Boon Cume Flashcards
Henderson-Hasselbach
pH = pKa + log([A-]/[HA])
All terms
pH is pH of solution ( unitless log concentration of H+ in aqeous solution (estimate of buffer solution))
pKa is pKa of our acid in question - acid dissociation constant of acid (unitless)
[A] is concentration fo conjugate base (concentration needs to be same as HA but typically M)
[HA] is concentration of acid - concentration M
Importance: allows a quick way to determine pH of weak acid solution - derived from Ka
also allows us to quickly make buffers of certain pH’s or determine how to make a solution of a certain pH with a weak acid or base
Nernst Equation
E cell = E(naught)cell -(RT/nf)ln(Q)
E cell - is potential of a cell at non standard conditions (V)
E naught cell is potential of cell at standard state conditions
R is the ideal gas constant - will change with units standard 8.314 - J/(mol *K)
T is temperature in Kelving
n is # of moles of electrons in balanced equations (transferred in redox) - unitless
F is Faradays constant (95,458.56 C/mol or 96,000)
Q reactant quotient or products/reactants - unitless? or has units depending on rate
Used for determining electrical cell potential under non standard conditions
Also relates our thermodynamic equations to our cell potential equations G = -RTln(K) - there are 2 others
Ohms Law
V = IR
Voltage (in V)
I is current (in amps)
R is resistance (in ohms)
Very fundamental relationship in electronics movement of electrons
Current through conductor proportional to voltage across two points
Thermal Noise in a resistor
Vrms = ROOT(4Kb * T * R * DELTA(F))
Vrms= root mean square noise voltage in V
Kb is Boltzmann constant – 1.38E-23 which is J/K)
T is temp in kelvin
R – Resistance of Element (ohms)
Delta F – is Frequency Bandwidth (Hz)
Signifigance: Thermal Johnson Noise – refers to the noise of thermal agitation of electrons in circuits – As such only disappears at absolute 0 and is a constant baseline noise -important in instrument detector readout. Frequency independent
An application – can reduce our noise by lowering temperature, reducing resistance, narrowing the bandwidth of electronic components of our detector
Biomolecular Reaction Rate
r = k[A][B] for A+B -> P
R = reaction rate (M/s)
K = reaction rate constant (2nd order so 1 /(M*s))
[A] and [B] are the concentration of reactants in Molarity
Signfigance – describes rate of chem reaction
Upper limit defined by frequency of collisions (eg limited by diffusion)
Arrhenius Equation
k = Ae^(-Ea / RT)
K is the rate constant – depends on rate order (1/s for first order?)
A is pre-exponential factor which can be broken down into frequency factor and orientation – also 1/s)
Ea is activation energy (J/mol)
R is gas constant 8.314 – J/(Kmol)
T is temp in kelvin
Signifigance: important factors that determine the rate of equationa dn show how we can manipulate the conditions to increase our rate (eg increase temperature)- also allows us to specifically calculate activation energy
Half lfie for first order reaction
t(1/2) = ln(2)/k
T ½ is the half life in seconds
K is the reaction rate (so first order 1/s)
Important because is an easy equation to get the half life of a reaction
Derived from first order rate equation
Half life time it takes to reach ½ fvalue (of reactant)
Fick’s Law of Diffusion 2 of them
1st)
J = -D(dn/dx)
2nd law )
dn/dt = D (LAPLACE(n(x,t)))
J is diffusion flux (m^2 * s)
D is diffusion coefficient (m^2/s)
N is concentration (mol/m^3)
X is position (m)
Delta here is laplace operator
T is time (s)
Signifigance: 1st law describes diffusion of a mixture in solution (from high to low concentration with magnitude proportional to concentration gradient)
2nd law – predicts how diffusion changes over time – using a partial differential equation . Used to model transport
Snell’s Law
nsin(theta) = nsin(theta)
N is the refractive index of a medium (unitless)
