2 measurement contents 2-1 measurement of matter: si (metric) units 2-2 converting units 2-3...
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2 Measurement Contents
2-1 Measurement of Matter: SI (Metric) Units 2-2 Converting Units
2-3 Uncertainty in Measurements 2-4 Significant Figures in Calculations2-5 Density2-6 Measuring Temperature2-7 Atomic Masses2-8 Formula Masses2-9 Amount of Substance
The rulers
The TEM
The speedometerThe SEM
2-1 Measurement of Matter: SI(Metric) Units.
The scientific community uses SI units ( the units of
International System of units) for measurement properties of
matters.
SI Units• There are two types of units:
– fundamental (or base) units;– derived units.
• There are 7 base units in the SI system.
There are seven SI base units from which all other necessary units (derived units) are derived.
Although the meter is the base SI unit used for length, it may not be convenient to report the length of an extremely small object or an extremely large object in units of meters.
Length
a very small object
a very large object
measured in
millimeters (1 mm = 0.001
m)
measured in kilometers (1 km
= 1000 m).
Decimal prefixes allow us to choose a unit that is appropriate to the quantity being measured.
2-2 Converting Units
Decimal prefixes allow us to choose a unit that is appropriate to the quantity being measured.
Selected Prefixes used in SI System
Derived Units
• Derived units are obtained from the 7 base SI units.
• Example:
m/ssecondsmeters
timeof unitsdistance of units
velocityof Units
Derived Units
The SI unit of mass and volume are
gram(g) and meter (m)
Density has units of grams per cubic centimeter, g/cm3.
the basic SI unit for density is
Derive
Note that there are no units of volume in SI system. For measurements of volume, density, and other properties, we must derive the desired units from SI base units.
Derived Units
The unit of volume is cubic
meter (m3)
The SI unit of length is meter
(m)
milliliters, mL (1 mL = 1 cm3).
liters, L (1 cubic decimeter, or 1 dm3)
the basic SI unit for volume is Deri
ve
Volume
• The units for volume are given by (units of length)3.– SI unit for volume is 1
m3.
• We usually use 1 mL = 1 cm3.
• Other volume units:– 1 L = 1 dm3 = 1000 cm3
= 1000 mL.
Volume
The SI unit of temperature is the Kelvin, although the
Celsius scale is also commonly used. The Kelvin scale is
known as the absolute temperature scale, with 0 K being the
lowest theoretically attainable temperature.
Temperature
T (K) = t(ºC ) + 273.15
Kelvin from Celsius
Celsius from Fahrenheit
t (ºC) = 5/9 [t (º F)-32]
SI units: The preferred metric units for use in science.
Celsius scale: A temperature scale on which
water freezes at 0° and boils at 100° at sea level.
Kelvin scale: The absolute temperature scale; the SI unit
for temperature is the Kelvin. Zero on the Kelvin scale
corresponds to -273.15°C; therefore, K = °C + 273.15.
Definition
Figure 1.12shows a comparison of the Kelvin, Celsius, and Fahrenheit scales.
2-3 Uncertainty in Measurements
Numbers obtained by measurement are always inexact.
Two kinds of numbers are encountered in scientific
work:
Exact Numbers (those whose values are known
exactly)
Inexact Numbers (those whose values have some
uncertainty).
Key points
Even the most carefully taken measurements are always inexact.
2-3 Uncertainty in Measurements
This inexactness can be a consequence of
human error
inaccurately calibrated instruments
any number of other factors
• All scientific measures are subject to error.
• These errors are reflected in the number of figures
reported for the measurement.
• These errors are also reflected in the observation
that two successive measures of the same quantity
are different.
Two terms are used to describe the quality of measurements.
precision
accuracy
The repeatability of measurements is called precision, which refers to how closely two or more measurements of the same property agree with one another.
The correctness of measurements is called accuracy, which refers to how close a measurement is to the true
value of a property.
The analogy of darts stuck in a dartboard pictured in Figure 2.1 illustrates the difference between the two terms.
The difference between the accuracy and precision
If a very sensitive balance is poorly calibrated, for example, the
masses measured will be inaccurate even if they are precise.
The relationship between the accuracy and precision
It is possible, however, for a precise value to be inaccurate.
In general, the more precise a measurement, the more accurate it is.
