Explain Langmuir isotherm model and derive its equation

Charge on Clay, Adsorption, Zn, NO3 problem,

1. The University of Agriculture Peshawar –Pakistan
Department of Soil and Environmental Sciences
hD Final Term Examination 2020
Advanced Soil Chemistry (SES-721)

Q.1 The following silicate minerals are generally found in our soils:
a. Classify these minerals into 1:1 and 1:2 silicate clays along with
dioctahedral or trioctahedral arrangement.
[Si4] Al4O10(OH)8 1:1 di-octahedral
Mx[Si6.8Al1.2]Al3Fe0.25Mg0.75O20(OH)4 2:1 di-tetrahedral
Mx [Si8] Al3.2Fe0.2Mg0.6O20(OH)4 2:1 di-octahedral
Si4] Mg6O10(OH)8 2:1 trioctahedral



b.

Explain the degree and extent of isomorphic substitution in these minerals.
The silicon in the tetrahedral layer and the aluminum in the octahedral
layer are subjected to replacement or substitutions by other cations of
same size but different valences. As in some silicate mineral, the part of
silicon atoms in the mineral are replaced by Aluminum by the process
called Isomorphous substitution. This substitution of a 4 valences ion Si
4+
by three valance ion Al
3+
is responsible for the negative charge on the
silicate layer and when Al
3+
replace by Mg++ than produce positive charge.
4
c. Calculate the permanent charge in mineral given at S.No. iii (Given that atomic
weights of Si, Al, Fe and Mg are 28.09, 27, 55.9 and 24.3 respectively)?
Solution:
??????=
??????
????????????
x 1000
X = range for smectites from 0.5 to 1.2 mol kg
-1

Mr = 8 (28.09) Si +3.2 (27) Al +0.2 (55.85) Fe +0.6 (24.3) Mg24 (16) O +4 (1) H = 725 g

2. Now put the values:
??????= −(
0.5
725??????
x
1000??????
????????????
)= −0.7 �??????�?????? �??????−1 when x =0.5
??????= When x = 0.5
??????= −(
1.2
725??????
x
1000??????
????????????
)= −1.70 �??????�?????? �??????−1 When x = 1.2

Q2. What is adsorption? Explain Langmuir isotherm model and
derive its equation?
Adsorption
A gas or liquid solute accumulates on the surface of a solid or a liquid
(adsorbent), forming a molecular or atomic film (adsorbate). The process
through which a chemical substance reacts with two adjoining phases. If the
reaction increases the product in an interfacial layer, the process is known
as positive adsorption process. If the reaction product is reducing the
substance the process is known as the negative adsorption process.
Langmuir Adsorption Isotherm Modal
Irving Langmuir proposed adsorption Isotherm modal in 1916, which
explained the relationship between the number of active sites of the surface
undergoing adsorption and pressure.
Assumptions
Langmuir proposed his model by assembly following assumptions.
1. the exchanging sites on surface of solid is fix.
2. All empty sites on solid surface are equal shape and size of adsorbent.
3. Each one site can grip only one gaseous molecule and released a fix
amount of heat energy in prosses.
4. Dynamic balance occurs between the free gaseous molecules and
adsorbed gaseous molecules.

Where A (g) is free gaseous molecule, B(s) is unoccupied metal surface and AB is
Adsorbed gaseous molecule.
5. Adsorption is monolayer or single layer.

3. Derivations and Calculation
Using the equilibrium equation, equilibrium constant can be calculated.

Ka = forward reaction Kd = backward direction.
In the derivation of Langmuir Equation and new parameter ‘ θ ’ is added. The
θ represent the number of sites which cover by the gaseous molecules.
Therefore, the free surface of gas molecules will be (1 – θ). Now, Langmuir
equation the rate of forward direction depends upon 2 factors 1). Number of
sited which present on the surface of adsorbent, (1 – θ) and 2). Pressure, P.
The rate of onward reaction is directly proportional to both mentioned factors.
Rate of forward reaction  P (1 - θ)
Rate of adsorption  P (1 - θ)
Or rate of adsorption = Ka P (1 - θ)
As same the rate of backward reaction depends upon number of sites
engaged by the gaseous molecules.
Rate of desorption  θ
Or Rate of desorption = Kd θ
Now the balance occur between the rate of adsorption is equal to rate of
desorption.
Ka P (1 – θ) = Kd θ
We can solve the above equation to write it in terms of θ.
KaP – KaP θ = Kd θ KaP = KaP θ + Kd θ KaP = (Kd + KaP) θ

Divide numerator and denominator on RHS by Kd, we get

4. Now put

in above equation we get

This is known as Langmuir Adsorption Equation modal.

