Answer
To demonstrate that the CPR is related to the corrosion current density, i, in $\frac{A}{cm^{2}}$ through the expression, CPR= $\frac{KAi}{np}$, where:
K is a constant, A is the atomic weight, n is the number of electrons ionized per metal atom, and ρ is the density of the metal, unit dimensional analysis will be used. In Equation 17.24, corrosion rate, r, has units in SI:
r = $\frac{i}{nF}$ = $\frac{C/m^{2}- s}{(unitless)(\frac{c}{mol}}$ = $\frac{mol}{m^{2}-s}$
The units of CPR in Equation 17.23 are length/time, or in the SI scheme, m/s. In order to convert the above expression to the units of m/s it is necessary to multiply r by the atomic weight A and divide by the density ρ as:
$\frac{rA}{p}$ = K''r = $\frac{K'Ai}{nFp}$
where, K' and K" are constants which will give the appropriate units for CPR. Also, since F (Faraday’s constant) is also a constant, this expression will take the form:
CPR = $\frac{KAi}{np}$,
where, K = $\frac{K'}{F}$
Work Step by Step
To demonstrate that the CPR is related to the corrosion current density, i, in $\frac{A}{cm^{2}}$ through the expression, CPR= $\frac{KAi}{np}$, where:
K is a constant, A is the atomic weight, n is the number of electrons ionized per metal atom, and ρ is the density of the metal, unit dimensional analysis will be used. In Equation 17.24, corrosion rate, r, has units in SI:
r = $\frac{i}{nF}$ = $\frac{C/m^{2}- s}{(unitless)(\frac{c}{mol}}$ = $\frac{mol}{m^{2}-s}$
The units of CPR in Equation 17.23 are length/time, or in the SI scheme, m/s. In order to convert the above expression to the units of m/s it is necessary to multiply r by the atomic weight A and divide by the density ρ as:
$\frac{rA}{p}$ = K''r = $\frac{K'Ai}{nFp}$
where, K' and K" are constants which will give the appropriate units for CPR. Also, since F (Faraday’s constant) is also a constant, this expression will take the form:
CPR = $\frac{KAi}{np}$,
where, K = $\frac{K'}{F}$
