Embed Size (px)
Citation preview
Chemistry and Calculations
Chemistry Honors
2
Accuracy & Precision
Precision: how closely individual measurements compare with each other
Accuracy: how closely individual measurements compare with the true or accepted value
Accurate or Precise?
Precise!(but not too accurate)
Ex: What is the temperature at which water boils?
• Measurements: 95.0°C, 95.1°C, 95.3°C
• True value: 100°C
Accurate or Precise?
Accurate!(but not too precise)
Ex: What is the temperature at which water freezes?
• Measurements: 0.2°C, 5.1°C, -5.0°C
• True value: 0.0°C
Accurate or Precise?
Accurate & Precise(it’s time to go pro)
Ex: What is the mass of one Liter of water?
• Measurements: 1.000 kg, 0.999 kg, 1.002 kg
• True value: 1.000 kg
Accurate or Precise?
Not Accurate & Not Precise(don’t quit your day job)
Ex: What is the atmospheric pressure at sea level?
• Measurements: 10.01 atm, 0.25 atm, 234.5 atm
• True value: 1.00 atm
To measure the time for a pencil tofall, compare a wall clock and a stopwatch.
To measure the volume of a liquid, compare a beaker and a graduated cylinder.
Uncertainty
42.1 mL:Two digits known (42)
and one estimated (1).
41. mL:One digit known (4) and one estimated (1).
40
2040.0
42.0
The stopwatch and graduated cylinder…• Are more precise instruments (are more
certain.)• Give measurements that are known to
more decimal places..
In a correctly reported measured value, the final digit is significant but not certain.
If the number 31.2 is reported. 3 & 1 are known with certainty, the 2 is significant but uncertain.
A more precise instrument will give more sig figs in its measurement
Significant Figures (“sig figs”):
All the digits known with certainty plus one final digit, which is somewhat uncertain.
When are digits “significant”?
“PACIFIC”Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit.
The “Atlantic-Pacific” Rule
40603.23 ft2
0.01586 mL= 7 sig figs= 4 sig figs
PACIFIC
PACIFIC
When are digits “significant”?“ATLANTIC”
Decimal point is ABSENT. Count digits from right
side, starting with the first
nonzero digit.
40600 ft2
1000 mL3 sig figs =1 sig fig =
ATLANTIC
ATLANTIC
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.4000306
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.000091
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
178215683210
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
900001
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
32710.5
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.0001003
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
2570.006
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
52303
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
5.05005
• 0.00932Decimal point present → “Pacific” → count digits from left,
starting with first nonzero digit= 3 sig figs
• 27510Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs
• If number is obtained by counting, ex: 8 beakers, or is used in a conversion factor, ex: 1000 mm= 1 meter it is an exact number.= unlimited number of significant figures.
Examples
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.4000306
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
67.204
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.000091
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
178215683210
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
900001
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
32710.5
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
0.0001003
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
2570.006
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
52303
Pacific Ocean
Decimal Present! Atlantic Ocean
Decimal Absent!
Significant Figures
On TheLeft!
On TheRight!
5.05005
Addition and Subtraction
• The answer has the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
• Ex: 56.31g – 14.1g =• Answer must be rounded so has only one
number to the right of the decimal point.
Multiplication and Division
• The answer has no more sig. figs. than are in the measurement with the fewest number of sig.figs.
• 7.2 cm X 8.141 cm =58 cm2 The answer can only have 2 sig. Figs.
2.4: Scientific NotationHow important is a change in the power of 10?Diameter of Earth’s orbit around the sun
≈ 100,000,000,000 m = 1.0*1011 m
Diameter of an atom
≈ 0.0000000001 = 1.0*10-10 m
Clearly show the # of sig figs in a a measurement
1. Move the decimal point in the original number so that it is located to the right of the first nonzero digit.
2. Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved.
The form is M x 10n
3. If the decimal point moves: To the left, the power of 10 is positive. To the right, the power of 10 is negative.
Writing in scientific notation
Write the following measurements in scientific notation, then record the number of sig figs.
1. 789 g2. 96,875 mL3. 0.0000133 J4. 8.915 atm5. 0.94°C
7.89*102 g9.6875*104 mL1.33*10-5 J8.915 *100 atm9.4*10-1 °C
3 sig figs5 sig figs3 sig figs4 sig figs2 sig figs
When Adding & Subtracting
• All values must have same exponent• Ex: 4.71 X 103 L+ 3.3 X 104 L =
4.71 X 103 L + 33. X 103 L = 37.71 X 103 L OR
.471X 104 L + 03.3 X 104 L =3.771 X 104 L Answer = 3.8 X 104 L
Convert answer to appropriate scientific notation. Least number of places past decimal
Multiplication & Division• Multiplication: the M factors are multiplied
and the exponents are addedEx: (8.19 x 102 mm)(1.0 x 105 mm) = 8.2 x 107 mm2
when length units multiplied, answer units is area
• Division: The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator.
