Question 1 The following expression is known as the ButlerVo

Question 1

The following expression is known as the Butler-Volmer equation, and it is used in elec- 46 CHAPTER 3. SERIES trochemistry to describe the kinetics of an electrochemical reaction controlled solely by the rate of the electrochemical charge transfer process. j = j0(e (1)f e f ), 0 < < 1 and f > 0, > 0 Show that j j0f when f << 1.

Solution

let f =x

since f and are both positive nd f is very very less than 1, we assume f approaches 0 i.e. x approaches 0.

equation can be written as j= j_o(e^(1-)x-e^-x)

^{divide both side by x ,then}

j/x=j₀((e^(1-)x-e^-x)/x

putting lt x tending to 0 on rhs and applying l\' hospital,

(e^(1-)x-e^-x)/x term becomes (1-)+=1

thus j/x=jo*1= jo

j=j_ox

j=j₀f