1. Proof?

2. “The Chemists of the 1800’s”
1662: Robert Boyle Volume vs. Pressure
1785: Jacques Charles Pressure vs. Temperature
1808: Joseph Gay-Lussac Volume vs. Temperature
1811: Amedeo Avogadro Avogadro’s Law
Ideal Gas Law: PV = kNT

3. “The Chemists of the 1800’s”
1794: Joseph Proust Law of Definite Proportions
1805: John Dalton Law of Multiple Proportions
1811: Amedeo Avogadro Avogadro’s Law
1865: Johann Loschmidt Approximates atomic size.
Evidence for Atoms…

4. “The Chemists of the 1800’s”
1794: Joseph Proust Law of Definite Proportions.
1805: John Dalton Law of Multiple Proportions.
1811: Amedeo Avogadro Avogadro’s Law
1865: Johann Loschmidt Approximates atomic size.
Evidence for Atoms…

5. Law of Definite Proportions
Compounds vs. Mixtures
Salt: % Na % Cl
Water: % H 89% O
Carbon: 27% C 73% O
Dioxide

6. “The Chemists of the 1800’s”
1794: Joseph Proust Law of Definite Proportions.
1805: John Dalton Law of Multiple Proportions.
1811: Amedeo Avogadro Avogadro’s Law
1865: Johann Loschmidt Approximates atomic size.
Evidence for Atoms…

7. Law of Multiple Proportions
Cu C O 5 : 1 : 4 10 : 1 : 4 5 : 1 : 8 5 : 2 : 4 10 : 1 : 8

8. Law of Multiple Proportions
Cu C O 5 : 1 : 4 Cu2 C O 5 : 1 : 8 5 : 2 : 4 10 : 1 : 8

9. Law of Multiple Proportions
Cu C O 5 : 1 : 4 Cu2 C O Cu C O2 5 : 2 : 4 10 : 1 : 8

10. Law of Multiple Proportions
Cu C O 5 : 1 : 4 Cu2 C O Cu C O2 Cu C2 O 10 : 1 : 8

11. Law of Multiple Proportions
Cu C O 5 : 1 : 4 Cu2 C O Cu C O2 Cu C2 O Cu2 C O2

12. Dalton’s Atomic Theory
Elements are made of extremely small particles called “atoms”.
Atoms of an element are identical in size, mass, etc. Atoms of different elements differ in size, mass, etc.
Atoms cannot be subdivided, created, or destroyed.
Atoms of different elements combine in simple whole-number ratios to form chemical compounds.
In chemical reactions, atoms are combined, separated, or rearranged.

13. “The Chemists of the 1800’s”
1794: Joseph Proust Law of Definite Proportions.
1805: John Dalton Law of Multiple Proportions.
1811: Amedeo Avogadro Avogadro’s Law
1865: Johann Loschmidt Approximates atomic size
Evidence for Atoms…

14. “The Chemists of the 1800’s”
1794: Joseph Proust Law of Definite Proportions.
1805: John Dalton Law of Multiple Proportions.
1811: Amedeo Avogadro Avogadro’s Law
1865: Johann Loschmidt Approximates atomic size
rA ≈ 1 x1010 meters
NA ≈ 6.02 x1023 particles

15. Kinetic Theory 1738 – Daniel Bernoulli 1857 – Rudolph Clausius
1859 – J.C. Maxwell
1871 – Ludwig Boltzmann
1905 – Albert Einstein

16. Kinetic Theory 1738 – Daniel Bernoulli 1857 – Rudolph Clausius
1859 – J.C. Maxwell
1871 – Ludwig Boltzmann
1905 – Albert Einstein

17. Brownian Motion (1827)
Small particles, like pollen grains, were seen to exhibit a ‘random-walk’ behavior when immersed in water and studied through a microscope. The random collisions of energetic water molecules from all sides produced this motion.

18. Brownian Motion (1827)
Small particles, like pollen grains, were seen to exhibit a
‘random-walk’ behavior when immersed in water and studied through a microscope. The random collisions of energetic water molecules from all sides produced this motion.

19. Brownian Motion (1827)
Einstein’s July 18, 1905 paper – "On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat” As the name implies – this paper showed mathematically that atomic kinetic theory produces the observed phenomenon of Brownian motion.