Theta is an angle between llight and normal (degrees)
Describe refraction of light moving through different media
Important in microscopy and spectroscopy
Indices = to reciprocal of phase velocities (so n2/n1 = v1/v2)
FRET efficiency
E = 1/(1 + r /Ro)^6)
E – efficiency – unitless
R – donor to acceptor distance (nm)
Ro = Forster distance (distance at which energy transfer efficiency is 50% related to overlap of donor and acceptor emission spectrums and molecular orientation – in nm)
Quantum yield of energy transfer – Efficiency dramatically decreases as afunction of distance (we see to the 6th power)
Important for describing molecular chromophores – useful for bio and chemical sensors
Energy of Molecular Vibration eg energy spacing
E = h(n+ ½)v
E is energy at specified state (j)
H is plancks constant (6.626 E-34) Js
N is quantum number (unitless)
V is frequency (1/s)
This approximates molecular energy fo a vibrational state when using a simple harmonic oscillator approximation
Useful in molecular spectroscopy for interpreting spectra
Van Deemter
HETP = a + B /u+ c*u
HETP is height in theoretical plates (it’s a number of plates – related to resolution – is mm)
A is eddy diffusion term – (multi path effect) in mm
B is Band Broadening term – longitudinal diffusion (as something goes through a path it naturally spreads out in mm
C is mass transfer (the peak broadening that occurs as something moves across phases) in mm (diffusion into MP pores)
U is linear velocity (mm/s)
Signifigances – used to demonstrate efficiency for chraomtography columsna nd used to make them more efficient
Relates plate height to velocity of mobile phase by considering aspects of diffusion during separation – can be used to minimize HETP to maximize resolution
Equation relating Gibbs free energy to Equillibrium constant
Delta G(naught) = -RTln(K)
Gibbs free energy at standard state (kj/mol)
Gas constant (8.314 – J/mol*K)
Temperature, Kelvin
And K – equilibrium constant (depends on rate)
Relates gibbs free energy to our equilibrium constant
Equation relating Gibbs free energy to standard state potential of cell
Delta G = -nfE(naught)cell
G is gibbs free energy kJ/mol
N is moles of electorns transferred in balanced equation
F is faradays constant (96,000) C/mol)
E cell – is potential at standard state (V)
Relates gibbs free energy to an voltaic cell
Gibbs free energy equation
G = H TS
note (delta G, H and S)
Change in Gibbs free energy (kj/mOl)
= change in enthalpy (kj/mol)
- Temperature (Kelvin)
- Times Entropy (J/mol)
Very fundamental key equation relating gibbs free energy to enthalpy and entropy – demonstrates the energy available in a system to do work and what that depends on and how we can manipulate that by manipulating H or entropy.
Also can indicate spontaneity of a reaction (gibbs free energy <0)
Strength of electric field
E = F/q
E being strenght of electric field in N/C or volts/m
F being force exerted on an ion - force in Newtons
and q being the charge of the ion - charge in Coulombs
Lorentz Force Law
F = qE + qvxB
E being strenght of electric field in N/C or volts/m
F being force exerted on an ion - force in Newtons
and q being the charge of the ion - charge in Coulombs
v is velocity m/s
B is magnetic field in T
note vxB is the cross product
can also be qvbsin(phi)
with phi beingthe angle between v and B
Ohms Law
V = IR
Voltage (in V)
I is current (in amps)
R is resistance (in ohms)
Very fundamental relationship in electronics movement of electrons
Current through conductor proportional to voltage across two points
Light equation
c = Lambda * frequency
c being m/s
Lambda being m and frequency being 1/s
(can also have waveneumber - recipricol of wavelength
Energy of electromagnetic radiation
E = hv = hc/lambda = hwavenumber
E is energy in joules
wavelength in nm m etc
frequency 1/s (or wavenumber 1m
