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For Peer Review Only

Quantities, Units and Symbols in Physical Chemistry,3rd Edition

Journal:

Pure and Applied Chemistry

Manuscript ID: PAC-REC-05-11-10

Manuscript Type: Recommendation

Date Submitted by the

Author: 10-Nov-2005

Complete List of Authors: Quack, Martin; Eidgenössische Technische Hochschule Zürich,

Laboratorium für Physikalische Chemie

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! ,6+ 6- . ;, 1 ?

+1/;,!

"# ,3

V

,3

V

m

=

V /n

<#! )3 +!$'=

+3

H

+3

H

m

=

H/n

-++1- L,- ,6M ,+ , 1

,3 - ! 41 9: ++ - ;,

,1 6 .1 4 - , < =! , - +

+6! 11 . ;,6, -,63

;, 6 P ,6+ 6 1 -

1 1 7 - 6/,! < 6 11 - +

;, #! 3+!%&3 1 #! ! <=3 +!%*!=

-4 4 15 12 /3

++ !

"# 6+X3

6+X3

ε

W

a/c

< #!'3 ##3 +!"'=

1,3

κ

1,3 W

κ/c

< #! "3 +!'#=

2

43 4 ,1 6 !

&

(18)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

1,- + ;, 6 4 -4

·

×

1 ;, 64

a/b

or

a

b

64/ +1, -

a

1

b

1

3!/!

ab

1

"#

F

=

ma

3

p

=

nRT /V

1, <

/

= 6 ,1 .+ ,+ ,1

6/,!

"#

(

a/b

)

/c

=

a/

(

b/c

)

3

a/b/c

,/ 6 - -3 ,+ 4 4, ,+ /

7 +1 1

a/bc

+1

a/

(

bc

)

1

(

a/b

)

c

P

43 , + 6/, ,1 ,3 ,

1/.+ - 71

a/bcd

! ,3

a/b

+

c

+1

(

a/b

) +

c

1

a/

(

b

+

c

)

! /3 , -+ 11!

1,1 ;, - , 6 4 43 .+ <

×

=

,1 ,+ / 64 ,! @ +1, - , 4 4,

,+/ +6- 64 ,6!

"# W 7/

2

= 1

·

7/

·

2

3 7/

2

#

0,+,1-4+1/,-1

-- 6! - /,1 - + ,/ .3 6, ;,

+0 / 4,1- 6 0. 1;,! -4/ ,

11 + ,- -++/,+ !

! / , / , - <+/= - <,+/=- +?

1 !"!#3+!%1$! 3+! )" 61

+! , +1 11 " J%K 1

))) J&K31 >, J"K!

#! , 6 +/ + ;, 6 3 6,

6 +/ ,3 3 63 !

61,646+;,/

<, 6=D /1 , ;,3 63 6 / ,3 6, 6

! U3 1 11 ,/ 61?- <= -3 6,

6 ;,!

"# 7

h

W&!&#& )&('&<%#=

×

)

34

B !

01/ +

E

x

, E

y

,

1

E

z

!

- +

m

W#$ /W)!)#$ 7/!

'

(19)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

"! 6 , ++ ;, 6 - 6 F7 1

+63 ,/ , +,/ F7 !

"# @6

μ

,11 + ;,<,+6

1,1 = ,1 6 3 6, 4 ,1 +0. ,

, /3 /3 4 ,1 6 - ,3 <

+/+ %64=3,1 6!

$! ,63 163 <,+/=3 .101!

"# /,11 0 .1 -

2

, 11

. . .

<#

1

=

2

< 6

2

=

2

<"

1

=

1

< 6

1

=

1

3

X

3

>

1

3 1

. . .

<#

1

=

2

< 6

2

=

2

<"

1

=

2

3

a

1

1

3 +?

! ? 0/, 1 - 6Q ,

/,1 11D

. . .

<

2u

=

2

<

1g

=

4

3

X

1

1g

! 6

61 !

