Chapter 1

weight% =msolute

msolvent

×100% volume% =VsoluteVsolvent

×100%

ppm =msubstance

Vsample×106 ppb = msubstance

Vsample×109

M conc ×Vconc = M dil ×Vdil

Chapter 3

relative uncertainty =absolute uncertainty

magnitude of measurement

per cent relative uncertainty = relative unceratinty × 100%

Chapter 4

x =xi

i∑n

s =(xi − x )2

i∑

n −1

sx×100%

mean standarddeviation

relative standarddeviation

y = 1σ 2π

e−(x−µ )2 /2σ 2 z = x − µ

σ≈x − xs

Gaussiancurve

Deviationsfrom the

mean

Confidence interval = x ± tsn

tcalc =| x1 − x2 |spooled

n1n2n1 + n2

spooled =s12 (n1 −1) + s2

2 (n2 −1)n1 + n2 − 2

t-test:replicate

measurements

tcalc =| d |sd

nPairedt-test

tcalc =| x − x |

snt-test

Fcalc =s12

s22F-test Grubbs

testGcalculated =

| questionable value − x |s

Chapter 5

Spikes

% recovery =Cspiked sample − Cunspiked sample

Cadded

×100%

Detection Limits

signal detection limit: ydl = yblank + 3s

calibration line: ysample − yblank = m × conc.

detection limit = 3sm

Standard Additions

[X]i[S] f + [X] f

=IXIS+X

[X] f = [X]iV0

V⎛⎝⎜

⎞⎠⎟

; [S] f = [S]iVSV

⎛⎝⎜

⎞⎠⎟

IS+XVV0

⎛⎝⎜

⎞⎠⎟= IX +

IXXi[ ][Si ]

VSV0

⎛⎝⎜

⎞⎠⎟

AX[X]

= F AS[S]

⎛⎝⎜

⎞⎠⎟

59-320 Analytical Chemistry: Equation Sheet #1

59-320 Analytical Chemistry: Equation Sheet #2Chapter 6

aA + bB cC + dD K =[C]c[D]d

[A]a[B]b

ΔG = ΔH − TΔS K = e−ΔG0 /RT

Equilibria

Thermodynamics

Ka iKb = Kw

Ka1iKb2 = Kw and Ka2 iKb1 = Kw

Chapter 7

µ =

12(c1z1

2 + c2z22 +) = 1

2cizi

2

i∑

Acids and bases

Ionic strength

K =

ACcAD

d

AAaAB

b =[C]cγ C

c [D]dγ Dd

[A]aγ Aa [B]bγ B

b

Activities

logγ =−0.51z2 µ

1+ (α µ / 305)

extended Debye-Hückel equation

pH = − logAH+ = − log[H+]γ H+pH and activities

Chapter 8

α =xF

Fraction of Dissociation

pH = pKa + log[A− ][HA]

pH = pKa + log[B][BH+ ]

Henderson-Hasselbalch Equation

Chapter 9

[H+ ] = K1K2F + K1Kw

K1 + F≈

K1K2FK1 + F

≈K1K2FF

= K1K2 pH ≈12(pK1 + pK2 )

Polyprotic acids

Fractional compositions

αHA =[HA]F

=[H+]

[H+]+ Ka

αA− =[A− ]F

=Ka

[H+]+ Ka

Chapter 11

αY4- =[Y4- ]

[H6Y2+ ]+ [H5Y

+ ]+ [H4Y]+ [H3Y− ]+ [H2Y

2− ]+ [HY3− ]+ [Y4- ]=

[Y4- ][EDTA]

Fraction of EDTA

Formation constant

Kf =[MYn−4 ][Mn+ ][Y4- ]

Kf′ = KfαY4- =

[MYn−4 ][Mn+ ][EDTA]

Conditional formation constant

αM =[M]Mtot

=[M]

[M]{1+ β1[L]+ β2[L]2 + ...}

=1

{1+ β1[L]+ β2[L]2 + ...}

Fraction of uncomplexed metal

In presence of complexing agent

Kf′′ = αZn2+αY4-Kf

59-320 Analytical Chemistry: Equation Sheet #3Chapter 13

Basic Concepts in Electricity

Nernst equation

q = niF w = Eiq ΔG = −w = −Eiq = −nFE

I = q / t = E / R P = EiI

E = Eo −

RTnF

ln ABb

AAa = Eo −

0.05916 Vn

log ABb

AAa

E = E+ + E−

Half

Full

Eo and K

Eo =0.05916 V

nlogK

Chapter 14

E = constant + 0.05916

nlogAo (volts at 25oC)

E potential difference for I.S.E.