c is speed olight m/s
h is plancsk constant 6.634 E - 34 JS
Apparent Transmittance
(P + S)/ (P0 +S)
with P being radiation power exiting sample
P0 being initial radiation
and S being stray light
all unitless
important because transmittance and absorption key for spectrochem
Intensity of Phosphorescence/Fluorescence
Ip = 2.303 * k * phi(p) * (epsilon) *b * C *P(naught) = k’ * P(naught)
Note this is the same s fluorescent or the other equation but just has a k as well
phi(p) is the phosphorescent quantum yield (the fraction of exicited state molecules that return to ground state through phosphorescence (0-1)
k is a constant that accounts for efficiency in collecting and detecting emissions
C is concentration (M)
erpsilon is molar absorptivity (1/cm*M)
b is path length (cm)
P0 is the inital radiation pre sample
k’ is a constant that combines the other constants to simplify the equation
Note fluroescence equation is the same
Turbideemetry equation
T = It/Io
-log(T = kbC - same idea as a beers law
LOD expressions
3.3 * Sa/b)
LOQ = 10 *Sa/b
S being standard deviation of response or a blank
and b being the slope of the regression line
importance in being a standard way LOD and LOQ is made when describing a method and circumscribing its capabilites
Diffraction grating equation
n* lambda = d(sin (theta) + sin(phi)
n is diffraction # /order
lambda is wavelength (in meters)
d is distance between slit centers
theta and phi are angles (angle of invidence and angle of diffraction)
This equation is key for showing constructive interference key for onstructing the grating on a UV vis
UV vis beers law for multicomponent
A = e1c1l + e2c2+l …
absorbance unitless
e is molar absorptivity 1/Mcm
l ispath legnth in cm
c is concentration 1 , 2 denote number of spcies
Definition of Current
Q = IT
q is charge coulomb
I is current =- amps
T is time - second
Power equation
P = EI
power in watts = E emf in volts
I is current in amps
Work equation
W = Fd
typically work = force * displacement
for electric field 2 equations
one F = qE
also Ed = delta V
we sub in
we get Fd / q = delta V
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html
On left its typically newton *m /C
Response Factor equation
A/Ac = F*(S/Cs)
A is signal of analyte
S is signal of standard
c is the concentration of each
F is response factor
Signal unitless? Depends on detector (volts?)
Concentration Moles
And F is the response factor –
Important because shows how with a standard we can show how the concentration and signal correlate and then use that to find the concentration of an unknown
Standard Addition Equation
Xi/(Sf + Xf) = Ix /(Is+x)
Xi is initial concentration
Xf is concentration of aalyte plus standard (S) in final solution
And I is signal from initial divided by signal from final
Important because useful for getting concentration where developing an external calibration curve in a blank matrix isn’t possible/feasible
Entropy change
S = qrev/T
entropy = heat divided by temp
S is entropy J/K
q rev is heat lost - Joules
Temp is Kelvin
Ionic Strength
u = 1/2(cz1^2 + c2z2^2…)
u is oinic strength (M)
C is concentration (M)
z is charge (unitless)
useful for getting total ionic charge to predict solution
Extended Debye Huckel
log(y) = -0.51 * z^2 * ROOT(u) / (1 + (alpha * ROOT(u)*305))
y is gamma - activitiy coefficient - unitless
z is charge - coulomb
u is ionic strength (M)
alpha is size in picometer (size of ion)
u is ionic strength
Davies equation
log (y) = -.51*z^2 (( ROOT(u) / (1 + ROOT(U)) - 0.3 U))
y is gamma - activitiy coefficient - unitless
z is charge - coulomb
u is ionic strength (M)
u is ionic strength
debye huckel but dont know the size - more general
Relationship between charge and moles
q = nNF
q is coulombs
n is unit charge per molecule
N is moles
F is coulombs/mole (Faradays)
Relation between free energy and electric potential difference (no cell)
