Chapter 2: Measurements in Chemistry
•Chemistry is an observation science
•Observations frequently require taking measurements
•Measurements have some degree of uncertainty
•All measured numbers have 2 parts:
Scientists use the Metric System:
Units of Measurement
Measurement
Length
Volume
Mass
Temperature
Time
Metric Base Unit
Metric Prefixes:
Prefix Symbol Numerical Value
Sci Notation
Equality
Prefixes that Increase the Size of the Unit:
Giga G
1,000,000,000
1 x 109
mega M
1,000,000
1 x 106
1 Mg = 106 g
or 1 g = 10-6 Mg
kilo
1,000
1 x 103
1 km = 1000 m
or 1 m = 10-3 km
1 dL = 0.1 L
or 1 L = 10 dL
k
Prefixes that Decrease the Size of the Unit:
deci d
0.1
1 x 10-1
centi
c
0.01
1 x 10-2
1 cm = 0.01 m
or 1 m = 100 cm
milli
m
0.001
1 x 10-3
1 ms = 10-3 s
or 1 s = 1000 ms
micro m
0.000001
1 x 10-6
1 mg = 10-6 g
or 1 g = 106 mg
nano n
0.000000001
1 x 10-9
What is the relationship between volume and length?
1 Liter = the space occupied by a 10 cm cube
Exact and Inexact Numbers?
Exact number = number whose value has no uncertainty
• defined numbers
• counted numbers
Inexact number = a number with a degree of uncertainty
• measured numbers
Uncertainty in Measurement
Significant figures = all digits that are known with certainty + 1 estimated digit
Precision = the degree to which a measurement is reproducible
The precision of a measurement is determined by the instrument used:
• Digital equipment – record all digits
• Analog equipment – incremental (closest) marks
Guidelines for Determining Significant Figures in Measured Numbers
Significant Figures
Digits known with certainty + one estimated digit
Nonzero Digits
1, 2, 3 … 9 are always significant
Leading Zeros
Zeros at the beginning of a number
are never significant
Zero
May or may not be significant
Confined Zeros
Zeros between non-zero digits
are always significant
Trailing Zeros
Are significant only if
the decimal point is shown
How many Significant Figures?
562.00
0.033
45,100
348
Calculations & Significant Figures:
The answer to a calculation involving measured numbers cannot have greater
significance than any of the measurements!
Addition and Subtraction:
The answer has the same precision as the least precise measurement.
Example: A graduted cylinder contained 25.5 ml of water. A glass marble was
added to the cylinder and the volume reading increased to 33.2 ml.
What was the volume of the marble?
Multiplication and Division:
The answer has the same number of significant figures as the
measurement with the fewest significant figures.
Example: The marble (from the previous example) has a mass of
22.0186 grams. What is it’s density?
Rules for rounding:
•If the digit to be dropped is less than 5, simply drop it
•If the digit to be dropped is 5 or greater, round up
Round to 2 significant figures:
258.59
0.06617
182,540
Perform the following calculations involving measured numbers,
express your answer to the proper number of significant figures:
a) 6.731 x 0.0021 =
b)
8.4
1.8
+ 5.2
c) 120  0.0045 =
(write the answer in scientific notation)
Scientific Notation:
a convenient way of expressing large or small numbers
1.23 x 10-34
A number in Scientific Notation has 2 parts:
coefficient - a number between 1 and 10 it includes only significant figures
exponential term – a number expressed as x 10n
n = an integer (positive or negative)
Convert to scientific notation:
47,000
0.00211
Convert to standard notation:
5.442 x 103
8.25 x 10-5
Scientific Notation & Calculators:
-enter the coefficient as you would for a regular number
-press EXP or EE
-enter the exponent
Examples:
a. (9.41 x 1012) x (2.7722 x 10-5) =
b. (2.5 x 104)  (6.8 x 106) =
Conversion Factors—Metric System:
What does it mean?
1 cm = 0.01 meter
or 100 cm = 1 meter
Write the equality as a ratio:
A ratio can be used as a conversion factor.
Consider a meterstick:
1 meter = 100 cm
How many cm are equal to 2.5 meters?
1 meter = 1000 mm
How many meters are equal to 650 mm?
Unit Conversion within the Metric System:
•Start with the given measured number
•What units are to be changed?
•Find the relationship between units (equality)
•Write as a ratio with the “old” unit in the denominator &
the “new” unit in the numerator
•Cancel the units
•Multiply/divide the numbers
•Record your answer to the proper number of sig. figs.
a. Convert 1.5x105 milliseconds (ms) to seconds
b. Convert 35 microliters (mL) to Liters
c. Convert 2130 decigrams (dg) to kilograms (kg)
Unit Conversion within the English System:
a. Convert 349 inches to feet
English-to-Metric & Metric-to-English Conversions:
Example: Convert 128 lb to kiligrams
Example: Convert 36.5 inches to cm
Multistep conversions:
•Start with the given measured number
•What units are to be changed? (make a unit map)
•Find the relationship between units for each step
•Write each as a ratio with the “old” unit in the denominator
& the “new” unit in the numerator
•Write the conversion as a series of multiplication steps.
•Cancel the units
• Multiply/divide the numbers
•Record your answer to the proper number of sig. figs.
Example: convert 9.85 Liters to gallons
(given that 1 Liter = 1.057 qt; 1 gallon = 4 qt.)
Example: Convert 35 mi/hr to m/min
(given that 1 mile = 1609 meters)
Example: A 150 lb. man requires a drug dosage of 2.5 mg/kg.
How many milligrams of the drug should he take?
(1 kg = 2.205 lb.)
Converting squared or cubed units:
1. Convert 0.25 m2 to cm2.
2. One side of a sheet of paper has an area of 93.5 in2.
Convert this to square cm?
Density = mass
volume
Density = mass
volume
Density Animation
http://www.wiredchemist.com/anim-density
Example: A piece of metal has a mass of 78.12 g and a volume
of 9.5 cm3. What is it’s density? What metal is it?
Metal Density (g/cm3)
Mg
1.7
Al
2.7
Zn
7.1
Sn
7.3
Fe
7.9
Brass 8.4
Cu
8.9
Pb
11.4
Au
19.3
Pt
21.1
Example: A shiny gold-colored nugget has a mass of 26.5
grams and a volume of 3.4 cm3.
Is it gold?
Example: Carbon dioxide has a density of 0.001963 g/ml.
What is the mass of a 5.0Liter sample of CO2?
Example: An empty graduated cylinder has a mass of 215 grams.
After filling it with liquid (946 ml) it is weighed again;
the mass of the cylinder + liquid is 1854 grams.
What is the density of the liquid?
215 grams
1854 grams
Temperature - a measure of the intensity of heat
Temperature Scales:
• Celcius (C)
• Fahrenheit (F)
• Kelvin (K)
Conversions between temperature scales:
Converting from Celcius to Fahrenheit:
A mixture of salt and water has a temperature of -5.0C.
What is the temp on the Fahrenheit scale?
Converting from Fahrenheit to Celcius:
A child has a temperature of 103.1F.
What is the temp on the Celcius scale?
Converting from Celcius to Kelvin:
On the planet Mercury, the average daytime temperature is 683 K.
What is the temp on the Celcius scale?