Transcript Practice Problem

Problem Solving in Chemistry
Dimensional Analysis
conversion
• Used in _______________
problems.
*Example: How many seconds are there in 3 weeks?
• A method of keeping track of the_____________.
units
Conversion Factor
ratio of units that are _________________
equivalent
• A ________
to one another.
*Examples:
1 min/ ___
60 sec (or ___
60 sec/ 1 min)
7 days/ 1 week (or 1 week/ ___
7 days)
___
1000 m/ ___
1 km
(or ___
1 km/ 1000 m)
• Conversion factors need to be set up so that when multiplied, the unit
of the “Given” cancel out and you are left with the “Unknown” unit.
top and the
• In other words, the “Unknown” unit will go on _____
“Given” unit will go on the ___________
bottom
of the ratio.
How to Use Dimensional Analysis to Solve Conversion Problems
• Step 1:
Identify the “________”.
Given
This is typically the only number
given in the problem. This is your starting point. Write it down! Then
write “x _________”. This will be the first conversion factor ratio.
• Step 2:
Identify the “____________”.
This is what are you trying to
Unknown
figure out.
• Step 3:
Identify the ____________
Sometimes you will
conversion _________.
factors
simply be given them in the problem ahead of time.
• Step 4:
By using these conversion factors, begin planning a solution
to convert from the given to the unknown.
• Step 5:
When your conversion factors are set up, __________
multiply all the
divide
numbers on top of your ratios, and ____________
by all the numbers
on bottom.
If your units did not ________
cancel ______
out correctly, you’ve messed up!
Practice Problems:
(1)How many hours are there in 3.25 days?
3.25 days x 24 hrs = 78 hrs
1 day
(2) How many yards are there in 504 inches?
504 in. x 1 ft
12 in.
x 1 yard
3 ft
= 14 yards
(3) How many days are there in 26,748 seconds?
26,748 sec x 1 min x 1 hr x 1 day
60 sec 60 min
24 hrs
= 0.30958 days
Scientific Measurement
Qualitative vs. Quantitative
•
Qualitative measurements give results in a descriptive nonnumeric
adjective describing
form. (The result of a measurement is an _____________
the object.)
short
heavy
cold
*Examples: ___________,
___________,
long, __________...
•
Quantitative measurements give results in numeric form. (The
number
results of a measurement contain a _____________.)
600 lbs.
5 ºC
*Examples: 4’6”, __________,
22 meters, __________...
Accuracy vs. Precision
•
single
Accuracy is how close a ___________
measurement is to the
true __________
value
________
of whatever is being measured.
•
several measurements are to
Precision is how close ___________
each ___________.
other
_________
Practice Problem: Describe the shots for the targets.
Bad Accuracy & Bad
Precision
Good Accuracy & Bad
Precision
Bad Accuracy & Good
Good Accuracy & Good
Significant Figures
•
Significant figures are used to determine the ______________
of a
precision
measurement. (It is a way of indicating how __________
precise a
measurement is.)
*Example: A scale may read a person’s weight as 135 lbs. Another
scale may read the person’s weight as 135.13 lbs. The ___________
second
more significant figures in the
scale is more precise. It also has ______
measurement.
•
•
•
Whenever you are measuring a value, (such as the length of an object
with a ruler), it must be recorded with the correct number of sig.
figs.
ALL the numbers of the measurement known for sure.
Record ______
Record one last digit for the measurement that is estimated. (This
reading in between the
means that you will be ________________________________
marks of the device and taking a __________
guess
__________
at what the next
number is.)
Significant Figures
•
Practice Problems: What is the length recorded to the
correct number of significant figures?
length = ________cm
11.65
(cm) 10
20
30
40
58
length = ________cm
50
60
70
80
90
100
•
•
The SI System (The Metric System)
Here is a list of common units of measure used in science:
Standard Metric Unit
Quantity Measured
mass
kilogram, (gram)
______________
length
meter
______________
volume
cubic meter, (liter)
______________
seconds
______________
time
temperature
Kelvin, (˚Celsius)
_____________
The following are common approximations used to convert from our
English system of units to the metric system:
1 yard
1 m ≈ _________
2.2 lbs.
