Download Measurements and Mathematics in Physics

Measurements and Mathematics
in Chemistry
Precision
• refers to the degree of reproducibility of a
measured quantity, that is, the closeness of
agreement when the same quantity in measured
several times
Accuracy
• Refers to how close a measured value is to the
accepted or “real” value. High precision
numbers are not always accurate. But it is
more likely that measurements of high
precision are more accurate.
Metric Units
Basic units
• The basic metric unit for the measurement of length is known as the ______________.
•
•
The basic metric unit of volume is the _____________.
Volume can also be measured using cm.
1 cm3 = _____ mL
– Tool used to measure volume is the ________________________________________
– Smallest increment marked: __________________________________
•
Measurements should be read to the nearest: _______________________
The basic metric unit of mass is the _____________.
– Tool used to measure mass is the _________________________________
– Smallest increment marked: __________________________________
Measurements should be read to the nearest: _______________________
The basic metric unit for temperature is ________________________.
– Tool used to measure temperature is the ______________________________
– Smallest increment marked: __________________________________
– Measurements should be read to the nearest: _______________________-
The temperatures in this scale can easily be converted to the Kelvin scale, or
the absolute scale, by the following formula:
****K =
Prefixes
Prefix
symbol
(times greater than base)
numerical value
10x
____________
_______
1,000,000
_______
____________
_______
1,000
_______
____________
_______
100
_______
____________
_______
10
_______
Basic unit (_____,_____,_____)
1
Prefixes
Prefix
symbol
numerical value
10x
(times greater than base)
____________
_______
0.1
_______
____________
_______
0.01
_______
____________
_______
0.001
_______
Practice
.0063 m = ____________ mm
377 mm = ____________ cm
390,000 g = ____________ kg
275 K = ____________ °C
0.0018 kL = ____________ L
42,000 cm = ____________ km
22.4 mL = ____________ cm3
250cm = ____________ m
25 °C = ____________ K
432 cm3 = ____________ L
Percent Error
• For example, if you measure the mass of
oxygen in a sample to be 25.0 grams and the
theoretical value is 30.0 grams, the percent
error would be:
What is the length of the following?
Significant Figures
Definition: all the known values from a
measurement including a last estimated digit
Determining the # of Sig Figs in a
measurement
1. Is the decimal present
or absent?
2. Begin at the
appropriate ocean side
of the measurement
3. Move to the first nonzero digit
4. Count all digits moving
across
Recall the measured value from
earlier:
How many significant digits are there in our
measured value?
Practice
Indicate the number of significant figures in the
following measurements:
0.00734 cm3
_____
510 mL
_____
510. mL
_____
Do Now:
Indicate the number of significant figures in the
following measurements and identify the
estimated digit:
20200 g
_____
0.0050 atm
_____
22.4 L
_____
101.3 kPa
_____
5000 mol
_____
Addition and subtraction with Sig Figs
• The answer has only as many decimal places as
the measurement having the least number of
decimal places.
Procedure:
1. line up all measurements by decimal points
2. perform the calculation on your calculator
3. draw a line down next to the least decimal place
4. round your answer off the answer to the digit to
the left of the line
Example:
Given: 2 H2 + O2 → 2H2O
If 4.0318 g of H2 are combined with 32.0 g of
O2, how many grams of H2O are formed?
4.0318
+ 32.0____
Multiplication and Division
• Rule: The solution to a multiplication or division
problem can only have as many significant figures
as the starting measurement with the least
number of significant figures.
Procedure:
1. perform the calculation on your calculator
2. count the number of significant figures in the
starting measurements
3. round your answer off the answer to the least
number of significant figures
Example:
• A student found the mass of an object to be
50.11 grams and the volume of the object to
be 22.0 mL. What is the density of the object?
Example:
• Gold has a density of 19.320 g/mL. If a piece
of gold has a volume of 14.8 mL, what is the
mass of the object
Example:
What is the mass of 75.2 mL of mercury?
(density of mercury is 13.546 g/cm3)