Download Chapter 5 - Measurements and Calculations

Measurement and
Calculations
• Chemistry –
the science that deals with the materials of the
universe and the changes these materials undergo
• Qualitative Measurement –
Qualities or observations that can be made about a
substance ex: the substance is a yellow solid
• Quantitative Measurement –
a measurement that consists of a number and a unit
ex: the substance weighs 3.45 grams
Units
•
•
tells what scale or standard is being used to represent the measurement
International System (SI)
•
SI Base Units:
– Length: meter
• measures distance
– Mass: grams
• quantity of matter present in an sample
– Volume: Liter, centimeter cubed, decimeter cubed
• 1 mL = 1 cm3 1 L = 1 dm3
• three-dimensional space occupied by a sample
– Temperature: Kelvin, Celsius
• TK = T°C + 273
– Time: second
– Pressure: Pascals
– Energy/Heat: Joules
– Counting Atoms: moles
Units
Common metric prefixes (MEMORIZE)
Giga
1 x 109 _ = 1 G_
Mega
1 x 106 _ = 1 M_
Kilo 1000 _ = 1 k_
Hecto 100 _ = 1 H_
Deka 10 _ = 1 D_
(base) – meter, liter, gram…
deci1 _ = 10 d_
centi1 _ = 100 c_
milli1 _ = 1000 m_
micro1 _ = 1 x 106 _
nano1 _ = 1 x 109 n_
pico1 _ = 1 x 1012 p_
*
*
*
*
*
( = lowercase Greek Mu)
Scientific Notation
Expresses a number as a product of a
number between 1 and 10 and the
appropriate power of 10
If you move the decimal pointleft  positive exponent
Ex: 200 g
2 1
2 x 102 g
right  negative exponent
.00314 mL
1 2 3
3.14 x 10-3 mL
Converting from Scientific
Notation to Ordinary Numbers
move the decimal pointpositive exponent  right
negative exponent  left
Ex: 6.32 x 101 cm
3.92 x 10-3 m
1
63.2 cm
3 2 1
.00392 m
Learning Check
Try these:
1. 657000000000 m 6.57 x 1011 m
2. 0.000000235 g 2.35 x 10-7 g
3. 9.34 x 102 cL
934 cL
4. 3.35 x 10-3 L 0.00335 L
Limits to Measurements
• When measuring you should always
______________
the _______
estimate
last digit of your
measurement
• Your measurement should be recorded to ONE
PLACE VALUE BEYOND the
______________marking
calibration
uncertain
• Your Estimate (or _____________
number) should
be the final one on the right.
record the given number–
• If the tool is digital, _________
no estimated number.
• Measurements always
have some degree of
uncertainty (estimation)
Ex 1: Measure the volume of
liquid in the Graduated
cylinder.
Remember: The volume is read
at the bottom of the liquid
curve (called the meniscus).
Ex 3: Measure the
volume of liquid in
the buret.
Ex 2: Measure
the line using
both rulers.
42.8 mL
7.5 cm
7.56 cm
15.75 mL
Learning check
Read the following pieces of equipment, record your
answer with the estimated digit and units.
1.
4.
2.
3.
5.
Significant Figures
All certain numbers plus first uncertain digit
Rules for counting Sig. Figs.
3578 = 4 SF
1. All nonzero numbers are significant.
236 =
3 SF
2. Zeros
a. Leading Zeros – precede all nonzero digits, they NEVER
COUNT .0025 = 2 SF
.0009 = 1 SF
b. Captive (Trapped) Zeros – fall between two nonzero digits,
they ALWAYS COUNT
6008 = 4 SF
20502 = 5 SF
.00705 = 3 SF
c. Trailing Zeros – come at the end of a number and count IF there
is a DECIMAL POINT
.001500300 = 7 SF
3000 = 1 SF
3000. = 4 SF
2580.0 = 5 SF
3. Exact numbers – have infinite number of sig. figs., they arise from
definitions
1 inch = 2.54 cm, 1 g = 1000 mg
Rounding
If the digit to be removed is –
a. less than 5, the preceding digit stays the same
b. equal or greater than 5, increase the preceding digit
by 1
When rounding off, use ONLY the first number to
the right of the last significant figure
Ex: Round to 3 SF
$ 10,079 = $10,100
0.002978 g = 0.00298 g
0.03296 cm = 0.0330 cm
1000. mL = 1.00 x 103 mL
Learning Check
Determine the number of significant figures
in the following numbers:
a. 0.00340 g
b. 9.00 mm
c. 30.390 mL
Round each number to 2 significant figures.
a. 0.00340 g
b. 9.00 mm
c. 30.390 mL
Calculations Notes
Uncertainty in Measurement
close
• Accuracy: - How _________
a measurement is
accepted
to the actual or _________value.
To evaluate
know
accuracy you must __________
the true value.
For example, knowing a watch is 5 min
not
fast…The time on the watch is ________
accurate and you know it is not accurate b/c you
adjustment
know the real time and can make an ________.
• Shooting Free Throws - Accuracy can be
measured by how many are __________.
baskets
Precision:
1st Meaning of Precision
set
How close a ____________
of measurements are to the
_________________.
To evaluate precision you must
actual value
compare the values of 2 or more _______________
similar
measurements.
• Ex. Measure the temperature of water three times.
Which set of measurements are more precise?
Thermometer 1: 22.3oC, 22.3oC, 22.4oC
Thermometer 2: 24.5oC, 20.1oC, 18.7oC
• Shooting Free Throws - Precision can be measured by
how many _______
Ex.
shots in the same _________.
spot
side
Consistently hitting the ___________
of the rim and
missing. Not accurate b/c not making the shots, but
precise b/c results are repeated.
