Download Chapter 2: Measurements and Problem Solving

CHEMISTRY 100
CHAPTER 2: MEASUREMENT and PROBLEM SOLVING
Homework problems: 27, 29, 31, 33, 37, 39, 41, 45, 47, 49, 51, 53, 57, 63, 69, 73, 77, 81, 87,
89, 91, 93, 97, 105
Outline
I. Measurements
A. Scientific Notation (exponential notation)
1. for very large or very small numbers
2. shows exactly how many significant figures there are (see D. below)
B. Count vs Measurement
C. Counts and Definitions are not measurements – no uncertainty
1. Definition (exact): not the same as conversion factor (inexact or uncertain)
2. Definition: 1 foot = 12 inches, 16 oz = 1 pound
a. within the same system
3. Conversion factor 1 inch = 2.54... cm, 1 pound = 454.... g
a. converting from one system to another (English to metric, etc)
D. Measurements have uncertainty
1. Include all known digits plus one estimate digit
a. estimate between the lines when measuring temperature or distance or..
2. Significant figures
a. nonzero digits: always significant
123.41
(5 sig. figs.)
b. enclosed zeros: always significant
130.053
(6 sig. figs.)
c. leading zeroes: never significant
0.0000403
(3 sig. figs.)
d. trailing zeroes:
i.
after decimal: always significant
2.3400
(5 sig. figs.)
ii.
before decimal: can’t tell so assume not significant
2300
(2 sig. figs.)
E. Measurements have units
1. SI system
2. Metric system
a. Liter not SI but used very frequently
b. 1 cc = 1 mL
3. Derived Units (area, volume, etc.)
4. conversion factors (factor label, unit analysis, factor conversion method)
5. density and specific gravity (what are these)
a. units (g/mL) and unitless (ratio of densities)
II. Significant Figures and Mathematical Operations
A. All digits known to be correct plus one uncertain
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B. Always estimate between the smallest division when measuring
C. Rules for Addition/Subtraction
1. subtraction and addition the same operation
a. subtraction is adding a negative number
2. it is the largest uncertain digit that limits how many sig figs you have.
3. it is possible to have more, or less, or the same number of sig figs when done with
this operation
examples: 29 + 406.2 + 4.894 = 440 with 3 sig figs or 4.40 x 104
the 29 has uncertainty in the one’s place, so that is where our final number must
stop because we only include one uncertain digit.
D. Rules for Multiplication/Division
1. multiplication and division the same operation
a. division is multiplication by the reciprocal
b. dividing by four is the same as multiplying by one fourth
2. it is the smallest number of sig figs in your entries that governs how many sig figs
in your answer
E. Plugging numbers into a calculator does NOT make them more or less accurate
III. More Calculations
A. Percent Calculations
1. percents are fraction/whole, then multiplied by 100
example 1: you get 94 questions correct out of 100 on an exam.
% = 94.00 (fraction you got correct)/100 (total number of problems) x 100
example 2: if you have 13 males and 17 females in a class, what is the percent of
males and females?
female % 17/30 x 100 = 56.67
male % 13/30 x 100 = 43.33
both of these examples are counts, so they have an infinite number of sig figs.
obviously, I can’t write an an infinite number of digits, so I took them out to 4 places
B. Density (D= m/V) (look at units if cannot remember)
1. Density = m/V, or rearrange to get VD = m, or V = m/D
If gold has a density of 19.3 g/mL, how much mass would a standard gold bar (volume = 728
mL) have? How many pounds would that weigh ( 1 lb = 454 g)
m = VD = 728 mL x 19.3 g/mL = 14050.4 g or 14100 g to correct sig figs
this is 14050.4 g x 1 lb/454 g = 30.9 lbs
If a metal has dimensions of L = 3.57 cm, W = 2.46 cm, H = 19.89 cm and mass = 1973.86 g,
what is its density?
D = m/V = m/(LxWxH) = 1973.86 g /(3.57 cm x 2.46 cm x 19.89 cm) = 11.3 g/cm3
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C. Unit conversions
If we have 18 inches and we want to know how many feet that is, we can use a conversion factor.
A unit conversion factor is a statement that so much of one unit = so much of another unit, for
example, 12 inches = 1 foot. We can take this equality and divide both sides by the same thing,
getting 12 inches = 1 foot or 1 = 1 foot (since anything divided by itself = 1). Multiplying
12 inches 12 inches
12 inches
anything by 1 will not change it, so we can use this conversion factor and our original 18 inches
to convert it to feet. Always start with your original measurement on the left hand side:
18 inches x (1 foot/12 inches) = 1.5 feet
Note several things about this. First, we do the unit analysis to make sure the units cancel. We
have inches in the numerator of our original number, so we want inches in the denominator of
our conversion factor. We could have used (12 inches/1 foot) for our conversion factor, but this
would not cause inches to cancel out, so we have to choose our conversion factor to cancel out
units, which is what happened here. If the units don’t cancel, you have not set up the problem
correctly. Try it again. In this case it did cancel and we are left with the units of “feet,” which is
what we want. Next, note the sig figs. There are 2 sig figs in 18 inches and an infinite # of sig
figs in our conversion factor (remember, the very definition of a foot is 12 inches). For instance,
if we had 18.0 inches, this would be 1.50 feet.
D. How to approach word problems
1. Read the problem through once. Just read it – don’t try to solve it in 1 step
2. Determine what the questions is asking – this is usually at the end right
before the question mark.
3. Inventory your available information – what info do you have?
4. Plan how to get from what you have to what the question is asking
5. Set up the problem according to your plan map
6. do unit analysis (factor label method)
7. check for sig figs
8. plug numbers into calculator
Chapter Objectives
Knowledge
Recognize the SI units and its abbreviation (g and m) for mass and distance.
Memorize the prefixes mega-, kilo, centi-, milli-, and microMemorize formula for density (D = m/V) and specific heat (Q = smΔT)
Recall what specific gravity is
Comprehension
Use scientific notation to show correct number of significant figures
Determine how many sig figs a number does have, and how many it should have
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Application
Do calculations (addition/subtraction and multiplication/division) using the
correct number of significant figures
Analysis
Demonstrate the ability to do dimensional analysis with any conversion factors
Solve problems involving multiple conversion factors
Given any two of density, mass, and volume, be able to find the third
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