Author details

∂ΔT ∂logKS

∂ΔT ∂KT

Eq. (53) we get

∂ΔT ∂log KT

error

E

þ 1 2 ¼ ln 10KS

144 Redox - Principles and Advanced Applications

<sup>¼</sup> ln10

<sup>¼</sup> <sup>2</sup> ffiffiffiffiffiffi KS p <sup>1</sup> <sup>þ</sup> ½ � <sup>X</sup> <sup>a</sup>

KS

From Eqs. (18), (20), and (34), we get

∂ΔT ∂KT

¼

¼ ln 10KT

¼ � ln 10 2

<sup>1</sup> � KS½ � <sup>X</sup> <sup>a</sup>

<sup>¼</sup> <sup>2</sup> ffiffiffiffiffiffi KS p <sup>1</sup> <sup>þ</sup> ½ � <sup>X</sup> <sup>a</sup>

> � ffiffiffiffi KS KT q

KT as a function of the derivative against KT and then

ΔT

∂ΔT KT

sysð Þ <sup>Δ</sup><sup>T</sup> <sup>¼</sup> ln 10Δ<sup>T</sup> <sup>p</sup> � aKS½ � <sup>X</sup> <sup>a</sup>

<sup>1</sup> <sup>þ</sup> KS½ � <sup>X</sup> <sup>a</sup> � cothð Þ <sup>C</sup>ΔpX � �

KT <sup>1</sup> <sup>þ</sup> ½ � <sup>X</sup> <sup>a</sup> ð Þ KS

¼ �ln 10

<sup>1</sup> <sup>þ</sup> ½ � <sup>X</sup> <sup>a</sup>

KS

E

� � � �

KS

½ � <sup>X</sup> <sup>p</sup> �<sup>1</sup>

½ � <sup>X</sup> <sup>p</sup>

<sup>2</sup> <sup>K</sup>�<sup>3</sup> 2

∂ΔT ∂KS

<sup>2</sup> <sup>Δ</sup><sup>T</sup> <sup>1</sup> � KS½ � <sup>X</sup> <sup>a</sup>

½ � <sup>X</sup> <sup>p</sup> <sup>∂</sup> ∂KT

<sup>¼</sup> <sup>Δ</sup><sup>T</sup> 2sinhð Þ CΔpX

� �

1 ffiffiffiffiffiffi KT p � �

<sup>1</sup> <sup>þ</sup> KS½ � <sup>X</sup> <sup>a</sup> � �

In order to differentiate ΔT against KT we put (from Eq. (22))

<sup>1</sup> � KS½ � <sup>X</sup> <sup>a</sup> <sup>1</sup> <sup>þ</sup> KS½ � <sup>X</sup> <sup>a</sup> � �

� sinhð Þþ <sup>C</sup>ΔpX <sup>1</sup>

<sup>¼</sup> �<sup>1</sup> 2KT

<sup>T</sup> sinhð Þ� <sup>C</sup>ΔpX �<sup>1</sup>

� �

ffiffiffiffiffiffi KT

> <sup>2</sup> <sup>K</sup>�<sup>3</sup> 2

� �

� cothð Þ CΔpX

<sup>C</sup>∂ΔpX ∂KT

By differentiating 1/√KT against KT in Eq. (52) and combining the resulting expression with

As before with the case of [X] and KS, we may express the partial derivative of ΔT against log

ffiffiffiffi KS KT q

KS ½ � <sup>X</sup> <sup>p</sup>

sinhð Þ <sup>C</sup>ΔpX <sup>ð</sup>sinhð Þþ <sup>C</sup>ΔpX coshð Þ <sup>C</sup>ΔpX ޼� ln 10

By combining Eqs. (28), (44), (51), and (55), we get for the standard deviation of systematic

� qcothð Þ CΔpX

2

sysð Þ log KS � <sup>1</sup>

<sup>1</sup> <sup>þ</sup> ½ � <sup>X</sup> <sup>a</sup>

sinhð Þ� CΔpX coshð Þ CΔpX

<sup>p</sup> cosh Cð Þ <sup>Δ</sup>pX <sup>C</sup>∂ΔpX

<sup>T</sup> coshð Þ CΔpX

ð Þð sinhð Þþ CΔpX coshð Þ CΔpX 105Þ

ð Þ sinhð Þþ CΔpX coshð Þ CΔpX

Esysð Þ pX

ð Þ 1 þ cothð Þ CΔpX E

∂KT

<sup>2</sup> <sup>Δ</sup>Tð Þ <sup>1</sup> <sup>þ</sup> cothð Þ <sup>C</sup>ΔpX

sysð Þ logKT

�

ð106Þ

ð107Þ

ð102Þ

ð103Þ

ð104Þ

� �

Julia Martín, Laura Ortega Estévez and Agustín G. Asuero\*

\*Address all correspondence to: asuero@us.es

Department of Analytical Chemistry, Faculty of Pharmacy, The University of Seville, Seville, Spain

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150 Redox - Principles and Advanced Applications


**Biological Applications**

**Provisional chapter**