• Science – should be both accurate (___________)
and
right
precise (can ____________
it consistently)
repeat
2nd Meaning of Precision
• Precision can also refer to how __________
a
precise
measurement is (more decimal __________
=
places
more precise)
Consider mass of sugar in bubble gum
– 5 g - wide range of values that it could be! - Could be
between 4.5 g and 5.4 g and rounded to 5 g.
– 5.0 g gives you more information – Could be between
4.95 g and 5.04 g.
– 5.00 g gives you even more information – Could be
between 4.995 g and 5.004 g
right
• More numbers to ______________
of decimal,
more precise the measurement is!
Learning Check
Think of an example, from your life, of
accuracy and precision.
Multiplication and Division
Number of the sig. figs. is the result of the
measurement with the smallest number of sig. figs.
(least accurate). LEAST NUMBER OF SIG FIGS!
3 sf
2 sf
Ex 1: 4.63 m x 7.5 m
34.725
35 m2
4 sf
2 sf
Ex. 2: 8.460 m2 / 2.1 m
4.0285714286
4.0 m
Addition and Subtraction
Align the decimal points and carry out the
calculation. First column from the left with an
uncertain digit determines the number of sig.
figs. in your answer (Chop & round at the GAP)
LEAST NUMBER of DECIMAL PLACES!
Ex 1: 6.341 g + .789 g + 4.2 g
6.341
.789
4.2 GAP
11.330
11.3 g
Ex. 2: 6.799 m - 2.41 m
6.799
2.41 GAP
4.389
4.39 m
Learning Check
1. 22.4 L x 9.3 L
2. 9.63 g + 17.3251 g
Scientific Notation and
Multiplication and Division
Multiplication – Multiply coefficients, ADD exponents,
multiply units, round to proper S.F.
Division - Divide coefficients, SUBTRACT exponents,
divide units, round to proper S.F.
Ex 1: (1.00 x 103 m)(3.2 x 102 m)
3.2 x 105 m2
Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3)
3.0 x 102 g/cm3
Scientific Notation and Addition and
Subtraction
must be in the same power of ten and same
unit before you add or subtract
coefficients, convert to larger exponent
Ex 1: 3.0 x 1023 m + 1.0 x 1022 m
1
3.0 x 1023 m + .10 x 1023 m
3.0 GAP
.10
3.10
3.1 x 1023 m
Learning Check
1. 2.29 x 105 g - 9.3 x 104 g
2. 6.02 x 1023 m ÷ 1.7 x 1022 m
Problem Solving and
Dimensional Analysis
Conversion factor – ratio of two parts of the
statement that relates the two units
2.54 cm = 1 inch
100 cm = 1 m
Equivalence Statement – true statement in fraction
form
2.54 cm or 1 inch
1 inch
2.54 cm
100 cm or 1 m
1m
100 cm
Dimensional Analysis – when used properly all
units will cancel out except the desired unit
Given with UNITS
Wanted
UNIT
x ________________
#
#
Given
UNIT
Desired
UNIT
x ______________
=
# Wanted
UNIT
#
1 km = 1000 m
Ex. 1: 250 m = ___________ km
250 m x ___________
1 km
1000 m
=
.25 km
Ex. 2: 3.54 g = ___________ mg
3.54 g
1000 mg
x ___________
1 g
=
1 g = 1000 mg
3540 mg
1 kg = 1000 g
Ex. 3: 0.542 kg = __________ mg
0.542 kg
1000 g x __________
1000 mg
x ________
=
1 kg
1 g
1 g = 1000 mg
542000 mg
Learning Check
1. 0.542 mm = __________ km
2. 0.542 g = __________ µg
Determining Error
accepted
___________________value
- correct value
based on reliable references
experimental
___________________value
- value
measured in the lab
Error = experimental value – accepted value
(Note: error can be positive or
absolute
negative) You will take the ___________
value of this when you calculate percent
error.
Determining Percent (%) Error
Percent error = absolute value of error divided by accepted
value and multiplied by 100%
% error = (experimental value – accepted value) x 100%
accepted value
Example: You take three temperature readings of a beaker
of boiling water and record: 91.3oC, 90.9oC, and 91.1oC.
Evaluate accuracy, precision, and error.
Accurate?
No, water boils at 100oC
Precise?
Yes, values are close to each other
Error
1. Find average experimental data
2. Use formula
(91.3oC + 90.9oC + 91.1oC)/3 = 91.1oC
% error = (91.1 oC – 100 oC)
100 oC
x 100% = 8.90 %
Learning Check
1. At a track meet, you time a friend running
100 m in 11.00 seconds. The officials time
her at 10.67 seconds. What is your
percentage error?
For Fun!
Hagrid instructed Harry to give the delivery owl five
Knuts for a newspaper (p. 62). A weekday newspaper
costs $0.25. At Gringots, Harry learned that there are
seventeen Sickles to a Galleon and twenty-nine Knuts to
a Sickle (p. 75). Harry then paid seven Galleons for his
new wand-Holly and phoenix feather (p. 85). Use
dimensional analysis to calculate how much Harry’s
wand would cost in dollars?
7 Galleons x ___________
17 Sickles x ___________
29 Knuts
.25 dollars
x ______________
= $172.55
1 Galleon
1
Sickles
5
Knuts
On the train, Harry paid eleven Sickles and seven Knuts
for junk food from the snack trolley. How much money
did he spend?
29 Knuts x ___________
.25 dollars
11 Sickles x __________
= $ 15.95
5 Knuts
1 Sickle
$16.30
7 Knuts
.25 dollars = $ 0.35
x ___________
5 Knuts