20. Kinetic Theory 1738 – Daniel Bernoulli 1857 – Rudolph Clausius
1859 – J.C. Maxwell
1871 – Ludwig Boltzmann
1905 – Albert Einstein

21. Kinetic Theory
Gases contain a vast number (N) of particles moving at random velocities.
Gas particles are sufficiently far apart that they don’t exert significant forces upon one another.
Gas particles follow classical Newtonian laws of motion and interaction.
Gas particles collide in a perfectly elastic fashion with no loss of kinetic energy.

22. Kinetic Theory
Gases contain a vast number (N) of particles moving at random velocities.
Gas particles are sufficiently far apart that they don’t exert significant forces upon one another.
Gas particles follow classical Newtonian laws of motion and interaction.
Gas particles collide in a perfectly elastic fashion with no loss of kinetic energy.

23. Kinetic Theory
Gases contain a vast number (N) of particles moving at random velocities.
Gas particles are sufficiently far apart that they don’t exert significant forces upon one another.
Gas particles follow classical Newtonian laws of motion and interaction.
Gas particles collide in a perfectly elastic fashion with no loss of kinetic energy.

24. Kinetic Theory
Gases contain a vast number (N) of particles moving at random velocities.
Gas particles are sufficiently far apart that they don’t exert significant forces upon one another.
Gas particles follow classical Newtonian laws of motion and interaction.
Gas particles collide in a perfectly elastic fashion with no loss of kinetic energy.

25. Kinetic Theory Avogadro’s Law V ~ N Boyle’s Law V ~ 1/P
Charles’ Law V ~ T
Gay-Lussac’s Law P ~ T
Kinetic theory correctly leads to the observed characteristics of gases as described in the above gas laws
- and –
it provides a physical basis for the quantity of “temperature”.

26. Kinetic Theory Avogadro’s Law V ~ N Boyle’s Law V ~ 1/P
Charles’ Law V ~ T
Gay-Lussac’s Law P ~ T
Kinetic theory correctly leads to the observed characteristics of gases as described in the above gas laws
- and –
it provides a physical basis for the quantity of “temperature”.

27. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

28. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

29. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

30. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

31. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

32. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

33. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

34. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

35. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

36. Kinetic Theory Avogadro’s Law
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
Avogadro’s Law

37. Kinetic Theory Boyle’s Law
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
Boyle’s Law

38. Kinetic Theory Charles’ Law
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
Charles’ Law

39. Kinetic Theory Gay-Lussac’s Law
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
Gay-Lussac’s Law

40. Kinetic Theory
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T

41. Kinetic Theory KE = 3/2 k T ½ mv2 = 3/2 k T v = √ (3 k T / m)
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
KE = 3/2 k T
½ mv2 = 3/2 k T
v = √ (3 k T / m)

42. Kinetic Theory KE = 3/2 k T ½ mv2 = 3/2 k T v = √ (3 k T / m)
f = ma f = mΔv/Δt f Δt = mΔv f (2L/v) = m(2v) f L = 2 (½ mv2) f L = 2 (KE) F L = (1/3 N) 2 (KE) F L = (2/3 N) (KE) (F/A) (L A) = (2/3 N) (KE) P V = (2/3 N) (KE)  KE = C T P V = (2/3 N) (C T) P V = N k T  k = 2/3 C k = 2/3 (KE/T) KE = 3/2 k T
KE = 3/2 k T
½ mv2 = 3/2 k T
v = √ (3 k T / m)
Boltzmann’s Constant :
k = 1.38 x10-23 m2kg/s2K

43. PV = NkT KEave = 3/2 kT vrms = 3 kT
Kinetic Theory
PV = NkT KEave = 3/2 kT vrms = 3 kT m
Boltzmann’s Constant :
k = 1.38 x10-23 m2kg/s2K

45. Atom
Consider ,000,000,000,000,000,000,000 atoms of lead… could you lift it?
Consider one mole of M&M’s… what would that look like?

46. Mendeleev’s Table : 1869
In 1863 there were 56 known elements… and the number was growing by the year… there was a clear need to discover some organization among them.