%! 6 - +1 6 ! 6 ,1

+ +4 ! <343 +/+*64- ,

- ?+,1 !=

"# 3 3 3 >3 >3 3 3 3 3 3 !!! - P - 3 + -

+3 - ,3 - ,3- ++3!

&! 6 - + ;, /3 .+ 4 - F7

+63 6, -;, ,++1 4 ,6+3 ,++

+ +- -, ;,! , 6 ,1 4

1+1/ 4 +!

"#

H

1 +3 6,

H

m

1 + < 6

- 3 1 - =!

C

p

1

C

V

1 +

+,

p

1 ,

V

3+ < 6,

p

1

V

=! + - / / 6 11

μ

Ar

μ

<=36,

+ -

i

+ ., 4,1611

μ

i

3

4

i

6, 61.!

'! 6 - + 4 ! ++ 6

Δ

123 - 0 3 1 - 0 12 < ,,=3

1 +

Σ

1

Π

- , 1 +1, /3 +! 6

<"! $ %*#

. . .

=3 <#!' ( #(

. . .

3 6 - , /=3 <;, - , =3

! 4 3 6 - +01 -, ,

log

</3 6=3

.+3 3 3 3-3 13 /13 3 ! +/1 1 1 +1/

6

- /13

∇×

- 31

∇·

- 1 +161- 1

! - 3 !/!

e

- /3 ,1

+ + ;,P-, 6 3 1/,-

+1/ 6!

"#

Δ

H

=

H

(final)

H

(initial)

P <1

p

G1

t

= ,1 - - / - +,P

x

,1 1 0 -

x

! >, - 1+1

+,1

F

-, -

t

/ 6 .+1 6

;,

F

=

F

0

exp(

δt

) sin(

ωt

)

4

δ

1 X < ,D

+G= 1

ω

/, -;, < ,D 1G=! , -

- + 0 -

x

3

x

3 6,

δ

-

1 X +1,

δt

! +1,

δt

1

ωt

6

13 6,161/, +<+W = 1 1

<1W =3+!

(

(20)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

(! -,1+4/11;,,65,

< ,/ 11 66= 1 ,1 1/4 6

! -,1 + ,1 ,/ 4 ,3 6,

/ 6! .+ 3

E

h

< "!*!#3 +!*%=!

43 3 U3 ,01 ,3 ,3 1 ,3

,3 6 /Q1 , 6 - > 1 1/ /

6!

"#

c

0

- +1 -/ ,,3

m

e

- 3

h

- 7

3

N

A

L

- /1 3

e

- /3

a

0

- > 1,3!

U W

e

·

U W !&)# '& %"< $=

×

)

19

B!

*! F7 ,1 /3 /3 ,3 1 6

,! ,1 6 <,+/=3 6 - +

;,! 1/ + - ,6, 1 3 //? ?

161//11+,131/,+,,?61

,3 1 61 1, +1,! 6

- 4 ?+,1 1/ ?

?3 !/!

O

?3

N

?3

S

?3 1

P

?! 6

H

1 11

111 1/! -J "K!

"# ?+ 1

??$?++.

6<

η

4

?#?1++? 3"?1= ,

?<=?

ω

?+< 3$?+=

? ?/,+

% ?1?" ?

N

?6Q1

O

? .

"

H

?+

+?#<

H

=?

*

(21)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

(22)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

-4/ 6 11 16- +

;, 7 6 ,1 6 ! , ;, 1 6 6 -,1

1 6 J$K 1 J%K!

,/ , - 6 4 - ;, 1,3

+11 10 1 - / , 11 + 3

1 0 , - 4 / -4 11 !

6 64 6 - 4 , ,/ 1 Q 8

+6! - 11 6 -6 16 +,

,3 ++ 6 11/ 1-/,6+ ,++3 6 ,

,++ 4 ! @ 1 ,65 6 +6 +- 3

- .+ 6/ ;,-/,6+ ,++34, 1,/ 6/,!

1+1 ,1 4 6 101! 5 1 - 11

6,1 6 +, -, 101!

