Transcript Avogadro`s number

Review: Why Atoms?
• Chemical combination rules (Dalton)
• Success of kinetic theory in describing behavior of matter
– Predictions that follow from the theory are confirmed, although
atoms are not “directly” observed
• Brownian motion
– A way of seeing atoms “directly”
– Again, predictions based on atomic theory are confirmed by
experiments
• X-ray diffraction
– Studied in detail in the early 20th century
How Big are They?
• Clearly, very small!
• Too small to be visible in the best optical microscopes
– Microscopes can only resolve an object that is comparable in size
or larger than the wavelength of the light used to illuminate it
– For visible light, the smallest structures that can be seen are about
400 nanometers, or 4  10–7 m
– Atoms must be smaller than this!
What is Light?
• Light is a type of wave
• Other common examples:
water waves, sound
• A wave is a disturbance
in a medium (water, air,
etc.) that propagates
• Typically the medium
itself does not move
much
Anatomy of a Wave
crest
wavelength
2 x amplitude
trough
direction of wave motion
Electromagnetic Waves
• Medium: the electric and magnetic field
• Speed = 3  105 km/sec (about 186,000 mi/sec)
The Electromagnetic Spectrum
Visible Light
• The color of visible light is
determined by its wavelength
• White light is a mixture of all
colors
• We can separate out individual
colors with a prism
Visible Light
400–440 nm
440–480 nm
480–530 nm
530–590 nm
590–630 nm
630–700 nm
Violet
Blue
Green
Yellow
Orange
Red
1 nm = 1 nanometer
= 10–9 m
Longer wavelength
Shorter wavelength
Superposition and Interference
• When several waves pass
through the same place,
the total wave is obtained
by adding together the
individual wave
displacements (Principle
of Superposition)
X-Ray Diffraction
• X-rays have wavelengths
comparable to atomic sizes
• We can “see” atoms and
molecules by bouncing Xrays off them
• Crystals and molecules
reflect X-rays in patterns
depending on their structures
• From the reflection pattern
one can figure out the
structure!
X-ray diffraction pattern of DNA
Interaction of X-Rays with Atoms
• Involves the electrons, primarily
More Information
• Intensities (brightness) of
diffraction maxima can vary –
more information about detailed
structure
• The symmetry of the crystal
structure is reflected in the
diffraction pattern
So, How Big are They?
• Earliest estimate: Johann Loschmidt
(1865)
– Used results from kinetic theory to estimate
the size of an “air molecule”
• We no know there are several types of
molecules present in air
• They are roughly the same size, though!
– His result was about one millionth of a
millimeter
• In other words, about 10–3 m/106 or 10–9 m
• This is about 400 times smaller than the
smallest object visible in an optical
microscope
Brownian Motion
• Discovered in 1828 by Robert Brown,
a Scottish botanist
• He observed that microscopic pollen
grains suspended in a liquid move
around erratically, even though the
liquid itself has no observable motion
• Explanation: the grains are being
jostled and buffeted by unseen atoms
• The smaller the grain, the more
violently it is agitated
Size of Atoms
• In 1905, Einstein worked out several predictions regarding
Brownian motion using atomic theory
• Confirmed by Jean Perrin (1908)
– Nobel Prize for Physics 1926
• Based on his measurements, Perrin gave an accurate
estimate of the size of atoms: about 1-2  10–10 m
• The atomic scale is about a tenth of a nanometer
Avogadro’s Hypothesis
• Equal volumes of gases under the same conditions of
temperature and pressure have equal numbers of molecules
• Derived from the observations by Gay-Lussac and others
– gases unite in simple proportions by volume
– if a reaction of two gases produces a gas, the volume of gas
produced is also related by a simple proportion
• He also proposed that some gases (like oxygen and
hydrogen) are not made up of single atoms
• Why weren’t his idea quickly accepted?
– they indicated that Dalton’s atomic weights were wrong
– there was no agreement as to what a “molecule”
– he was not a particularly accomplished experimentalist
Loschmidt’s Number
• Avogadro’s Hypothesis predicts that one cubic
centimeter of any gas under standard conditions will
always contain the same number of molecules
• Avogadro, however, never calculated this number (he
had neither the experimental or theoretical
background to accomplish this)
• The first estimate of this quantity was made by
Loschmidt in 1865 from the kinetic theory of gases
• (Cannizzaro first promoted Avogadro’s ideas at the
Karlsruhe Conference of Chemists in 1860)
Avogadro’s Number
• Chemists prefer to use what we now call
“Avogadro’s Number” for many calculations
• Avogadro’s number is the number of oxygen
(O2) molecules in 32 grams of oxygen, or the
number of H2 molecules in 2 grams of H2
or the number of molecules per mole of molecules
• It is an honorary name (first used by Perrin in
1909) – still called Loschmidt’s Number in
Germany
• NA = 6.022 x 1023 (atoms or molecules) per mole
Estimating Avogadro’s Number