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Question

The extent of adsorption from Langmuir adsorption isotherm is given by
xm=aP1+bP
The value of a and b are, respectively:

where,
ka and kd are rate constant of adsorption and desorption respectively.
K1 is proportionality constant.

A
kakd and kakd
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B
K1kakd and kakd
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C
K1kakd and kdka
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D
K1kdka and kakd
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Solution

The correct option is B K1kakd and kakd

In Langmuir adsorption isotherm,
θ : Fraction of surface covered on adsorbent
1θ : Free surface are
P : Pressure of gas
By langmuir adsorption isotherm,
Rate of adsorption Fraction of surface available for adsorption
Rate of adsorption Pressure of gas

Rate of adsorption P(1Θ)
Rate of adsorption =ka P(1Θ)

Rate of dessorption Fraction of surface covered on adsorbent
Rate of desorption Θ
Rate of desorption =kd Θ
ka and kd are rate constants.

At equilibrium condition,
Rate of adsorption =Rate of desorption
ka P(1Θ)=kd Θ
kdP ka=1ΘΘ
1+kdP ka=1Θ
Θ=P kaP ka+kd
Θ=KPKP+1

According to Langmuir, extent of adsorption is proportional to Θ
xmΘ
xmKP1+KP

xm=K KP1+KP

xm= KKP1+KP
xm= aP1+bP

where,
a=KK=Kkakd
b=K=kakd

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