6/16,65! 0,6/-;,3

116<=36-1036- ,<4,,+

,6,++0.3 "!&3 +!* =31 -! @4 6

113 ,1 + 6 ;, +63 1 6

1 +, +! ,1 +6 - / 12

;,! 10 / + - 10 +,+ 1

+P ,1 6 /11 ,-, - 10!

;,1+310/ , 1,1

J $K! -, 10 - + ;, + / 6 -,1 J %K

1 + J &K! 1 ;, 1 ,

, <"! )3+!*'=! , - 11131 . 64

63 +++! 6 ,1 101 4 6 <

1- ++= 1!

(23)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

(24)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

1 6 11 / 4 11 6

J$K 1 J%!63K!

, -* % ,

#. . /

+ 1

1 1

ρ

P

ϑ

P/ 3 3

+ + P

ϑ

P

ϕ

3 3

1

/Q1 1 !3!

i

<=

+ W#

x

Y

y

Y/

z

/

+6D

/

61

7 3

δ

1

1,

1

+ /

/ -

3

3

2

, '3

(

v

)

3

+/

α

3

β

3

γ

3

ϑ

3

ϕ

!!!

α

W

s

G

r

13 #

1/ 3<

ω

= W

A

G

r

2

3 #

3 1,

+1 W

/

, "

-;,

ν

3

ν

W G Q3

1

/, -;,

ω

ω

W#

ν

1

1

3

1

#3$

τ

3

τ

W

|

1G1 #

|

3

. 3

/,

ω

ω

W1

ϕ

G1 1

1

3

1

#3%

3 3 3 3

.

W1G1

1

+1 33 03 W

|

|

1

&

W1G1

2

'

< = 0 6 /11 +,1

n

13 4

n

,

+! 6

6 ,1 4 1 -, 4

Q/!

<#= , 1 <1= 1 1 <=3 - + / 1 1 / +3

11! - 1 <!! 1=3 6 ,11 .+

- 11 , -+++3 1-1 / 6!

<"=

N

,6- 1<+1=

t

!

<$= ,Q 6,1- /, -;,!

<%=/, 6 1 3

ω

ω

ω

!

<&= +1 -/ 1,1 6 ,!

<'= -- -6 ,1!

"

(25)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

1 6 11 / 4 11 6

J$K 1 J%!1K! 11 ;, 1 6,1, 6 -,1 J$3%!K!

, -* % ,

7/

1,1

μ

μ

=

m

1

m

2

/

(

m

1

+

m

2

)

7/

131

ρ

ρ

=

m/V

7/

3

1

d

d

=

ρ/ρ

,- 1

ρ

A

3

ρ

S

ρ

A

=

m/A

7/

2

+0 ,

v

v

=

V /m

= 1

3

7/

1

,

=

m

7/

1

/, ,

=

×

B #

-

I, J

I

=

i

m

i

r

2

i

7/

2

"

- W1 G1

t

=

m

--3 3

(

)

=

×

;,

/

E

B

+ /

E

3

V

3

E

=

·

1 B $

7 /

E

3

T

3

K

E

= (1

/

2)

mv

2

B

47

W

3

A

W

=

·

1 B

+4

P

P

=

·

W1

W

G1

t

@

/Q1 1

q

<=

/Q1 ,

p

<=

// -,

L

L

(

q,

q

˙

) =

T

(

q,

q

˙

)

V

(

q

)

B

-,

H

H

(

q, p

) =

i

p

i

q

˙

i

L

(

q,

q

˙

)

B

S

S

=

L

1

t

B %

+,

p,

(

P

)

p

=

F/A

3

2

,-

γ, σ

γ

=

1

W

G1

A

1

3B

2

4/

G,

(

W, P

)

G

=

mg

/

G

F

=

Gm

1

m

2

/r

2

2

7/

2

< = ,

ρ

=

ρ

<

2

3 $

=!

<#= 6, 1 , ++< #!&3 +!#%=!

