# (a) Interpretation: The surface area should be determined in cm 2 , neglecting the area of the nanotube attachment. Concept introduction: Surface area of a sphere = 4 π r 2 r = radius of the sphere.

### Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213

### Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213

#### Solutions

Chapter 25, Problem 25.15QAP
Interpretation Introduction

## (a)Interpretation:The surface area should be determined in cm2, neglecting the area of the nanotube attachment.Concept introduction:Surface area of a sphere = 4πr2r = radius of the sphere.

Interpretation Introduction

### (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:∂cA∂x=cA0(1πDt+1r)∂cA∂x - concentration gradientcA0 - concentration of AD − diffusion coefficientt- time after the voltage is appliedr − radius of the spherei=nFADcA0(1πDt+1r)i − time dependent faradaic currentn − number of moles of electrodeF − Faraday constantA − surface areaD − diffusion coefficientcA0 - concentration of At- time after the voltage is appliedr − radius of the sphere

Interpretation Introduction

### (c)Interpretation:The steady state current should be foundConcept 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.

Interpretation Introduction

### (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.∂cA∂x=cA0(1πDt+1r)∂cA∂x - concentration gradientcA0 - concentration of AD − diffusion coefficientt- time after the voltage is appliedr − radius of the spherei=nFADcA0(1πDt+1r)i − time dependent faradaic currentn − number of moles of electrodeF − Faraday constantA − surface areaD − diffusion coefficientcA0 - concentration of At- time after the voltage is appliedr − radius of the sphere

Interpretation Introduction

### (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 mm2Concept introduction:The formula used:∂cA∂x=cA0(1πDt+1r)∂cA∂x - concentration gradientcA0 - concentration of AD − diffusion coefficientt- time after the voltage is appliedr − radius of the spherei=nFADcA0(1πDt+1r)i − time dependent faradaic currentn − number of moles of electrodeF − Faraday constantA − surface areaD − diffusion coefficientcA0 - concentration of At- time after the voltage is appliedr − radius of the sphere

Interpretation Introduction

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