We again confide in the accuracy of a measurement if we
obtain nearly the same value in many different experiments.
Measurement = a number + a unit
Measurement = quantity + units + uncertainty
In order to convey the appropriate uncertainty in a reported number, we must report it to the correct number of significant figures.
2-4 Significant Figures in Calculations
Significant figures
Example
The number 83.4
has three digits. All three digits are significant. The 8 and the 3 are "certain digits" while the 4 is the "uncertain digit."
Figure 1.14 Number of Significant figures
The number 83.4
Thus, measured quantities are generally reported
in such a way that only the last digit is uncertain.
All digits, including the uncertain one, are called
significant figures.
this number implies uncertainty of plus or minus 0.1, or error of 1 part in 834.
Guidelines
457 cm (3 significant figures);
2.5 g (2 significant figures). 2. Zeros between nonzero digits are always
significant.
1005 kg (4 significant figures);
1.03 cm (3 significant figures).
0.02 g (one significant figure);
0.0026 cm (2 significant figures).
1. Nonzero digits are always significant.
3. Zeros at the beginning of a number are never significant.
0.0200 g (3 significant figures);
3.0 cm (2 significant figures).
5. When a number ends in zeros but contains no decimal point, the zeros
may or may not be significant
130 cm (2 or 3 significant figures);
10,300 g (3, 4, or 5 significant figures).
4. Zeros that fall at the end of a number and after the decimal point
are always significant
To avoid ambiguity with regard to the number of significant
figures in a number with tailing zeros but no decimal point,
we use scientific (or exponential) notation to express the
number.
Example
Scientific (or exponential) notation
If we are reporting the number 700 to three significant figures,
We can express it as 700 or 7.00 × 102
if there really should be only two significant figures
we can write 7 × 102. if there should be only
one significant figure,
we can express this number as 7.0 × 102
Scientific notation is convenient for expressing the
appropriate number of significant figures. It is also
useful to report extremely large and extremely small
numbers.the number 1.91 × 10-24
we can express the number
0.00000000000000000000000191.
When measured numbers are used in a calculation, the
precision of the result is limited by the precision of the
measurements used to obtain that result.
Significant figures in calculation
If we measure the length of one side of a cube to be 1.35 cm,
calculate the volume of the cube to be 2.460375 cm3.
Original number had three significant
figures
If we report the volume to seven significant figures, we are implying an uncertainty of 1 part in over two million! We can't do that.
Guidelines
In order to report results of calculations so as to imply a realistic
degree of uncertainty, we must follow the following rules.
If A x B or A / B = C
1. the C must have the same number of significant figures as the A or B with the fewest significant figures.
If A + B or A - B = C
2. the C can have only as many places to the right of the decimal point as the A or B with the smallest number of places to the right of the decimal point.
If we measure the length of one side of a cube to be 1.35 cm,
The volume of the cube should to be 2.46 cm3.
Original number had three significant
figures
The significant figures of volume should not be more than three.
Using above rules,
In rounding off numbers, look at the leftmost digit to be
removed:
1.If the leftmost digit removed is less than 5, the
preceding number is left unchanged.
Thus, rounding 7.248 to two significant figures gives
7.2.
2. If the leftmost digit removed is 5 or greater, the
preceding number is increased by 1.
Rounding 4.735 to three significant figures gives 4.74,
and rounding 2.376 to two significant figures gives 2.4.
Rounding off Numbers
Question
1. What is the answer to the following problem, reported to the correct number of significant figures. 0.11807 0.1181 0.118 0.12 0.1
2. How many significant figures are there in the number 0.0012?
12345
3. How many significant figures are there in the number 1020.5?
23456
2-5 Density and percent Composition: Their Use in Problem Solving
Density
If you answer that they weigh the same, you demonstrate a clear understanding of the meaning of mass----a measure of a quantity of matter.
cottonstone
What weighs more, a ton of stones or a ton
of cottons?
WHAT IS THE DIFFERENCE BETWEEN MASS AND WEIGHT?
Mass is defined as the amount of matter an object has. One of the qualities of mass is that it has inertia. Mass is a measure of how much inertia an object shows.
The weight of an object on earth depends on the force of attraction (gravity) between the object and earth. Weight will change according to the force of attraction.
Since the moon has 1/6 the mass of earth, it would
exert a force on an object that is 1/6 that on earth.
