Chemical Thermodynamics of Tin - Volume 12 - OECD Nuclear ...

498
C Assigned uncertainties
Eq. (C.24) : K = 4(3.75 ± 0.12) 3 = (210.9 ± 20.3)
Eq. (C.25) :
K
ο
−ΔrG
ο m
RT
= e ;
rG ο
m
K ο = (2.97 ± 0.36).
Δ = − (2.7 ± 0.3) kJ·mol −1
−1
R = 8.3145 J·K
−1·mol
T = 298.15 K
Note that powers of 10 have to be reduced to powers of e, i.e., the variable has
to be multiplied by ln(10), e.g.,
log 10 (ln(10) log 10
log )
10
(2.45 0.10); 10 K
⋅ K
K = ± K = = e = (282 ± 65).
Eq. (C.26) :
rG ο
ο
Δ
m
=− RTln K ; K ο = (8.2 ± 1.2) × 10 6
Δ
rG ο
m
= − (39.46 ± 0.36) kJ·mol −1
ln K ο = (15.92 ± 0.15)
10
−1
R = 8.3145 J·K
−1·mol
T = 298.15 K
ο
ο
log K = ln K / ln(10) = (6.91±
0.06).
Again, it can be seen that the uncertainty in log10
K ο cannot be the same as in
ln K ο . The constant conversion factor of ln(10) = 2.303 is also to be applied to the
uncertainty.
C.6.3 Rounding
The standard rules to be used for rounding are:
1. When the digit following the last digit to be retained is less than 5, the last digit
retained is kept unchanged.
2. When the digit following the last digit to be retained is greater than 5, the last
digit retained is increased by 1.
3. When the digit following the last digit to be retained is 5 and
a) there are no digits (or only zeroes) beyond the 5, an odd digit in the
last place to be retained is increased by 1 while an even digit is kept
unchanged;
b) other non-zero digits follow, the last digit to be retained is increased
by 1, whether odd or even.
This procedure avoids introducing a systematic error from always dropping or
not dropping a 5 after the last digit retained.
CHEMICAL THERMODYNAMICS OF TIN, ISBN 978-92-64-99206-1, © OECD 2012