2. 520 + 94.98
3. 0.0045 + 2.113
4. 6.0 x 102 - 3.8 x 103
5. 5.4 - 3.28
6. 6.7 - .542
7. 500 -126
8. 6.0 x 10-2 - 3.8 x 10-3

Calculating with Sig Figs (con’t)
› Exact Numbers do not limit the # of sig figs in the
answer.
 Counting numbers: 12 students
 Exact conversions: 1 m = 100 cm
 “1” in any conversion: 1 in = 2.54 cm
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
Addition Subtraction
› Round your answer to the same number of
decimal places as your least significant
number.
› Think of it as the leftmost uncertainty.
124.0 m
+
.12 m
420
m
544.12 m
540 m

Multiplication and Division
› Round answer to the same number of
significant digits as the measurement with the
least number of significant digits.
238.63 m 5
×
12.0 m
2863.56
m2
3
2860 m2
2. Metric – Developed in France in 1790.
•
•
•
Simple base units
Interchangeable prefixes
Decimal (base 10) system
Prefix
Symbol
Meaning
1 km = 1000 m
kilo-
k
hecto-
h
deca-
da
deci-
d
centi-
c
100 cm = 1 m
milli-
m
1000 mm = 1 m
1 hm = 100 m
1 dam = 10 m
10 dm = 1 m
Quantity
Unit
Symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
kelvin
K
Temperature
Amount of
Substance
Electrical current
mole
mol
ampere
A
Luminous intensity
candela
cd
No Cussing!
The following 4-Letter
words are forbidden here:
Inch
Foot
Yard
Mile
Pint
Acre
And we never swear the BIG F (useoC)
Please keep it clean and
Metric
Metric Conversions
kilo(k)
1000
hecto
(h)
100
deca(da)
10
base unit
Meter (m)
Liter (L)
Gram (g)
Second (s)
deci(d)
1/10
centi(c)
1/100
To convert from 1 prefix to another, just move the
decimal to the left or right that many places!
milli(m)
1/1000
1
kilo(k)
hecto
(h)
deca(da)
2
base unit
3
deci(d)
centi(c)
milli(m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many centigrams (cg) are in 5dag?
3 places to the ________
right
Just move the decimal ___
5
0 0 0
5000 cg
3
kilo(k)
2
hecto
(h)
1
deca(da)
base unit
deci(d)
centi(c)
milli(m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many kilometers (km) are in 12 meters m?
Just move the decimal ___
3 places to the ________!
left
12
0
.012 km
calculated by multiplying L x W x H
 Liter the volume of a cube 1 dm (10 cm)
on a side
 so 1 L = 10 cm x 10 cm x 10 cm
 1 L = 1000 cm3
 1/1000 L = 1 cm3
 1 mL = 1 cm3

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143
1 kg = 2.5 lbs
 1 g = 1 paper clip
 1 mg = 10 grains of salt or 2 drops of
water.

D = M
V
M
M = DxV
ass
D
ensity
V
olume
V = M
D
Substance
Air
Lithium
Ice
Water
Aluminum
Iron
Lead
Gold
*at 0oC and 1 atm pressure
Density
(g / cm3)
0.0013*
0.53
0.917
1.00
2.70
7.86
11.4
19.3
Mass
Density =
Volume
Equal volumes…
…but unequal masses
The more massive object
(the gold cube) has the
GREATER
_________ density.
aluminum
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71
gold
Consider Equal Masses
Equal masses…
…but unequal volumes.
aluminum
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71
The object with the
larger volume
(aluminum cube) has
the smaller density.
gold
Density
 An object has a volume of 825 cm3 and a density of 13.6
g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M=?
M
D
V
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 g
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
A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V=?
M = 25 g
M
D
V
WORK:
V=M
D
V=
25 g
0.87 g/mL
V = 29 mL
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
Heat – type of energy transferred
because of a difference in temperature.
› Can’t be measured directly

Temperature – measure of the average
kinetic energy of the particles in a
sample of matter.
› Determines the direction of heat transfer
2.12 Temperature
What contains more heat?
a glass of boiling water or an iceberg
What does your body sense?
temperature or heat

Fahrenheit (F) – zero based on equal mix
of snow and ammonium chloride.
32F = freezing point of water
212F = boiling point of water
• Celsius (C) – based on water
0C = freezing point of water
100C = boiling point of water

Kelvin (K) - only temperature scales that is
proportional to the speed of the particles.
0 K = all particle motion stops
273 K = freezing point of water
373 K = boiling point of water

T(K) = t(C) + 273
What is 25C (room temp.) in
kelvin?
T(K) = 25C + 273 = 298 K
• t(C) = T(K) – 273
Accuracy is very important when making
measurements in the lab.
 In order to evaluate the accuracy of a
measurement, you must be able to
compare the experimental value to the
accepted value.
 Accepted value = the true or correct
value based on reliable references
 Experimental value = the measured
value determined in the experiment in
the lab.


Indicates accuracy of a measurement
expressed as a percentage
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
A student determines the density of a
substance to be 1.40 g/mL. Find the % error if
the accepted value of the density is 1.36
g/mL.
% error 
1.36 g/mL  1.40 g/mL
1.36 g/mL
% error = 2.9 %
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 100