Transcript Chapter 3

Scientific Measurement
A quantity that has both a number and a unit.
Units used in sciences are those of the
International System of Measurements (SI).
Sometimes in chemistry numbers can be very
large or very small
1 gram of hydrogen =
602,000,000,000,000,000,000,000 atoms
Mass of an atom of gold =
0.000 000 000 000 000 000 000 327 gram
A given number is written as the product of two
numbers: a coefficient and 10 raised to a power.
M x 10n
Example: 602,000,000,000,000,000,000,000
will be written as 6.02 x 1023.
Accuracy is a measure of how close a measurement
comes to the actual or true value
Precision is a measure of how close a series of
measurements are to one another
Table T
accepted value −experimental value
% error =
x 100%
accepted value
A student estimated the volume of a liquid in
a beaker as 200mL. When she poured the
liquid into a graduated cylinder she measured
the volume as 208mL. Calculate the % error.
Include all of the digits that are known, plus the
last digit that is estimated.
1. Every nonzero digit is significant, numbers 1-9.
o Example: 24.7 meters (3 sig. figs.)
2. Zeros between nonzero digits are significant.
o Example: 40.79 meters (4 sig. figs.)
3. Zeros appearing to the left of nonzero digits are
not significant. They are only place holders.
o Example: 0.0071 (2 sig. figs)
7.1 x 10-3 (2 sig. figs.)
4. Zeros at the end of a number and to the right
of a decimal point are significant.
o Example: 43.00 meters (4 sig. figs.)
1.010 meters (4 sig. figs)
5. Zeros at the right end of a measurement that
lie to the left of an understood decimal point
are not significant.
o Example: 300 meters (1 sig. figs.)
27,210 meters (4 sig. figs.)
• How many significant figures are in
each measurement?
• 123 meters = 3
• 9.8000 x 104 m = 5
• 0.07080 m = 4
• 40,506 mm = 5
• 98, 000 m = 2
Count the significant figures in each
length
0.05730 meters 4
8765 meters 4
0.00073 meters 2
40.007 meters 5
How many significant figures are in each
measurement?
143 grams 3
0.074 meters 2
8.750 x 10-2 grams 4
1.072 meters 4
A calculated answer cannot be more
precise than the least precise
measurement from which it was
calculated.
Round off each measurement to the
number of significant figures shown in
parentheses.
314.721 meters (four) 314.7
0.001775 meter (two) 0.0018
8792 meters (two) 8800
•Round each measurement to three
significant figures.
•87.073 meters 87.1
•4.3621 x 108 meters 4.36 x 108
•0.01552 meter 0.0155
•9009 meters 9010
•1.7777 x 10-3 meter 1.78 x 10-3
•629.55 meters 630.
The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of decimal
places
Calculate the sum of the three measurements.
Give the answer to the correct number of
significant figures.
12.52 meters
349.0 meters
+ 8.24 meters
369.76
Perform each operation. Express your answers
to the correct number of significant figures.
61.2 meters + 9.35 meters + 8.6 meters 79.2
9.44 meters – 2.11 meters 7.33
1.36 meters + 10.17 meters 11.53
34.61 meters – 17.3 meters 17.3
You need to round the answer to the same
number of significant figures as the
measurement with the least number of
significant figures.
Perform the following operations. Give
the answers to the correct number of
significant figures.
7.55 meters x 0.34 meter 2.6 m2
2.10 meters x 0.70 meter 1.5 m2
2.4526 meters / 8.4 meters 0.29 m
Solve each problem. Give your answers to the
correct number of significant figures.
8.3 meters x 2.22 meters 18 m2
8432 meters / 12.5 meters 675 m
Calculate the volume of a warehouse that has
inside dimensions of 22.4 meters by 11.3
meters by 5.2 meters (volume = l x w x h)
1300 m3
•A technician experimentally determined
the boiling point of octane to be 124.1C.
The actual boiling point of octane is
125.7C. Calculate the percent error.
1.27 %
•Determine the number of significant
figures in each of the following.
a. 0.070020 meter 5
b. 10,800 meters
3
c. 5.00 cubic meters 3
Table D
Length
Meters (m)
Mass
Kilograms (Kg)
Volume
Liter (L)
cm3
A measure of how hot or cold an object is.
Heat moves from the object at the higher
temperature to the object at the lower
temperature
Celsius (C)
• Freezing point of water (0C)
• Boiling point of water (100C)
Kelvin (K)
• Freezing point of water (273 K)
• Boiling point of water (373 K)
• Absolute Zero (0K), the coldest possible
temperature ( ? Celsius)
K = C + 273
C = K -273
Normal human body
temperature is 37 C. What is
that temperature in Kelvins?
310 K
Liquid nitrogen boils at 77.2 K.
What is this temperature in
degrees Celsius?
-195.8 K
The element silver melts at 960.8 C and boils at
2212 C. Express these temperatures in Kelvins.
Melting Point: 1,233.8 K
Boiling Point: 2485 K
What is the volume of a paperback book, 21cm
tall, 12cm wide, and 3.5cm thick?
882 cm3
Surgical instruments may be sterilized by
heating at 170 C for 1.5 hr. Convert 170 C to
Kelvins.
443 K
• A conversion factor is a ratio of equivalent
measurements.
• When a measurement is multiplied by a conversion
factor, the numerical value is generally changed, but
the actual size of the quantity measured remains the
same.
Dimensional analysis is a way to analyze and
solve problems using the units, or dimensions,
of the measurements
How many seconds are in a workday that lasts
exactly 8 hours?
28800 seconds
How many minutes are there in exactly one
week?
10,080 minutes
How many seconds are in exactly a 40 hour
work week?
144,000 seconds
Problems in which a measurement with one
unit is converted to an equivalent measurement
with another unit are easily solved using
dimensional analysis
•Convert the following
a. 0.044 km to meters 44 m
b. 4.6 mg to grams 0.0046 g
c. 0.107 g to centigrams 10.7 cg
d. 7.38 g to kilograms 0.00738 kg
e. 6.7 s to milliseconds 6700 ms
f. 94.5 g to micrograms 94500000 μg
Convert the following.
•Light travels at a speed of 3.00 x 1010 cm/sec.
What is the speed of light in kilometers/hour?
Density is an intensive property that depends
only on the composition of a substance, not on
the size of the sample.
The density of a substance generally decreases
as its temperature increases (inverse
relationship)
A copper (Cu) penny has a mass of 3.1g and a
volume of 0.35 mL. What is the density of
copper?
8.9 g/mL
A student finds a shiny piece of metal that she
thinks is aluminum (Al). In the lab, she
determines that the metal has a volume of 245
cm3 and a mass of 612 g. Calculate the density.
Is the metal aluminum?
2.45 g/cm3
A bar of silver (Ag) has a mass of 68.0 g and a
volume 6.48 cm3. What is the density of silver?
10.5 g/cm3
What is the density of silver (Ag) if a 27.50 g
sample has a volume of 2.62 mL?
10.5 g/cm3
A sample of ethylene
glycol has a volume of
45.8 mL. What is the
mass of this sample if the
density of ethylene glycol
is 1.11g/mL?
50.8 g
• What is the volume of a
pure silver coin that has
a mass of 14 g.
1.33 cm3
What is the volume in cubic centimeters, of a
sample of cough syrup that has a mass of 50.0
g? The density of cough syrup is 0.950 g/ cm3.
52.6 cm3