chapter 3 scientific measurement measurement in chemistry, #’s are either very small or very large...
TRANSCRIPT
Chapter 3
Scientific Measurement
MeasurementIn chemistry, #’s are either very small or very
large
1 gram of hydrogen =
602,000,000,000,000,000,000,000 atoms
Mass of an atom of gold =
0.000 000 000 000 000 000 000 327 gram
Scientific Notation
• Condensed form of writing large or small numbers• When a given number is written as the product of 2 numbers• M x 10n
M must be:• greater than or equal to 1 • less than 10
n must be:• whole number • positive or negative
Find M by moving the decimal point over in the original number to the left or right so that only one non-zero number is to the left of the decimal.
Find n by counting the number of
places you moved the decimal:
To the left (+) or
To the right (-)
Scientific Notation Examples
20 =
200 =
501 =
2000 =
2.0 x 101
2.0 x 102
5.01 x 102
2.000 x 103
More examples…
0.3 =
0.21 =
0.06 =
0.0002 =
0.000314 =
Rule:If a number starts out as < 1, the exponent is always negative.
3 x 10-1
2.1 x 10-1
6 x 10-2
2 x 10-4
3.14 x 10-4
Scientific NotationAdding & Subtracting:
• if they have the same n, just add or subtract the M values and keep same n
• if they don’t have the same n, change them so they do
Scientific Notation
Multiplying:• the M values are multiplied• the n values are added
Scientific Notation Division:
• the M values are divided• the n values are subtracted
Accuracy & Precision
‘How close you are really counts!’
Accuracy• Accuracy – a measure of how close a
measurement comes to the actual or true value of what is measured
To evaluate… the measured
value must be compared
to the correct value
Precision
• Precision – a measure of how close a series of measurements are to one another
To evaluate… you must compare the values of 2 or more repeated measurements
Accuracy vs. Precision
Errors are Unavoidable
• Measuring instruments have limitations
• Hence, there will always be errors in measurement.
Not All Errors are Equal• Consider the following two errors:• You fly from NY to San Francisco
• Your plane is blown off course by 3cm
• You are an eye surgeon
• Your scalpel misses the mark by 3cm
The errors sound equal… but are they?
Absolute Error• The error in each of the previous examples is 3cm• But the error in each is not equivalent!• This type of error is the absolute error.
Absolute error = | measured value – accepted value |
Accepted value is the most probable value or the value based on references
Only the size of the error matters, not the sign
Significance of an Error• The absolute error tells you how far you are from
the accepted value• It does not tell you how significant the error is.
o Being 3cm off course on a trip to San Francisco is insignificant because the city of San Francisco is very large.
o Being 3cm off if you are an eye surgeon means your operating on the wrong eye!
• It is necessary to compare the size of the error to the size of what is being measured to understand the significance of the error.
Percentage Error
• The percentage error compares the absolute error to the size of what is being measured.
% error = |measured value – accepted value| x 100%
accepted value
• Example: Measuring the boiling point of H2O
Thermometer reads – 99.1OCYou know it should read – 100OC
Error = measured value – accepted value
% error = |error| x 100% accepted value
Sample Problem
% error = |99.1oC – 100.0oC| x 100%
100oC
= 0.9o x 100%
100o
= 0.009 x 100%
= 0.9%
C
C
Significant Figures• Used as a way to express which numbers
are known with certainty and which are estimated
What are significant figures?
Significant Figures –
all the digits that are known, plus
a last digit that is estimated
Rules1) All digits 1-9 are significant Example: 129
2) Embedded zeros between significant digits are always significant Example: 5,007
3) Trailing zeros in a number are significant only if the number contains a decimal point Example: 100.0
3600
3 sig figs
4 sig figs
4 sig figs
2 sig figs
4) Leading zeros at the beginning of a number are never significant
Example: 0.0025
5) Zeros following a decimal significant
figure are always significant
Example: 0.000470
0.47000
6) Exceptions to the rule are numbers with an
unlimited number of sig figs
Example = Counting – 25 students
Exact quantities – 1hr = 60min, 100cm = 1m
2 sig figs
3 sig figs
5 sig figs
Significant Figure Examples 123m = 9.8000 x 104m = 0.070 80 = 40, 506 = 22 meter sticks = 98, 000 = 143 grams = 0.000 73m = 8.750 x 10-2g =
35
4
5
unlimited
2
32
4
Calculations Using Significant Figures
• Rounding1st determine the number of sig figs
Then, count from the left, & round
If the digit < 5, the value remains the same.
If the digit is ≥ 5, the value of the last sig fig is increased by 1.
Try your hand at rounding…
Round each measurement to 3 sig figs.
87.073 meters = 4.3621 x 108 meters = 0.01552 meter = 9009 meters = 1.7777 x 10-3 meter = 629.55 meters =
87.1m
0.0155m or 1.55 x 10-2m
4.36 x 108 m
9010m
1.78 x 10-3m
630. m or 6.30 x 102m
• Multiplying and Dividing
Limit and round to the least number of significant figures in any of the factors.
23.0cm x 432cm x 19cm =
Answer =
Because 19 only has 2 sig figs
190,000cm3 or 1.9 x 103cm3
188,784cm3
• Addition and SubtractionLimit and round your answer to least number of decimal places in any of the numbers that make up your answer.