<"= / % ;,D

I

αα

=

i

m

i

β

i

2

+

γ

i

2

3 1

I

αβ

=

i

m

i

α

i

β

i

-

α

=

β

3

4

α

3

β

3

γ

+,-

x

3

y

3

z

! ,,16,,+1

6 /!

<$= +7/3 + / 12 + /03 , /

6+1 10 /3 -

E

p

(

r

1

, r

2

) =

r

2

r

1

·

1

+64 ,++ 0

E

p

(

r

) =

r

·

1

<%= / // -,

L

34 ;,

p

1

q

H

1

t

< J 'K=!

$

(26)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

, -* % ,

σ

σ

=

F/A

&

τ

τ

=

F/A

&

3

ε, e

ε

= Δ

l/l

/

1,, -3

E

E

=

σ/ε

&

,/M 1,,

γ

γ

= Δ

x/d

&3'

1,,3

G

G

=

τ /γ

&

,6M1,,

, 3

ϑ

ϑ

= Δ

V /V

0

&

6,7

6,7 1,,3

K

K

=

V

0

(

1

p

G1

V

)

&

+ 1,,

3

η,

(

μ

)

τ

xz

=

η

(

1

v

x

G1

z

)

1

8,1

ϕ

ϕ

= 1

7/

1

7

ν

ν

=

η/ρ

2

1

1 --

μ,

(

f

)

F

=

μF

,1/ 8,.

P, P

P

=

1

E

G1

t

@

,-3

8

ρ

ρ

=

P

/P

0

(

6+

α

,

(

α

)

α

= 1

ρ

*

τ

τ

=

P

/P

0

(

1+

δ

δ

=

α

τ

<&= / 6 ;,!

<'=

d

164 1+16

Δ

x

!

<(=

P

0

1 ,1/ 8,.3

P

81 8,.1

P

1 8,.!

<*= 10 + , 1 12 - ,/ 13 4

6+- +1 , 1+-!

%

(27)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

$

1 6 11 / 4 11 6

J$K 1 J%!-K!

, -* % ,

,

I, i

, 1

,

I

=

·

n

1

2

#

/3

Q

Q

=

I

1

t

;,-

/1

ρ

ρ

=

Q/V

3

,- 1-/

σ

σ

=

Q/A

2

+

V, φ

V

=

1

W/

1

Q

U3B

1

+ 123

U

3

Δ

V,

Δ

φ

U

=

V

2

V

1

U

-

E,

E

=

(

/Q

)

·

1 U

(

E

mf

, E

MK

)

"

01/

=

/Q

=

−∇

V

U

1

8,.

=

·

eee

n

1 #

1+

∇ ·

=

ρ

2

+

C

C

=

Q/U

3 U

1

+

ε

=

ε

1

$

3

ε

0

ε

0

=

μ

1

0

c

2

0

1

%

+- ,,

+

ε

ε

=

ε/ε

0

&

1 +Q3

=

ε

0

2

+Q

< 1+

+,=

,+6

χ

χ

=

ε

1

+?,+6

χ

(2)

χ

(2)

=

ε

1

0

2

P/

E

2

B

1

3U

1

'

#1 +?,+6

χ

(3)

χ

(3)

=

ε

1

0

3

P/

E

3

2

2

B

2

3

2

U

2

'

< = ,

I

6;, A!

<#=

eee

n

1

A

- < 3+! "=!

<"= -1 6-/113

+ 12 - < $3+!')=!

<$=

ε

6 17 !

<%=

c

0

+1 - / ,,!

<&=;, 4-11 !

<'= +?,+6 X - ? .+ -

/,1

P

-1+Q+4-/,1

E

-01/D

P

=

ε

0

[

χ

(1)

E

+ (1

/

2)

χ

(2)

E

2

+ (1

/

6)

χ

(3)

E

3

+

· · ·

]

4

χ

(1)

,, ,+6

χ

3;,

ε

1

6 - / !

1, +

χ

(1)

3

χ

(2)

1

χ

(3)

- 7#3"1 $3+!

