(a)
Interpretation:
The surface area should be determined in cm2, neglecting the area of the nanotube attachment.
Concept introduction:
Surface area of a sphere =
r = radius of the sphere.
Answer to Problem 25.15QAP
Explanation of Solution
Using formula:
Surface area of a sphere =
Substituting the values:
(b)
Interpretation:
The concentration gradient and the current for A at a concentration of 1.00 mM at different times should be calculated.
Concept introduction:
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
i − time dependent faradaic current
n − number of moles of electrode
F − Faraday constant
A − surface area
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
Answer to Problem 25.15QAP
t, s | Concentration gradient | I, A |
1.00E-08 | 4.55E+05 | 6.75E-15 |
1.00E-07 | 3.19E+05 | 4.73E-15 |
1.00E-06 | 2.76E+05 | 4.09E-15 |
1.00E-05 | 2.62E+05 | 3.88E-15 |
1.00E-04 | 2.58E+05 | 3.82E-15 |
1.00E-03 | 2.56E+05 | 3.80E-15 |
1.00E-02 | 2.56E+05 | 3.79E-15 |
1.00E-01 | 2.56E+05 | 3.79E-15 |
1.00E+00 | 2.56E+05 | 3.79E-15 |
1.00E+01 | 2.56E+05 | 3.79E-15 |
Explanation of Solution
When the time is
Likewise, the other concentration gradients and current can be calculated using a spreadsheet.
t, s | d, m | 1/d + 1/r | Concentration gradient | I, A |
1.00E-08 | 5.012E-09 | 4.55E+08 | 4.55E+05 | 6.75E-15 |
1.00E-07 | 1.5849E-08 | 3.19E+08 | 3.19E+05 | 4.73E-15 |
1.00E-06 | 5.012E-08 | 2.76E+08 | 2.76E+05 | 4.09E-15 |
1.00E-05 | 1.5849E-07 | 2.62E+08 | 2.62E+05 | 3.88E-15 |
1.00E-04 | 5.012E-07 | 2.58E+08 | 2.58E+05 | 3.82E-15 |
1.00E-03 | 1.5849E-06 | 2.56E+08 | 2.56E+05 | 3.80E-15 |
1.00E-02 | 5.012E-06 | 2.56E+08 | 2.56E+05 | 3.79E-15 |
1.00E-01 | 1.5849E-05 | 2.56E+08 | 2.56E+05 | 3.79E-15 |
1.00E+00 | 5.012E-05 | 2.56E+08 | 2.56E+05 | 3.79E-15 |
1.00E+01 | 0.00015849 | 2.56E+08 | 2.56E+05 | 3.79E-15 |
(c)
Interpretation:
The steady state current should be found
Concept introduction:
If r << d, which occurs at long times, the 1/r term predominates, the electron transfer process reaches a steady state. The steady state current only depends on the size of the electrode.
Answer to Problem 25.15QAP
Explanation of Solution
(d)
Interpretation:
The time required for the electrode to achieve steady state current following the application of the voltage step should be determined.
Concept introduction:
Current should be used for the calculation is 1.01 x steady state value.
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
i − time dependent faradaic current
n − number of moles of electrode
F − Faraday constant
A − surface area
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
Answer to Problem 25.15QAP
Explanation of Solution
Using equation,
(e)
Interpretation:
The calculations should be repeated for a 3 µm spherical platinum electrode and for a spherical iridium electrode with a surface area of 0.785 mm2
Concept introduction:
The formula used:
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
i − time dependent faradaic current
n − number of moles of electrode
F − Faraday constant
A − surface area
D − diffusion coefficient
t- time after the voltage is applied
r − radius of the sphere
Answer to Problem 25.15QAP
For platinum electrode with radius of 3 3 µm, time required to achieve steady state is
Explanation of Solution
For the spherical platinum electrode area is calculated as:
Steady state current is calculated as:
For the spherical iridium electrode,
Steady state current
(f)
Interpretation:
The results for the three electrodes should be compared and the differences should be discussed.
Answer to Problem 25.15QAP
When the size of the electrode is higher than the thickness of the Nernst diffusion layer, it takes more time to achieve the steady state.
Explanation of Solution
For platinum electrode with radius of 3 3 µm, time required to achieve steady state is
When r <<< d, the 1/r term predominates. The electron transport process reaches the steady state. At this time, steady state current depends only on the size of the electrode. If the size of the electrode is small than the thickness of the Nernst diffusion layer, the steady state is achieved very rapidly.
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Chapter 25 Solutions
Principles of Instrumental Analysis
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