123.25mL + 46.0mL + 86.257mL =
Answer =
Because 46.0 has only 1 decimal place
255.5mL
255.507mL
The International System of Units
• Based on the #10
• Makes conversions easier
• Old name = metric system
Units and Quantities• Length – the distance between 2 points or
objects
Base unit = meter
• Volume – the space occupied by any sample of matter
V = length x width x height
Base unit = liter
Based on a 10cm cube (10cm x 10cm x 10cm = 1000cm3)
1 liter = 1000cm3
• Mass – the amount of matter contained in an object
Base unit = gram
Different than weight…
Weight - a force that measures the pull of gravity
MMeettrriicc CCoonnvveerrssiioonn CChhaarrtt
1000 100 10 1 10-1 10-2 10-3
10-6 10-9
KILO – HECTA – DEKA – [BASE] – DECI – CENTI – MILLI – MICRO - NANO Meter Liter Gram
IF YOU ARE MOVING THE DECIMAL POINT: IF YOU ARE MULTIPLYING OR DIVIDING:
1. Start with the unit given to you 1. Start with the unit given to you. 2. Count how many times you need to move to get to the new unit 2. If moving to the Right Multiply: x10 for 1 jump, 3. Move the decimal in the number that many spaces and x100 for 2 jumps, x1000 for 3 jumps, etc.
in the same direction. 3. If moving to the Left Divide: /10 for 1 jump, 4. Re-write the number with the new units. /100 for 2 jumps, /1000 for 3 jumps, etc.
4. Rewrite the number with the new units.
Move Decimal Left OR Divide
Move Decimal Right OR Multiply
• Temperature – a measure of the energy of motion
How fast are the molecules moving?
When 2 objects are at different temperatures heat is always transferred from the warmer → the colder object
Temperature Scales• Celsius scale –
Freezing point of H2O = 0oCBoiling point of H2O = 100oC
• Kelvin scale –Freezing point of H2O = 273.15KBoiling point of H2O = 373.15K
K = C + 273
C = K - 273
Temperature Scale Conversions
Conversion Factorsand
Unit Cancellation
A physical quantity must include:A physical quantity must include:
NumberNumber + Unit+ Unit
1 foot = 12 inches1 foot = 12 inches
1 foot = 12 inches1 foot = 12 inches
1 foot1 foot
12 inches12 inches= 1= 1
1 foot = 12 inches1 foot = 12 inches
1 foot1 foot
12 inches12 inches= 1= 1
12 inches12 inches
1 foot1 foot= 1= 1
1 foot1 foot
12 inches12 inches
12 inches12 inches
1 foot1 foot
“Conversion factors”“Conversion factors”
1 foot1 foot
12 inches12 inches
12 inches12 inches
1 foot1 foot
“Conversion factors”“Conversion factors”
3 feet3 feet12 inches12 inches
1 foot1 foot= 36 inches= 36 inches(( ))(( ))
How many inches are in 3 feet?
How many cm are in 1.32 meters?
conversion factors:
equality:
or
X cm = 1.32 m =
1 m = 100 cm
______1 m100 cm
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.
______1 m
100 cm
( )______1 m
100 cm 132 cm
How many meters is 8.72 cm?
conversion factors:
equality:
or
X m = 8.72 cm =
1 m = 100 cm
______1 m100 cm
Again, the units must cancel.
______1 m
100 cm
( )______ 0.0872 m1 m100 cm
How many feet is 39.37 inches?
conversion factors:
equality:
or
X ft = 39.37 in =
1 ft = 12 in
______1 ft 12 in
Again, the units must cancel.
( )____ 3.28 ft1 ft12 in
______1 ft
12 in
How many kilometers is 15,000 decimeters?
X km = 15,000 dm = 1.5 km( )____1,000 m
1 km10 dm
1 m ( )______
How many seconds is 4.38 days?
=
1 h60 min24 h
1 d 1 min60 s____( ) ( )____( )_____X s = 4.38 d
378,432 s
3.78 x 105 sIf we are accounting for significant figures, we would change this to…
Why do some objects float in water while others sink?
• Need to know the ratio of the mass of an object to it’s volume
• Pure H2O at 4oC = 1.000g/cm3
• If an object has a lower ratio it will float
• If an object has a greater ratio it will sink
Density• The ratio of an object’s mass to it’s volume
Density = mass volume
Example: A 10.0cm3 piece of lead has a mass of 114g. What is the density of lead?
114g = 10.0cm3
11.4g/cm3
Recall…
What type of property is density?
Does the density of a material change in relation to the sample size?
NO… density is an Intensive property
it depends only on the composition of
the material
What might affect a substance’s density?
• Temperature The volume of most substances ↑ withan ↑ in
temperature the mass remains the same
If the volume increases… what affect does it have on a substance’s density?
The density decreases
*Exception –Water’s volume ↑ with a ↓ in temperatureIts density decreases & ice floats
H2O
Calculating Density
What is the volume of a pure silver coin that has a mass of 14g, and a density of 10.5g/cm3?
D = 10.5g/cm3
M = 14gV = ?
Rearrange the density formula to solve for V
D
M
V
V = M
D
V = 14g = 14 x 1 cm3 =
10.5g/cm3 10.5g
g 1.3cm3
What is the mass of mercury that has a density of 13.5g/cm3 and a volume of 0.324cm3?
Once again, rearrange the
density formula… and solve
for M.
D
M
VM = D x V
M = 13.5g x 0.342 cm3
cm3
= 4.62g