delta G = -nNF*E
deltaG is Joules
n is units of charge per molecule
N is moles
F is C/mol
E is volts
Electric potential for ion selective electrode
E = constant + (0.05916/n ) * log(A)
(can also be 2.03RT/nf)
E is potential (V)
N is charge of analyte iopn - coulomb
Ao is activity in the outer unknown solution(unitless)
Moles reacted equation (current and time)
Moles reacted = (It) / (nF)
I is amps, t is time, n is # of moels of electrons and F is faradays (COulomb/Mole)
Ecell equation
E = E(cathode) - E(anode) - IR - overpotential
E is voltage - potential
IR is amps and ohms for current and resistance (voltage needed to overcome electrical resistance
overpotential is the difference between actual and theoretical
Cyclic Volttametry - difference between andoe adn cathode wave peaks
Epa -Epc = 2.22RT/nF = 57/n
so Epa and Epc are the peaks of the anode and cathode
R is gas constant 8.314 J/mol*K
T is temp in kelvin
n is moles of electrons tranaferred
F is faradys COulombs/mole
Peak current for reversible reaction in cyclic voltammetry
Ipc = 2.69E5 * (n^3/2) * AC(D^1/2) * v^1/2
n is numebr of electrons in half reaction
A is area of electrode (m^2
C is concentration M
D is diffusion coefficient m^2/s
v is sweep rate (V/s
Scatchard Equation
(Delta(A))/[X] = K* (delta(epsilon)) P(naught) - K (delta(A))
delta A is change in absorbance - unitless
X is concentration M
P is initial concentration of Protein
K is equillibrium constan t(depends on rate (1/Ms)
epsilon is molar absorptivitiy (1/Mcm)
Produces a plot of bidning antigen to antibody (X to P)
Can give equilibrium expression for binding
From absorbance measurements
Stern Volmer Equation
phi(naught) / phi(Q) = (k(e) + k(d) + k(q)[Q])/(k(e) + k(d)) = 1 + ( (k(q))/(k(e) + k(d))[Q]
phi naught is photons emitted per second/photons absorbed per second (or emission rate)
phi naught is the quantum yield (numebr between 0 and 1 ratio of emission obver absorption with NO quencher
phi Q is that same rate (quantum yield) with a quencher
Ke is rate constant for emission 1/Ms
Kd is rate of deactivation (1/Ms)
Kq is the quenching constant (1/M^2s))
Q is concentration of quencehr
Signifigance – this si the setup of a luminescnece experiment where it is done with and without a quencherand the relative emission as a function of quencher concentration and plot against [Q}plot – should observe a straight line –
Somewhat similar to absorbance/transmission (in that there Io and I)
Relative Efficiency of Grating
E grating / E mirror
E(grating) is irradiance at particular wavelength diffracted in the order of interest, n
And E(mirror) is irradiance at same wavelength that would be reflected by a mirror with the same coating as the grating
Interferogram Equation
maybe look at
I(o) = B(v)cos (2*pi (o) / Lambda)) = Bv * cos (2 *pi *v * o)
note o is retardatation (difference in pathlength of two waves in an FTIR
v is wavelnumber (1/frequency)
I is intensity of light reaching detector
B(v) is a constant
plotted against v - as v (wavenumber) changes to produce our spectra
Equation for constructive interference for monochromator
n*lambda = a-b
n is diffraction order
lambda is wavelength (m)
a-b is difference in pathlength (m)
Signifigance – is that we get fully concstrutive interference when the difference in pathlength is an integral multiple of the wavelength of light – gives guidance on how to construct the grating
Resoljtion of grating
Lambda/(delta Lambda) = n * N
lambda is wavelength
n is diffraction 3
and N is number of grooves in grating that are illuminated (essentially groove width by light width)
Lets you know the resolution necessary based on physical dimensions of the grating
Dispersion of Grating
Delta Phi / Delta Lambda = n/(dcos (phi)
phi is angle of diffraction
lambda is wavelength (m)
n is diffraction order
d is distance between grooves (nm)
and phi is diffraction angle
