SME
Analytical Chemistry · Problem type
Calibrate a pH meter with two buffers
Use this for “A pH electrode reads +0.1650 V in a pH 4.01 buffer and −0.0120 V in a pH 7.00 buffer. A sample reads +0.0800 V. Find the slope, its percent of the ideal and the sample’s pH.”
Chart
E(6.07) = 0.05
This is an example. Type your own values to start a new problem.
S (V)
=
(
E₂ (V)
−
E₁ (V)
)
÷
(
pH₂
−
pH₁
)
pHₓ
=
pH₂
+
(
Eₓ (V)
−
(
E₂ (V)
)
)
÷
(
S (V)
)
%
Percent of the ideal slope
worked out (not typed) · %
Formulas
S
=
E₂
−
E₁
pH₂ − pH₁
−0.05900
=
−0.0050 − 0.1720
7.00 − 4.00
%
=
100
×
|
S
|
÷
0.05916
99.73 = 100 × |−0.05900| ÷ 0.05916
pHₓ
=
pH₂
+
Eₓ −
E₂
S
6.07
=
7.00
+
0.0500 − (−0.0050)
−0.05900
Assumptions
•
The electrode’s potential is a straight line in pH, E = K + S × pH, and two buffers fix K and S.
•
At 25 °C the ideal slope is −0.05916 V per pH unit; a real electrode gives a little less, quoted as a percent of the ideal.
•
Choose buffers on either side of the sample’s pH, so the sample is read between them.
Step-by-step
WE KNOW
pH₁ = 4.00, E₁ = +0.1720 V, pH₂ = 7.00, E₂ = −0.0050 V, Eₓ = +0.0500 V
FIND
slope (V per pH unit) (S), percent of the ideal slope (%), sample’s pH (pHₓ)
Step 1 · Find slope (V per pH unit): S
Use S = (E₂ − E₁) ÷ (pH₂ − pH₁)
Rise over run between the two buffers: the change in reading per pH unit.
S
=
−0.0050 − 0.1720
7.00 − 4.00
S
=
−
0.177
3
S
=
−0.05900
V
Step 2 · Find percent of the ideal slope (%)
Use % = 100 × |S| ÷ 0.05916
Compare the slope’s size with the ideal 0.05916 V per pH unit at 25 °C.
% = 100 × |−0.05900| ÷ 0.05916
%
=
100
×
0.059
0.05916
%
=
5.9
0.05916
% = 99.73% → Within 95–102% of the ideal: the electrode is fine to use.
Step 3 · Find sample’s pH (pHₓ)
Use pHₓ = pH₂ + (Eₓ − E₂) ÷ S
Divide the sample’s change from the second buffer by the slope, and add it to that buffer’s pH.
pHₓ
=
7.00
+
0.0500 − (−0.0050)
−0.05900
pHₓ
=
7
+
0.055
−0.059
pHₓ = 7 + (−0.9322)
pHₓ = 6.07
Check
Put the numbers back in. Both sides should match.
−0.05900
=
−0.0050 − 0.1720
7.00 − 4.00
✓
99.73 = 100 × |−0.05900| ÷ 0.05916 ✓
6.07
=
7.00
+
0.0500 − (−0.0050)
−0.05900
✓
Topic check
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