1 kg ≈ _______
1.609 km ≈ 1 mile
mass of a small paper clip
1 gram ≈ ______________________
sugar cube’s volume
1mL ≈ _____________
1 L ≈ 1.06 quarts
dime
1mm ≈ thickness of a _______
The SI System (The Metric System)
•
Metric Conversions
The metric system prefixes are based on factors of _______.
mass
Here is a list of the common prefixes used in chemistry:
kilo- hecto- deka-
•
•
deci- centi- milli-
The box in the middle represents the standard unit of measure
such as grams, liters, or meters.
Moving from one prefix to another involves a factor of 10.
cm = 10 _____
dm
m
*Example: 1000 millimeters = 100 ____
= 1 _____
•
The prefixes are abbreviated as follows:
k
h
da
g, L, m
d
c
m
grams
Liters
meters
*Examples of measurements: 5 km 2 dL 27 dag 3 m 45 mm
Metric Conversions
•
To convert from one prefix to another, simply count how many places you
move on the scale above, and that is the same # of places the decimal point
will move in the same direction.
Practice Problems:
380,000
380 km = ______________m
0.00145
1.45 mm = _________m
4.61
461 mL = ____________dL
0.0004
0.4 cg = ____________
dag
260
0.26 g =_____________
mg
230
230,000 m = _______km
Other Metric Equivalents
1 mL = 1 cm3
1 L = 1 dm3
For water only:
1 L = 1 dm3 = 1 kg of water
or
1 mL = 1 cm3 = 1 g of water
Practice Problems:
300 L
(1) How many liters of water are there in 300 dm3 ? ___________
0.5 kg
(2) How many kg of water are there in 500 mL? _____________
Area and Volume Conversions
•
If you see an exponent in the unit, that means when converting
you will move the decimal point that many times more on the
metric conversion scale.
*Examples:
twice
cm2 to m2 ......move ___________
as many places
m3 to km3 ......move _____
3 times as many places
2
380,000,000
Practice Problems: 380 km2 = _________________m
3
0.00461
4.61 mm3 = _______________cm
k
h
da g, L, m
grams
Liters
d
meters
c
m
•
Scientific Notation
Scientific notation is a way of representing really large or small
numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
(1) Write down all the sig. figs.
(2) Put the decimal point between the first and second digit.
(3) Write “x 10”
(4) Count how many places the decimal point has moved from its
original location. This will be the exponent...either + or −.
(5) If the original # was greater than 1, the exponent is (__),
+ and if the
−
original # was less than 1, the exponent is (__)....(In
other words, large
+ exponents, and small numbers have (_)
− exponents.
numbers have (__)
Scientific Notation
•
Practice Problems: Write the following measurements in scientific
notation or back to their expanded form.
477,000,000 miles = _______________miles
4.77 x 108
0.000 910 m = _________________
m
9.10 x 10−4
−
9
6,300,000,000
6.30 x 10 miles = ___________________ miles
0.00000388
3.88 x 10−6 kg = __________________
kg
Evaluating the Accuracy of a Measurement
•
The “Percent Error ” of a measurement is a way of representing the
accuracy of the value. (Remember what accuracy tells us?)
% Error = (Accepted Value) − (Experimentally Measured Value) x 100
(Accepted Value)
(Absolute Value)
Practice Problem:
A student measures the density of a block of aluminum to be
approximately 2.96 g/mL. The value found in our textbook tells us
that the density was supposed to be 2.70 g/mL. What is the accuracy
of the student’s measurement?
% Error = |2.70−2.96| ÷ 2.70 = 0.096296…x 100 = 9.63% error