Solutions to exercises
275
3. a. In the case of normal diffusion, the relation between the limiting current I ℓ
and the molar fraction x O 2 of oxygen in the gaseous mixture is
I
K ln (1 x )
O 2
=
−
,
#
K is a constant that depends on the oxygen diffusion coefficient in the
gas, the temperature, and the diameter and length of the orifice. Note
that the limiting current does not depend on the total pressure of the gas.
b. For diffusion in the Knudsen regime, the relation becomes
I
K P x
t
O 2
=
,
#
#
l
where P t is the total pressure of the gas and K ′ is a constant.
4. a. 2 Figure 111 shows the curve for the diffusion-limited current I ℓ as a
function of the oxygen molar fraction at 1 bar. We see that I ℓ is proportional to ln(1− x O 2 ).
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D
E
,
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[ 2
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Figure 111 – Diffusion-limited current under 1 bar total pressure
as a function of oxygen molar fraction (a) x O 2 and (b) ln(1 − x O 2 ).
The equation for the limiting current is
I
423 ln (1 x ) [ A]
O 2
μ
= −
−
,
2 Figure 112 shows the curve for the limiting current I ℓ as a function of
oxygen molar fraction at 1.33 # 10
−3
bar and 400 °C. We see that I ℓ is
proportional to x O 2 .