Ex: 9.2 x 104 g = 9.2 g x 104-2 g/mL 4.55 x 102 mL 4.55 mL
Rounding Rules: round at the last step in a multistep process
Digit Following Last Digit Is…
Change to Last Digit
Example(Rounded to 3
Sig-Figs)Greater than 5 Increase by 1 42.68 g ==>
42.7 g
Less than 5 Stay the same 17.32 m ==> 17.3 m
5, followed by nonzero #(s)
Increase by 1 2.7851 cm ==> 2.79 cm
5, not followed by nonzero #(s), preceded by an odd #
Increase by 1 4.635 kg ==> 4.64 kg
5, not followed by nonzero #(s), preceded by an even #
Stay the same 78.65 mL ==> 78.6 mL
Système International d'Unités• The metric system or Système International
d'Unités (S.I.), was first organized in Paris as part of the French Revolution & adopted by France in 1795. At that time, the meter & kilogram were standardized.
• Every country in the world uses SI units except the USA, Myanmar, & Liberia.
• By 2009, all products sold in Europe must use the metric system. No dual-labeling will be permitted.
The Metric Prefixes
Prefix Symbol Value Power Use
mega M 1,000,000 106 megaton
kilo k 1,000 103 kilometer
deci d 0.1 10-1 decimate
centi c 0.01 10-2 centipede
milli m 0.001 10-3 millimeter
micro 0.000001 10-6 microscope
nano n 0.000000001 10-9 nanotechnology
giga G 1,000,000,000 109 gigabyte
The Standard Units
Quantity Unit name Abbreviation
length meter m
mass kilogram kg
temperature kelvin K
time second s (or sec)
amount mole mol
More on S.I
• The S.I. unit for volume is the cubic meter (m3).
• The Liter,not S.I. Unit, is defined as a cube measuring 1 decimeter on each side, or 1 dm3, or 1000 cm3.
• 1 cm3 = 1 mL.• The S.I. unit for mass is the kilogram,
and is defined as the mass of 1 dm3 of water at 4°C.
1 dm
1 dm
1dm
What is a kelvin?
• The S.I. unit for temperature is the kelvin, and is defined as 1/100 of the temperature difference between the boiling point & freezing point of water at one atmosphere of pressure.
• The kelvin (K) and the degree Celsius (°C) are exactly the same size, although 1 degree Fahrenheit (°F) is equal to about 1.8°C.
• To convert:
• K = °C + 273.15• °F = (1.8 * °C) + 32
• kelvin is based on water and absolute zero (the coldest temperature possible.)
What is density?
• Density (d) is the ratio of the mass (m) of a substance divided by its volume (V).
density = mass / volume• The most common units of
density are: g/cm3 or g/mL.
1 cm3 = 1 mL• The density of water is 1.0 g/mL at
4.0 ° C
1.0 g/mL
0.80 g/mL
1.2 g/mL
Percent Error• Used to compare the accuracy of an
individual or an average experimental value to the accepted value.
Value acc – Value experimental X 100Value acc
• Ex: What is the % error for a measurement of 46.1 g, given that the correct value is 45.9g?
Direct Proportions• Equation Forms:
y
xk
OR
y kx
Indirect ProportionsEquation Forms:
y 1
xOR
xy k
Dimensional Analysis• A method for converting unitsExample: A sample has a mass of 1245 g; how
many kg is that?1. Determine a conversion factor between
the original units and the required units.__?__ kg = __?__ g
Recall that k = 1000 = 103.• So, 1 kg = 1000 g or 10-3 kg = 1 g.
2. Change the conversion factor into a fraction.1000 g or 1 kg1 kg 1000 g
• Similar to 5 = 5, so 5 / 5 = 1 or10 = 10, so 10 / 10 = 1.
You are creating a value equal to 1.
3. Multiply the original number and the conversion factor so that the original units “cancel.”
1245 g x 1 kg = 1.245 kg1 1000 g
3. Multiply the original number and the conversion factor so that the original units “cancel.”
1245 g x 1 kg = 1.245 kg1 1000 g
Practice
• Convert 1.65 L to mL.
• Convert 3.5 mm to m.
• Convert 2.00 L to quarts.(1 qt = 946 mL)
mL 1650L 101
mL 1
1
L 1.653-
m 103.5mm 1
m 101
1
mm 3.5 3--3
qt 2.11mL 946
qt 1
L 101
mL 1
1
L 23-
