Basic Math and Measurement Skills Review–AP

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Welcome to AP Chemistry !
DOR: Introductory Information
1) What was your favorite summer event?
2) Was the AP Chemistry summer assignment difficult for you?
3) As a review, what should I know about you so I can help you
succeed in AP Chemistry? (ie. What learning methods are best for
you?)
Scientific Measurements
• SI Units
• Significant Figures
SI Units
• Measurement system universal to scientists.
• Measurement standards (base vs. derived)
• Base unit—
• Quantity we can MEASURE
• Derived unit-• Quantity provided by CALCULATION
SI Units (cont.)
Base
• Mass = kilogram (kg)
• Length = Meter (m)
• Time = Second (s)
• Temperature = Kelvin (°K)
Derived
• Volume = m3, we will use cm3/ml
• ml is NOT an SI unit (1ml = 1cm3)
• Density = kg/m3, we will use g/cm3 or g/ml
Scientific Measurements
• SI Units
• Significant Figures
• ALWAYS WRITE YOUR UNITS ON YOUR ANSWER !!!!----units provide
meaning to numbers.
Significant Figures
• The number of digits in a scientific measurement known with
certainty and one estimated or uncertain digit.
• Method of reporting scientific measurements and calculations.
Significant Figure Basic Rules
• 1. All numbers that are NOT zeroes are significant
• Ex. 211, 345 =3
• 2. All zeroes BETWEEN 2 significant figures are significant.
• Ex. 2003, 1203 = 4
• 3. All zeros that are FINAL and PAST a decimal are significant.
• Ex. 0.00020 =2
• 4. Final zeros are only significant if a DECIMAL POINT is added to the end of
the number.
• Ex. 100 = 1
• Ex. 100. = 3
• Ex. 100.000 = 6
Examples
• 1) 567
• 2) 0.00022
• 3) 10.020
• 4) 200
Significant Figures:
Adding/Subtracting
• # of digits to RIGHT of decimal = # of digits RIGHT of decimal from
number with the LEAST digits.
• Ex.1 67.14 kg + 8.2 kg =
• 75.3 kg
• Ex. 2 101.23 g – 90.614 g =
• 10.62 g
Significant Figures:
Multiplying/Dividing
• # of significant figures = # of significant figures in number with
LEAST significant figures.
• Ex. 1 12.1 / 3.1 =
• 3.870967742 ~ 3.9
• Ex. 2
45.67 * 1.23 =
• 56.1741 ~ 56.2
Significant Figure Practice---If Necessary
•
•
•
•
•
•
•
•
1) 900
6) 804.5
2) 1020
7) 0.0144030
3) 0.00020
8) 1002
4) 100034
9) 0.000625000
5) 0.00010010
10) 17.982 g / 4.13 cm3 =
11) 12.4 + 1.345 =
12) 2.0 * 4.35 =
13) 20500.
14) 31400
15) 3500
Dimensional Analysis
Dimensional Analysis
• Method of converting one unit to another
• Conversion factor—ratio relationship between
2 units
• Write units, BE SURE THEY CANCEL ! ! !
• “Where are we starting? Where are we trying to
go?”
• KNOW
• 2.54 cm = 1 inch
Example 1:
• Science fiction often uses nautical analogies to describe space
travel. If the starship U.S.S. Enterprise is traveling at warp factor
1.71, what is its speed in knots?
• 1.71 Warp = 5.00 times the speed of light
• Speed of light = 3.00x108 m/s
• 1 knot = 2000 yd/h exactly
Example 2:
• Apothecaries use the following set of measures in the English
system:
•
•
•
•
20 grains ap = 1 scruple
2 scruples = 1 dram ap
8 dram ap = 1 oz. ap
1 dram ap = 3.888g
• What is the mass of 1 scruple in grams?
Example 3:
• BMI is a measurement to determine if a person is obese.
A BMI > 25 is considered overweight. Calculate the BMI
for a 100 lb person with a height of 52 inches. Is this
person overweight?
• Hint: Do conversion factors FIRST, then cancel units
Conversion Factors: In Detail
• = 1 value
• 12 inches = 1 ft.
• 2.54 cm = 1 inch
• 5280 ft. = 1 mile
• SO
• (12 inches = 1 ft.) 3 = 13 = 1 same conversion factor
In Detail Cont.
• Use same conversion factor but raise the factor to the correct
power for conversion.
• Cubic inches to ft3
• (12 inches = 1 ft)3
• When converting between squared and cubic units (m2 to cm2 /m3
to cm3)
Example 4:
• Volume of 2.56 cm3 convert to m3
Temperature Conversions
• °F = 1.8 (T°C) + 32
• °K = 273 + T°C
Accuracy
• How close measurements are to the true/accepted value.
Precision
• How close measurements are to each other.
• These measurements are not necessarily accurate.
Percent Error
• How much error you have in your lab measurements.
• Comparison between your experimental value/measurement
to the true/accepted value.
% Error =(True – Experimental/True)x 100
Percent Error Problems
• 1) True value = 21.2g, Measured value = 17.7g
• 2) True value = 4.15ml, Measured value = 4.26 ml.
Density and SI Units
Density
• Physical property of matter/substances
• Used for substance identification
• Provides information on how solids/liquids interact
• Ratio of a substance’s mass and volume
• Density = Mass/Volume
• Units = SI Unit (kg/m3), we will use g/cm3 or g/ml
Example 1: A student records V1=
2.7ml and V2= 3.4 ml after placing an
object in a graduated cylinder. The
mass of an empty beaker is 1.13g and
the mass of both the beaker and
substance is 4.13g. What is the
object’s density?
Example 2: It has been estimated that
there are 4 x 10-6 mg of gold per liter
of sea water. At a price of $22.30 per
gram of gold, what would be the value
of gold in 1.00 cubic kilometers of the
ocean?
Example 3: A metallic sphere has a
diameter of 0.200 inches and a mass
of 0.0066 ounces. What is the density
of this object, in units of g/cm3?
Specific Gravity
• Removes gravitational influence on a weighed object,
density should not vary with weight !
• Ratio of density of substance/density of reference
• = Dsubstance/Dreference
• Liquids/solids, Dwater = 1.000 g/ml at 3.98°C (decreases with
increase/decrease in temperature)
• Gases, Dair = 1.29 g/L
• At STP (1 atm, 0°C), 1 mole of gas = 22.4 L SO density can be
calculated with molecular mass of gas.
Ex. 1 A solid object has a mass of 3.04
kilograms and a volume of 3.0 x 104 cm3.
What is the density and specific gravity of
the solid object?
Ex. 2 Phosphorus trifluoride is present
at STP conditions. What is its density
and specific gravity?
Homework
• Read pp. 7-22
• Problems pp. 28-30 # 31, 37, 39-41, 42(b,c), 47, 49-50, 53, 5963, 71
• DUE MONDAY!!!
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