+ 1,<,;,1= - 4, 3

χ

(2)

Q6

! ;,Q11,4+Q6

α

1 +?+Q6

β

Q ,! /, + 1

&

(28)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

, -* % ,

1+

, μ

μ

μ

=

i

Q

i

i

(

/ 8,.13

=

Q

×

*

/ 1,

/ 8,.

=

·

n

1 @6 #

/ 01/3

∇ ×

=

1

/Q/01 /

+6

μ

W

μ

2

3

1

)

/ 3

μ

0

μ

0

= 4

×

10

7

1

1

+6 -,,

+6

μ

μ

=

μ/μ

0

/Q

=

0

1

</ 1+

+,=

/ ,+6

χ, κ,

(

χ

)

χ

=

μ

1

/ ,+6

χ

χ

=

V

χ

3

1

/ 1+

, μ

μ

μ

E

=

·

2

3B

1

R

R

=

U/I

Ω

#

1,

G

G

= 1

/R

#

/

δ

δ

=

ϕ

U

ϕ

I

1 "

X

X

= (

U/I

) sin

δ

Ω

+13

Z

Z

W

R

Y

X

Ω

<+. +1=

13

Y

Y

=

G

Z

<+. 1=

,+

B

Y

W

G

Y

B

ρ

=

ρ

Ω

$

1,

κ, γ, σ

=

κ

κ

κ

1

$3 %

-?1,

L

E

=

L

(

1

I/

1

t

)

3U

1

,, 1,

M, L

12

E

1

=

L

12

(

1

I

2

/

1

t

)

3U

1

/ +

=

∇ ×

@6

1

/

=

×

@

2

&

<'=<,1=1,- ,

V

,

V

m

α

=

ε

0

χ

V

α

m

=

ε

0

χ

V

m

<

&3+!#$ 1 #!'!#3+!$)=!

<(= @ 1+ +1 - 4 + /

Q

1

Q

+1 6 1

r

3

1 - 1+ 7 6- / + /! ++

,13 6, 6 1,/1! 1+ - 1+1

- /!

<*=;, ,1 61 L/ 01M!

< )=

μ

17 + !

< = 6

χ

,1 - / ,+63 6, ,1 6 1

/ ,+6!

< #= 4

R

= (

U/I

)

δ

31

G

=

R/

(

R

2

+

X

2

)

.

< "=

ϕ

I

1

ϕ

U

+ -, 1+ 12!

< $=;, + !

< %= /

γ

1

σ

36,

κ

!

< &=;, 1 /? !

'

(29)

For Peer Review Only

IUPAC GB3C 2005/OCT/26

1 6 - ;, ,1 ;,, 1 11

/ 4 11 6 J$K! 1 6 - ;, ,1

01 - ;,, 6 6 - , +

01! - ,1 6 +,61 6 J (KP

+ *3+! %%!

, -* % ,

,+

=

i

B

1

7 / +

T

T

=

(

2

/

2

m

)

2

B

+3

H

H

=

T

+

V

B

4-,3

, ψ, φ

=

<

3

/

2

= #3"

-,

1/?7

ψ

nlm

(

r, θ, φ

)

ψ

nlm

=

R

nl

(

r

)

Y

lm

(

θ, φ

)

<

3

/

2

= "

4-,

+

Y

lm

(

θ, φ

)

Y

lm

=

N

l

|

m

|

P

l

|

m

|

(cos

θ

)

e

i

$

-,

+661

P

P

=

ψ

ψ

<

3

= "3%

/1

ρ

ρ

=

eP

<

3

= "3%3 &

-

+66,

=

(i

/

2

m

)

×

<

2

1

= "

13

(

ψ

ψ

ψ

ψ

)

+668,.

, 1

=

e

<

2

= "3&

-

/ 1

τ

1

τ

=

1# 1 1/ <=

.

ij

3

|

|

1

ij

=

ψ

i

j

1

τ

<= '

- +

A

.+ ,

A

3

A

A

=

ψ

1

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