Dispersion measures the ability to separate wavelengths differing by delta lambda, through difference in angle as opposed to grating as above
So they both go up with smaller groove spacing
Again good for construction
Boltzmann equation
N/N(naught) = (g/g(naught))(e^-(deltaE)/kT))
N/Nnaught is relative population of two states
g and g0 is the number of states at each energy (degneracy
Delta E is the energy difference between the two energy levels (J)
K is boltzman constant J/K
1.381E-23
The Boltzmann distribution describes the relative populations of different states at
thermal equilibrium. If equilibrium exists (which is not true in the blue cone of a flame but is
probably true above the blue cone), the relative population (N*/N0) of any two states
Heisenberg Uncertaint principle
(o)E(o)t >= h/4pi
First term (oE) – is uncertainty in the energy difference between ground and excited states
oT is life time of excited state before it decays (s?) to ground state
h is plancks constant J*s
Gives us arelationships between time and the energy uncertainty
The shorter the liftem of excited state – the more uncertain its energy
Doppler Linewidth
(o)lambda = Lambda(7E-7)ROOT(T/M)
T is temp in kelvin
M is mass in daltons
Signifigiance – Shows a mechanism of linebroadiening in atomic scteroscopy
important because need to account for in a beam of ions/atoms etc instrument design (focusing)
equation to determine how interferogram is sampled
(o) = 1/2 *v)
(o) is retardation and v is wavenumber
covering a range of wavenumber requires sampling the interferogram at retardation intervals based on the wavenumber
FTIR resolution
(1/(delta)) cm^-1
with delta being max retardation
Entropy to microstates
S = kb*ln(ohm)
S is entropy j/K
Kb is 1.3E-23 J/K
And ohm is # of microstates
Importances – helps determine entropy shows what contributes to it
Enthalpy equation
H = U + PV
Enthalpy kj/mol
PV is pressure *volume (Liter atmosphere)
U is internal energy (kj?)
Chemical potential equation
ui = uio + RTln(alpha)
Chemical potential i
Uio is the standard state chem pot (J/mol)
RT is gas phase 8.14 J/Mol*K
T is temp in K
And alpha is activity
Has 2 terms enthalpy (thermodynamic affinity)and entropy
Capacity factor
k and k’
moles in stationary/moles in mobile phase
vs
moles in mobile phase/moles in stationary
Distribution partition coefficient
Kc = [As]/[Am]
Fundmanetal quantity effecting chromatography
Alpha Selectivity factor
Kb/Ka
Retention or apactiy factor of one compound compared to another (can also be tr’b/tr’a)
Number of theoretical plates
N = (tr/stdev)^2
4*stdev = W
2.35 *stdev = W1/2
so can sub to get
N = 16(tr/W)^2
N= 5.54(tr/W1/2)^2
N is number of plates
tr is time in seconds
stdev is also in seconds?
W is also seconds?
H = L/N (H being Height equivalent to Theoretical Plate HETP)
L is length of column (mm) (or H as total bed height in mm)
N is number of plates (unitless)
Chromatographic resolution
R = 2 * (tr1 – tr2)/(w1+w2)
R is resolution (unitless)
Tr is retention time – seconds
W is width of peaks (s)
Gives a formula for resolution – which is ke – later eluting peaks broader due to more diffusion – trade off in time and resolution
Longer time givs better separaten of peaks
Instead otr it can be X or Z
Purnell
Rs = (Root(N)/4) * (alpha - 1 / alpha) * (k2 / (1+K2))
Rs is resolution – unitless
N is Number of theoretical plates – unitless
Alpha – is relative retention (selectivity factor)
K2 is capacity factor of analyte 2
All unitless
Demonstrates the 3 terms that effect resolution
# of plate (efficiencys, selectivity and capacity factor
Hagen Pouseuille
Vavg = r^2 *delta P / 8&Ln)
Delta P is pressure drop across a tube
N is solvent viscosity
L is tube length
R is tube radius
And vavg
Importance because shows a similar relation of pressure drop to the flow rate /or velocity of our fluid flowing through as related to viscosity!