Density
• Used to characterize substances.
• Defined as mass divided by volume:
• Units: g/cm3.
• Originally based on mass (the density was defined as the mass of 1.
00 g of pure water).
volumemass
Density
Density in conversion Pathways
Density (d) = mass(m) / volume(V)
Density is the ratio of
mass to volume.
If we measure the mass of an object and its volume, simple division gives us its density.
volume(V) = mass(m) / Density (d)
mass(m) = Density (d) x volume(V)
For example What is the volume of a 5.25-gram sample of a liquid with density 1.23 g/ml?
Using:
volume(V) = mass(m) / Density (d)
solution
Volume in mL = 5.25g x 1mL/ 1.23 g = 4.27 mL
Percent as a conversion factor
A common way of referring to composition is through percentages.
there is 3.5 g of sodium chloride in every 100 g of the seawater
a seawater sample contains 3.5% sodium chloride by mass means
Percentdefinition is the number of parts of a
constituent in 100 parts of the whole.
We can express this percent by writing the following ratios and we can use this type of ratio as a conversion factor.
3.5 g of sodium chloride /100 g of the seawater
100 g of the seawater/ 3.5 g of sodium chloride
a seawater sample contains 3.5% sodium chloride by mass means
1. A square metal sheet measures 12.3 cm on a side. It
is 3.6 mm thick and has a mass of 121.35 g. What is
the density of the metal?
Questions
choice
a. 2.22806 g/cm3,b. 0.22 g/cm3, c. 2.2 g/cm3, d. 0.76 g/cm3, e. 1.27 g/cm3.
2. How many cubicmillimeters are there in a cubic centimeter?
Questions
a. 10, b. 100, c. 1000,
d. 0.1, e. 1 x 103
choice
3. Which sample has the greater volume? 16.2 g
of a liquid with density 1.045 g/cm3 or 52.0 g of a
solid with density 3.354 g/cm3
a. The solidb. The liquidc. They both have d. The same volume
Questions
choice
2-6 Measuring Temperature
Temperature
There are three temperature scales:
•Kelvin Scale
–Used in science.
–Same temperature increment as Celsius scale.
–Lowest temperature possible (absolute zero) is zero
Kelvin.
–Absolute zero: 0 K = -273.15 oC.
Temperature
• Celsius Scale
– Also used in science.
– Water freezes at 0 oC and boils at 100 oC.
– To convert: K = oC + 273.15.
• Fahrenheit Scale
– Not generally used in science.
– Water freezes at 32 oF and boils at 212 oF.
– To convert:
32-F95
C 32C59
F
The SI unit of temperature is the Kelvin, although the
Celsius scale is also commonly used. The Kelvin scale is
known as the absolute temperature scale, with 0 K being
the lowest theoretically attainable temperature.
Temperature
T (K) = t(ºC ) + 273.15
Kelvin from Celsius
Celsius from Fahrenheit
t (ºC) = 5/9 [t (º F)-32]
Figure 2.2shows a comparison of the Kelvin, Celsius, and Fahrenheit scales.
• Make the following temperature conversions:
(a) 68 oF to oC; (b) -36.7 oC to oF
32-F95
C 32C59
F
Class Practice ExampleClass Practice Example
2-7 Atomic Masses
Proton: Small particles with a unit positive charge in the
nucleus of an atom.
Neutron: Particles with no charge and are present in the nuclei
of all atoms expect one isotope of hydrogen.
Atomic number: The number of protons in the nucleus.
Neutron number: The number of neutrons in the nucleus.
Isotopes: Atoms of an element that differ in mass.
Mass Number: The sum of the number of protons and
neutrons in the nucleus of an atom.
2-8 Formula Masses
Formula Masses of compounds are equal to the sum of atomic
masses of the atoms forming the compound.
Example: Na2SO4
Formula Masses of Na2SO4
=22.99×2+32.07+16.00×4=142.05
2-9 Amount of Substance
One mole is defined as the amount of substance in a sample
that contains as many units as there are atoms in exactly 12 g
of carbon-12.
Avogadro’s number: The number of units in a mole is
6.022137×1023
Molar mass: The mass of one mole in grams.
Homework
All the questions are from the textbook: Genaral Chemistry.
P28: 1.41
P66: 2.45
P67: 2.70, 2.75