Reference formulas
1) Temperature correction (to 25°C)
\[
E_{25}
=
E_{meas}
+
k_t \,\times\, (T - 25)
\]
\(E_{meas}\) = measured potential at temperature \(T\)
\(k_t\) = electrode temperature coefficient (mV/°C)
\(T\) = reference electrode temperature (°C)
2) General conversion (between reference electrodes)
\[
V_{Target}
=
V_{Measured}
+
(E_{Source} - E_{Target})
\]
\(V_{Target}\) = reading on target reference electrode scale
\(V_{Measured}\) = reading on source reference electrode scale
\(E_{Source}\) = standard potential of source reference (vs SHE)
\(E_{Target}\) = standard potential of target reference (vs SHE)
Problem 1 — CSE Temperature Correction (Cold)
A pipeline potential is measured as -850 mVCSE.
The reference electrode temperature is 5°C.
Calculate the corrected potential at the standard temperature of 25°C.
Reveal solution
\[
\begin{array}{c}
E_{25}
=
E_{meas}
+
k_t \,\times\, (T - 25) \\[10pt]
E_{25}
=
-850
+
0.9 \,\times\, (5 - 25) \\[10pt]
E_{25}
=
-850
+
0.9 \,\times\, (-20) \\[10pt]
E_{25}
=
-850
-
18
=
-868\ \text{mV}
\end{array}
\]
Answer: −868 mVCSE
Problem 2 — CSE Temperature Correction (Hot)
You measure a structure potential of -900 mVCSE.
The reference electrode temperature is 45°C.
What is the actual potential corrected to 25°C?
Reveal solution
\[
\begin{array}{c}
E_{25}
=
-900
+
0.9 \,\times\, (45 - 25) \\[10pt]
E_{25}
=
-900
+
0.9 \,\times\, 20 \\[10pt]
E_{25}
=
-900
+
18
=
-882\ \text{mV}
\end{array}
\]
Answer: −882 mVCSE
Problem 3 — Conversion (CSE to SCE)
A potential is measured as -850 mVCSE at 25°C.
Convert this reading to the Saturated Calomel Electrode (SCE) scale.
Reveal solution
\[
\begin{array}{c}
V_{SCE}
=
V_{CSE}
+
(E_{CSE} - E_{SCE}) \\[10pt]
V_{SCE}
=
-0.850
+
(0.316 - 0.244) \\[10pt]
V_{SCE}
=
-0.850
+
0.072
=
-0.778\ \text{V}
\end{array}
\]
Answer: −778 mVSCE
Problem 4 — Conversion (CSE to Ag/AgCl Seawater)
An offshore pipeline riser measures -0.950 VCSE.
What would this reading be if measured with a Silver/Silver Chloride (Seawater) electrode?
Reveal solution
\[
\begin{array}{c}
V_{SSC}
=
V_{CSE}
+
(E_{CSE} - E_{SSC}) \\[10pt]
V_{SSC}
=
-0.950
+
(0.316 - 0.256) \\[10pt]
V_{SSC}
=
-0.950
+
0.060
=
-0.890\ \text{V}
\end{array}
\]
Answer: −0.890 VSSC
Problem 5 — Multi-Step (Temperature and Conversion)
You measure -1125 mVCSE with the electrode at
-7°C. Convert this to the equivalent potential with respect
to SCE.
Reveal solution
\[
\begin{array}{c}
E_{25}
=
-1125
+
0.9 \,\times\, (-7 - 25) \\[10pt]
E_{25}
=
-1125
+
0.9 \,\times\, (-32) \\[10pt]
E_{25}
=
-1125
-
28.8
=
-1153.8\ \text{mV} \\[10pt]
V_{SCE}
=
-1.1538
+
(0.316 - 0.244) \\[10pt]
V_{SCE}
=
-1.1538
+
0.072
=
-1.0818\ \text{V}
\end{array}
\]
Answer: −1082 mVSCE (approx)
Problem 6 — SCE Temperature Correction
A lab sample measures -750 mVSCE.
The reference cell temperature is 35°C.
Calculate the potential corrected to 25°C.
Reveal solution
\[
\begin{array}{c}
E_{25}
=
-750
+
(-0.7) \,\times\, (35 - 25) \\[10pt]
E_{25}
=
-750
-
7
=
-757\ \text{mV}
\end{array}
\]
Answer: −757 mVSCE
Problem 7 — SSC Temperature Correction
You measure -900 mV using an Ag/AgCl (Seawater) electrode
in cold water at 5°C.
Calculate the potential corrected to 25°C.
Reveal solution
\[
\begin{array}{c}
E_{25}
=
-900
+
(-0.33) \,\times\, (5 - 25) \\[10pt]
E_{25}
=
-900
+
(-0.33) \,\times\, (-20) \\[10pt]
E_{25}
=
-900
+
6.6
=
-893.4\ \text{mV}
\end{array}
\]
Answer: −893 mVSSC (approx)
Problem 8 — Conversion (SSC to CSE)
A structure measures -800 mV vs Ag/AgCl (Seawater) at 25°C.
What is this potential with respect to CSE?
Reveal solution
\[
\begin{array}{c}
V_{CSE}
=
V_{SSC}
+
(E_{SSC} - E_{CSE}) \\[10pt]
V_{CSE}
=
-0.800
+
(0.256 - 0.316) \\[10pt]
V_{CSE}
=
-0.800
-
0.060
=
-0.860\ \text{V}
\end{array}
\]
Answer: −860 mVCSE
Problem 9 — Zinc Reference to CSE
You read a potential of +0.200 V on a pipeline with respect
to a permanent Zinc reference electrode (ZRE). Convert this to CSE.
Reveal solution
\[
\begin{array}{c}
V_{CSE}
=
V_{ZRE}
+
(E_{ZRE} - E_{CSE}) \\[10pt]
V_{CSE}
=
0.200
+
(-0.800 - 0.316) \\[10pt]
V_{CSE}
=
0.200
-
1.116
=
-0.916\ \text{V}
\end{array}
\]
Answer: −0.916 VCSE
Problem 10 — Criterion Check with Temperature
You measure a potential of -840 mVCSE.
The electrode temperature is 45°C.
Does this potential meet the NACE SP0169 −850 mV criterion
after temperature correction?
Reveal solution
\[
\begin{array}{c}
E_{25}
=
-840
+
0.9 \,\times\, (45 - 25) \\[10pt]
E_{25}
=
-840
+
18
=
-822\ \text{mV}
\end{array}
\]
−822 mV is more positive than −850 mV, so the criterion is not met.
Answer: No (corrected potential = −822 mV)