Pressure: Pascals
Viscosity – Newton *s / (m^2) or Pascal second
Tube length – cm
Tube radius – cm
V avg/ cm/s
Einsteins diffusion
(stdev^2) = 2D*t
stdev is m
D is diffusion - m^2 / s
t is time in seconds
Average displacement in random walk
x = Nl(2q-1)
x is average displacement (meters)
N is # of passes or moves (iunitless)
l is length of move (m)
and q is probability of moving in a specific direction (2d random walk)
Stokes law/drag
F = 6(pi)nR*v
F is the stokes drag (Newtons)
N is frction Pascal – seconds
R is radius of spherical object (m)
V is velocity (m/s)In fluid dynamics, Stokes’ law is an empirical law for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid.[1]
Einstein relation (einstein stokes)
Dmobility = KbT
* D is the diffusion coefficient;
* μ is the “mobility”, or the ratio of the particle’s terminal drift velocity to an applied force, μ = vd/F; - note the stokes drag coefficient has units of m/t (and is only multiplied by velocity to get friction
* kB is the Boltzmann constant;
* T is the absolute temperature.
Signifigance can solve for diffusion coefficient and determine how something diffuses
can also get the radius of the particle
Plate number approximation for LC column
N = 3000 * L / dp
N is numebr of plates
L in cm
and dp in um
quick way to get N for LC column
Zengs fluroescence
F = Iphi (1-10 ^ - epsioldon * dC) = 2.303 Iphiepsilondc)
F fluorescence intensity
I is intensity of excitation light
Phi is quantum yoeld
Epsilon is molar absorptivity
D is optical path length
C is concentration
F also = kIC
K is constant
I is excitation light intensity
C is concentration
Mean Free Path
L = kT /( (root(2) * p * sigma)
L is mean free path in meters
k is boltzman constant 1.3E-23 (J/K)
Temp is K
p is pressure (pascals)
sigma is ccs which is m^2 (area pid^2 where d is the sum of radii of colliding molecule and ion
Mach disk equation
Xm / D = 0.67 * ROOT( P0 /P)
Xm is lcoation of match disk
D is nozzle diameter
P0 =Pressure on high side
P is pressure on low side
charge state deconvolution MASS SPEC
M2 = (M+n1 – 1) / (n1-1)
Radial force on ions in a beam (repulsion)
F = eIo / (2pi * epsilon * v *r) = e * E
E is radial electric field (V)
R is radius (m)
Velocity (m/s)
Io is initial current (amps
Epsilon is vacuum permittivity (farad/m)
LIOUvilles Theorem
X1alpha1v1 = x2alpha2v2
Signifigance shows how to adjust angle to foxues things – so can accelerate x is position
Alpha is angle
And v is velocity
We want x to be smaller
TOF resolution
m/deltaM = t/(2delta*t)
signfigiance a change in time is 2x the change in mass
Barber’s Rule
Magnetic sectors entry and ecit needs to be obeyed
alpha + beta _ gamma need to equal 180
Kinetic Energy Electric sector
r = 2 Ek / qE
radius = radius of centirfugal force - m
Ek is electric field N/C
q E is the other electric field CN?c
REsolution of magentic sectior
2dr/r = dm/mm
but also (r/s1 + s2)
which is dr change in radius
to change in mass(change in radius relates to slit with
Quadrupole equation a
a is a mathieu term
a = 8eUm^r^2*Ohm^2
e is charge
U is strength of electric field V
m is mass
r is inscribed radius m
and drive is frequency 2 pi * f (or hz)
Secular frequency equation
W = (n + 1/2 * Beta) * ohm
where n is a term between 0 and infinity
Beta is a term based of a and q (Beta = ROOT(a + q^ 2 /2 ))
Note ohm is trapping frequency in hertz0
3d trap q and a
same as the other but multiply by 2 and inscribed radius becomes r^2 + 2z^2
Cyclotron Frequency FTICR
Angular frequency = z * e * B /m
angular frequency being frequency radians
z being # of charge
e being charge of electron
z and e can be reduced to q - just overall charge - Coulombs
B strength of magnet - Tesla
divided by m mass
Resolving power Mass spec
m/(delta m)
Orbitrap equation
angular frequency = ROOT (k*z /m)
with angular frequency in radians
k being the force constant of the potential (N/m)
m and z being m over z
Shot noise
i = ROOT(2 eI* delta f)
e is charge of elcetorn1.6E-19 Coulombs
I is amp
delta f is bandwidth of frequency
output is vrms - voltage noise?
