Transcript Measurements

Measurement
CHM 1010
PGCC
Barbara A. Gage
Measurement
• Determined magnitude of a property
• Based on a standard
• Must have a unit (which is based on the
standard)
• Number of digits in a measurement
depends on the device used
• Values must be expressed in scientific
notation if they are 1000 or more or in
the thousandths (0.00X)
CHM 1010
PGCC
Barbara A. Gage
Significant Figures
• When making a measurement you must
record all digits you are sure of and one
that is a reasonable estimate
(regardless of where the decimal place
falls)
• The object below is 4.86 cm. You can
be certain of the 4 and 8. The 6 is an
estimate and can vary +/- 1 between
measurements.
CHM 1010
PGCC
Barbara A. Gage
Significant figures
• The graduated cylinder at the
right contains 38.34 mL of liquid.
It is assumed that you can visually
divide the space between lines
into ten parts.
CHM 1010
PGCC
Barbara A. Gage
Significant Figures
• When you encounter a measurement
assume that all non-zero digits or zeros
between other digits are significant.
23.789 dm
2.04 gal
52 kg
CHM 1010
5 sig figs
3 sig figs
2 sig figs
PGCC
Barbara A. Gage
Significant Figures
• Zeros may serve as actual measured
values or place holders in estimated
measurements. Place holder zeros are
NOT significant because they are really
not measured values.
• Place holder zeros can be removed by
expressing the number in scientific
notation.
CHM 1010
PGCC
Barbara A. Gage
Significant Figures
120,000
2 significant figures
This is an estimate that can be written as
1.2 x 105.
0.0040500
5 significant figures
The zeros before and immediately after the
decimal point can be eliminated using
scientific notation. The last zeros remain
because they are actual measurements.
4.0500 x 10-3
CHM 1010
PGCC
Barbara A. Gage
Significant Figures –Addition and
Subtraction
•When you are adding and subtracting
numbers you only count the columns
where you are sure of all the values in
that column.
CHM 1010
PGCC
Barbara A. Gage
Significant Figures –
Multiplication and Division
• When multiplying or dividing two or more
values, the answer should contain the number of
digits in the value with the least number of
significant figures.
0.003570 4 sig figs
X
23.4 3 sig figs
0.083538 5 sig figs (calculator answer)
You can only trust the answer to 3 sig figs so the
correct answer is 8.35 x 10-2.
CHM 1010
PGCC
Barbara A. Gage
Measurement Systems
• Everyday measurements in the USA are
generally made using the English system.
• The scientific community and most
other countries use the metric system.
CHM 1010
PGCC
A. Gage
Barbara
Units
English System
Metric System
Length
inch, foot, yard, mile
meter (or metre) (m)
Volume
teaspoon, cup, gallon
liter (or litre) (L)
Mass
ounce, pound, ton
gram (g)
•The units in the English system do not have a common
conversion factor.
12 in = 1 ft
3 ft = 1 yd
1760 yd = 1 mi
•The units in the metric system have a common
factor which is 10. The metric system uses a common
base unit and prefixes to change the size of the unit.
CHM 1010
PGCC
Barbara A. Gage
Metric Prefixes
CHM
Barbara
The1010
boxedPGCC
prefixes
must
A. Gage
be memorized.
Converting Measurements
• Often it is necessary to convert a
measurement made in one unit to
another unit.
Ex. 2.45 cm = ? m
In the metric system you can just shift
the decimal point or set up a conversion
factor.
2.45 cm = 0.0245 m
CHM 1010
PGCC
Barbara A. Gage
Converting Measurements
• Using a conversion factor:
100 cm = 1 m
• 100 cm or
1m
both ratios = 1
1m
100 cm
1m
2.45 cm x
= 0.0245 m
100 cm
CHM 1010
PGCC
Barbara A. Gage
Converting Measurements
• If Baltimore is 35 miles away, how far is
it in km?
• Using a conversion factor:
1.61 km = 1 mi
1.61 km
35 mi x
= 56 km
1 mi
CHM 1010
PGCC
Barbara A. Gage
Converting Measurements
• How many mL are in 0.875 gal?
1.06 qt = 1 L 4 qt = 1 gal
4 qt
1L
1000 mL
.875 gal x
x
x
= 3.30 x 103 mL
1 gal
1.06 qt
1L
CHM 1010
PGCC
Barbara A. Gage
Problem…
• A gas particle has a velocity of 752 m/s.
What is its velocity in mi/hr?
1.61 km = 1 mi
m
1 km
1 mi
60 s
60 min
3 mi
752
x
x
x
x
= 1.68 x 10
s
1000 m
1.61 km
1 min
1 hr
hr
CHM 1010
PGCC
Barbara A. Gage
Problem…
• A synthesis process requires 6.2 fl. oz. of activator
for every 2.5 tons of starting material. What is the
concentration of activator in the final product in
mL/kg?
1 fl oz = 29.6 mL 2000 lb = 1 ton 2.20 lb = 1 kg
6.2 fl oz
1 ton
2.20 lb
29.6 mL
mL
x
x
x
= 0.081
2.5 ton
2000 lb
1 kg
1 fl oz
kg
CHM 1010
PGCC
Barbara A. Gage
Density
• Property derived from two
measurements, mass and volume
• Density = Mass/Volume
• Will have a unit that contains both mass
and volume such as g/cm3, lb/gal, kg/L
• Does not depend on the size of the
sample
CHM 1010
PGCC
Barbara A. Gage
Density
• What is the density of a sample of
metal that has a mass of 34.58 g and
when placed in 15.0 mL of water causes
the level to rise to 22.4 mL?
22.4 mL - 15.0 mL = 7.4 mL
M 34.58 g
D=
=
= 4.7 g/mL
V
7.4 mL
CHM 1010
PGCC
Barbara A. Gage
CHM 1010
PGCC
A. Gage
Barbara
Accuracy and Precision
• Accuracy = how close a result comes to
the true value
• Precision = reproducibility of a
measurement
CHM 1010
PGCC
Barbara A. Gage
Precision and Accuracy
Consider 3 persons shooting darts at a target…
“a” is precise but
not accurate
“b” is accurate
and precise
“c” is not precise
or accurate
CHM 1010
PGCC
Barbara A. Gage
Accuracy and Precision
• Measurements of the same object made by
three students; actual value = 15.71 cm
Student 1
Student 2
Student 3
14.72 cm
15.80 cm
15.72 cm
14.71
14.71
15.71
14.72
13.25
15.82
14.82
14.96
15.73
14.71
12.81
15.71
Precise not accurate Not accurate or precise Accurate and precise
CHM 1010
PGCC
Barbara A. Gage