59-320 Analytical Chemistry: Equation Sheet #1 Chapter 4

[Pages:3]59-320 Analytical Chemistry: Equation Sheet #1

Chapter 1

weight% = msolute ? 100% msolvent

volume% = Vsolute ? 100% Vsolvent

Chapter 4 mean xi

x= i n

standard deviation

(xi - x )2

s =

i

n-1

relative standard deviation

s ? 100% x

ppm = msubstance ? 106 Vsample

ppb = msubstance ? 109 Vsample

M conc ? Vconc = M dil ? Vdil

Gaussian curve

y=

1 2

e-( x - ? )2 /2 2

Confidence interval = x ? ts n

t-test

Deviations from the

mean

z

=

x

-

?

x

- s

x

tcalc

=

|

x

- s

x

|

n

Paired t-test

tcalc

=

|d sd

|

n

Chapter 3

t-test: replicate measurements

tcalc

=

|

x1 - x2 spooled

|

n1n2 n1 + n2

spooled =

s12 (n1 - 1) + s22 (n2 - 1) n1 + n2 - 2

F-test

Fcalc

=

s12 s22

Grubbs test

Gcalculated

=

|

questionable s

value

-

x

|

Chapter 5

relative uncertainty = absolute uncertainty magnitude of measurement

per cent relative uncertainty = relative unceratinty ? 100%

Spikes

% recovery = Cspiked sample - Cunspiked sample ? 100% Cadded

Standard Additions

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

=

IX IS+X

[X]f

=

[

X

]i

V0 V

;

[S]f

=

[S

]i

VS V

Detection Limits signal detection limit: ydl = yblank + 3s

calibration line: ysample - yblank = m ? conc. detection limit = 3s m

[ ] IS+ X

V V0

=

IX

+

IX Xi

[

Si

]

VS V0

AX [X]

=

F

AS [S]

Chapter 6

Equilibria aA + bB cC + dD Thermodynamics G = H - T S

Acids and bases

K

=

[C]c[D]d [ A]a [ B]b

K = e- G0 / RT

KaiKb = Kw

Ka1iKb2 = Kw and Ka2 iKb1 = Kw

Chapter 7

Ionic strength

?

=

1 2

(c1z12

+

c2 z22

+ )

=

1 2

i

ci zi2

Activities

K

=

ACcADd AAaABb

=

[C]c

Cc [

D

]d

d D

[

A]a

a A

[

B]b

b B

extended Debye-H?ckel equation

log

=

-0.51z2 ? 1 + ( ? / 305)

pH and activities

pH

=

-

log

A H

+

=

- log[H+ ] H+

59-320 Analytical Chemistry: Equation Sheet #2 Chapter 8

Fraction of Dissociation

= x F

Henderson-Hasselbalch Equation

pH

=

pKa

+

log

[A- ] [HA]

pH

=

pKa

+

[B] log [BH+

]

Chapter 9

Polyprotic acids

[H+ ] =

K1K2F + K1Kw K1 + F

K1K2F K1 + F

K1K2F = F

K1K2

Fractional compositions

HA

=

[HA] F

=

[H+ ] [H+] + Ka

A-

=

[A- ] = F

Ka [H+] + Ka

pH

1 2

(pK1

+

pK2 )

Chapter 11

Fraction of EDTA

Y4-

=

[Y4- ] [H6Y2+ ] + [H5Y+ ] + [H4Y] + [H3Y- ] + [H2Y2- ] + [HY3- ] + [Y4- ]

=

[Y4- ] [EDTA]

Formation constant

Kf

=

[MYn-4 ] [Mn+ ][Y4- ]

Conditional formation constant

K

f

=

Kf Y4-

=

[MYn-4 ] [Mn+ ][EDTA]

In presence of complexing agent

K

f

=

K Zn2+ Y4- f

Fraction of uncomplexed metal

M

=

[M] M tot

=

[M]{1 +

[M] 1[L] + 2[L]2

+

...}

=

{1 +

1[L]

1 + 2[L]2

+

...}

Chapter 13

Basic Concepts in Electricity

q = niF

w = Eiq

I =q/t = E/R

59-320 Analytical Chemistry: Equation Sheet #3

G = -w = -Eiq = -nFE P = EiI

Nernst equation

Half

E

=

Eo

-

RT nF

ln

ABb AAa

=

Eo

-

0.05916 n

V

log

ABb AAa

Full

E = E+ + E-

Eo and K

Eo = 0.05916 V log K n

Chapter 14

E potential difference for I.S.E.

E = constant + 0.05916 n

log Ao

(volts at 25oC)

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