Beers
A = log (Io/I) = epsilon * l c
A is absorbance unitless
Io and I are intensity of light before sample and ith sample (transmitted vs that flight source)
molar absorptivity is 1/Mcm
l is path length - cm
and c is conc M
describes ATTENTUATION of light through material - basis to understand concentration in spectrochem measurements like UV vis
TOF mass analhysis
t = D/(SQRT(2U) * SQRT(m/q)
t is drift time in seconds
D is length fo flight tube
U is accelerating potential (V)
m is mass ofion kg
and q is charge of ion Coulomb
Describess flight in TOF shows trends like larger ions take longer
Drift velocity of ion in an electric field (ion mobility
v = KE
v is velocity of ion m/s
K is mobility of ion (m^2/(V*s)
E is electric field strength (V/m)
describes mobility in an electric field - stronger field makes for greater velocity - used for IM
Effect of s/n ratio by averaging
SNRf = SNRi *sqrt (n)
SNR is signal to noise ratio
n is # of averages
unitless
important because shows that can only increase s/n so much by averaging
Nuclear spin energy in mag field
E = -u*Bo = - gamma * m * h * Bo
E is energy of magnetic dipole (J)
u is magnetic dipole moment (j/T)
B is strenght of mag field Tesla
gamma is gyromagnetic ratio (unique to each nucleus)- Hz/T
m is magnetic quantum number unitless
H is reduced plankcs (Js)
significance:
magnetic nuclei absorb RF energy when placed in mag field and resonate at frequencies unique to each atom
in spin 1/2 nuclei , two energy levels exist that can be occupied- high and low
the amount ofenergy (frequency) required to induce a spin flip between the energy levels is whats measured during NMR
used in MRI and chem analysis
Magentic moment of Nucleus
u = y I
u is mu y is gamma esque
y is the gyromagneti ratio (Hz/T)
I
Larmor frequency
omega = -y B0 (divided by 2 pi)?
omega is the larmor frequency (nculei in a magnetic field)
y is our gyromagnetic ratio (Hz/T)
sigma is
B is magnetic field
The frequency necessary fo r absorption to occur (NMR
v = gamma B / 2pi
v is the frequency of the particle
hz
h is plancsk Js 6.6E-34
B is magnet Tesla
gamma is gyromagnetic Hz/T
Integrated rate law first order
ln (Ao / At) = kt
for first order kA
relates concentration over time to rate constant
so concentration M
and rate is 1/M*s
t is seconds
Integrated rate law first order
ln (Ao / At) = kt
for first order kA
relates concentration over time to rate constant
so concentration M
and rate is 1/M*s
t is seconds
2nd order half life
t 1/2 = 1/(k*[A0]
Integrated rate law for 0th order reaction
[At]-[A0] = -kt for k[A]^0 = k
k is 1/s
2nd order integrated rate law
1/[At] - 1/[A0] = kt
for k[A]^2
same thing and units but k is 1/(M^2*t)
Half life for 0th order equation
t 1/2 = [A0] / (2k)
2nd order integrated rate law
1/[At] - 1/[A0] = kt
for k[A]^2
same thing and units but k is 1/(M^2*t)
Half life for 0th order equation
t 1/2 = [A0] / (2k)
Integrated rate law first order
ln (Ao / At) = kt
for first order kA
relates concentration over time to rate constant
so concentration M
and rate is 1/M*s
t is seconds
Randles Sevcik equation - note this is the same as the other peak current equation I have except that is at 25 C
In cyclic voltammetry relates the scan rate to peak current (increases with increases scan rate especially as current relates to time)
I = ..4463*nFAC *ROOT( nFVd / RT)
or
I = 2.69 E5 * n^(3/2) * AC * ROOT(Dv)
n is electrons
F is faradays A is are of eletrode c is concentration
v is scan rate V/s
D is diffusion coefficient cm^2/s
Coulombs law
F = qq/(4piereor^2)
Force newtons
charge is couloms
er and eo are Fards/meter
er is relative premitivvity
and eo is vacuum permittivity
and r^2 is distance
