Equations, Electrochem, and Polymers

• E=hv

  E=energy

  h=Planck's Constant (6.63 x 10^-34 J/hertz

  v=frequency
• Faraday's Constant

  9.65*10^4 C*mol^-1
• A=3cl

  A=absolute absorbance

  3(actually flipped)=molar absorbance coefficent

  c=concentration

  l=pathlength
• %T=$I_t/I_0*$$100$


  %T=percent transmittance

  I(t)=intensity of transmitted light

  I(0)=transmitted light through reference

  Note: %T is proportional to absorbance NOT concentration
• Wavelength=$c/v$


  c=speed of light (3.0*10^8)

  v=frequency
• E=$E_0(cathode) - E_0(anode)$


  E=reduction potential of galvanic cell

  E(c)=reduction potential of the cathode

  E(a)=reduction potential of the anode
• e=F/L

  Calculating the charge of 1 election

  e=electron charge

  F=Faraday's Constant

  L=Avogadro's Number
• E=$E_0-RT/nF(ln[Ox]/[Red])$


  E=reduction potential of cell

  E_0=standard reduction potential

  R=gas constant 8.314 J/mol

  n=moles/number of electrons

  F=Faraday's Constant (9.65*10^4 C*mol^-1)

  [Ox] = Concentration of Anode or species being oxidized

  [Red] = Concentration of Cathode or species being reduced
• delta G = $-nFE^0$


  delta G=standard free energy change

  n=number/moles of electrons

  F=Faraday's Constant (9.65*10^4 C*mol^-1)

  E^0=standard reduction potential

  NoteL The more positive the cell potential=the greater tendency for the reaction to proceed to the right
• v- = $1/2pi c (sqrt(k/m)$


  v- = stretching frequency

  c=speed of light (3.0 *10^8 m/s)

  k=force constant

  m=mass average
• E=$E_0-0.0592/n(log[Ox]/[Red])$


  E=reduction potential

  E_0=standard reduction potential

  n=number of electrons

  [Ox] = concentration of anode or oxidative species

  [Red]=concentration of cathode or reductive species
• Number Average Molar Mass Mn=$sumNiMi/sumNi$


  Ni=number of chains/moles with molar mass Mi

  Mi = molar mass
• Mass Average Molar Mass Mw =$sumNiMi^2/NiMi$


  Mw=Mass average molar mass

  Ni=number of chains/moles at molar mass Mi

  Mi=molar mass
• Heterogeneity Index: $M_w/M_n$ 


  Mw= mass average

  Mn=number average molar mass
• I=$V/R$


  I=Current (Amps)

  V=Voltage (V)

  R=Resistance
• Don't forget about H in between methyl groups
• What orbitals are involved in a C-C bond?

  $sp^3$
• What orbitals are involved in C double bonded to C?

  p and sp^2
• What orbitals are involved in C triple bond to C?

  2p and sp
• The more positive the reduction potential, the more powerful the oxidant
• i_p=$kC_0sqrt(v)$


  i_p=peak current

  k=simple constant including square root of diffusion coefficient

  C0=concentration of bulk solution (mol/cm^3)

  v=scan rate
• Planck’s Constant

  6.63 x 10^-34
• The more positive the oxidant, the weaker the reductant species
• The more positive the reduction potential, the more powerful the oxidant
• $(C+1) +$$(N/2) - (H/2)$


  Double Bond Equivalence

  C= # of carbon atoms

  N = # of nitrogen atoms

  H = # of hydrogen atoms OR # of halogen atoms
• Nuclei with both p and n even (Charge and mass are even) have a spin of 0
• Nuclei with p and n odd have integral spin (Charge is odd but mass is even). Calculated by charge (oxidation number) minus mass
• Nuclei with odd mass have half integral spin
• The peak current increases linearly as a function of the squareroot of v.
• A=$log(I_0/I_t)$


  I_0= Intensity of light passed through reference

  I_t= Intensity of light passed
• $10^A=$$(I_0/I_t)$$=$$I_0/(I_0-I_a)$


  A= absolute absorbance (unitless)

  I_0= Intensity of light through reference

  I_t= Intensity of light transmitted

  I_a =Intensity of light absorbed
• delta E= yh/B0

  E= Energy of NMR spectrum

  y= Magnoyro Ration (y) = 2.68 x 10^8 s^-1 T^-1

  h = Reduced Planck's Constant (1.05 x 10^-34 J*s)

  B0=Boltzmann Constant (1.38 x 10^-23 J*K^-1)
• Aromatic Proton (NMR Spectrum)

  7-8
• Vinyl Protons

  5-6

  
  

  Note: Vinyl Protons are directly attached to a C-C DOUBLE bond
• Acetylenic Protons

  2.5
• Aldehyde Protons

  9-10
• Carboxylic Acid Protons

  12
• The peak current (Ipkc or Ipka) is directly related to the square root of scan rate (v)
• Wavelength=c/v

  c=speed of light

  v=frequency

  Note: because v- (stretching frequency) is reciprocal of wavelength,

  v- = v/c
• What IR band is a nitrile?

  2250 cm^1