Q. 3 Explain the following
(i) CEC increases with increase in pH
The cation exchange capacity of soil will be increase with increasing pH.
At high pH, the maximum number of cations available which can increase
the CEC.
(ii) Organic matter increases the pH dependent charge
Organic matter decomposes into CO2 and several acids which eventually
produce H+ in the soil solution, thus significantly reduce the pH. The
various functional groups of soil humus dissociate and release H+ into the
soil solution which change pH depend charge in soil.
(iii) Acid soil has more AEC and alkaline soil has more CEC
The acidic soil having low pH below than 7 and maximum number of
anions are available which altimetry increased the anion exchange
capacity while alkaline soil having high pH and more cations are present
which directly increased the cation exchange capacity.
Q.4 Give reasons for the followings
(i) A researcher reported that application of Fe and Mn improved the wheat
crop but they did not show any response in rice on the same soil
In rice field is anaerobic conditions, oxygen release from rice roots
allows the formation of Fe and Mn depositions, that deposition Fe
plaque, on the surface of rice roots. The Fe plaque may prevent the
uptake of Fe2+, Mn2+ and other toxic compounds formed in

5. waterlogged soils, and could also have a role as a phosphorus
reservoir.
(ii) A farmer complained that he usually noticed Zn deficiency in rice but the
same plot did not show Zn deficiency in wheat crop.
Availability of zinc in submerged soils is decreased due to the
formation of different complexes such as insoluble ZnS, insoluble
franklinite (ZnFe2O4), insoluble ZnCO3, and insoluble Zn (OH)2
while in wheat crop the deficiency of Zn is low due to normal soil
as compare to paddy soil.
(iii). In alkaline soil condition nitrate fertilizer is preferred over urea for
wheat and maize but urea is preferred over nitrate for rice in the same
condition.
In alkaline soil condition nitrate fertilizer are easily available due
negative charge and low fixation while In rice field nitrate fertilizer
is less efficient due denitrification processes by soil microbes
which convert the NO3- back into N2 gas (reduction process), In
alternate of NO3- fertilizer in rice, use urea because urea is in
reduce form.
Q.5.Calculate the CEC if Na concentration in final solution was 100 mg L
-1
after time
dilution. Assume that 5 g soil was finally extracted with 100 mL of NH4
-
acetate
solution
Solution:
CEC = m mol kg
-1
Na+ = 100 mg L
-1
NH4
-acetate solution = 100 ml
Soil Sample = 5g


CEC =
��� �??????
���� ��
x
��� ��
?????? ??????
x
���� ??????
��??????
x
�??????
���� �??????

=
�??????
��??????
x
� �??????�?????? ????????????+
��?????? ????????????+

= 0.0869 mole kg
-1

CEC = 86.9 m mole kg
-1

6. Q. 6.

Redox potential:
The E (redox potential) simply express the electron availability of in
soil system. The milli vote potential difference between a platinum
electrode and with standard H+ electrode is called E. E is converted
to pe, using the principle of Nernst’s equation.
p
e
=
E (mv)
59.2

The constant 59.2 comes from 2.303 RT/F, where R is the gas
constant, T is absolute temperature, and F is the faraday constant.
In reduced soils or water logged having low oxygen and abundance of
electrons. The anoxic or anaerobic condition prevail the reducing
condition. Where the oxygen is depleted due microorganism, which
take O2 from soil compounds such NO3
-
SO4- etc.
Example: NO3- + 2e- + 2H+ = NO2 + H2O
The pE is defined as the negative log of the electron activity. when the
pE values is low it represents a reducing condition while high pE values
represent an oxidizing condition. The pE scale is projected the
concentration of the reducing agent (the e-) analogously to the pH scale
representing the concentration of standard acid (H+). pE values are
obtained from reduction potentials by dividing Eo by 0.059.
Q.7 Being an agriculturist, how you can reduce and reclaim the soil
pollution?
1. To reduce the use of pesticides because it’s the first source of
soil pollution. Once the pesticides have been sprayed or apply in
flood irrigation, it does not dissolve completely soil and it can
mix with water and leach down into the ground water. The
remaining compound is absorbed by plant itself.

7. 2. The limited or neglect the use of chemical fertilizers, manure and
OM wastes holding heavy metals such as mercury, arsenic,
cadmium, arsenic and lead can also lead to an accumulation of
these heavy metals in the soil. These heavy-metals can cause
contaminated soil, water or food.

3. Contaminated or waste water used for irrigation is one of the
supplementary sources of soil pollution. Use clean and pure
water for irrigation and do not use waste water of industrial and
agricultural waste in local bodies .

4. Reduce soil erosion and practical’s sedimentation problems, due
to improper practices, the soil left by erosion and leads to
decreasing soil fertility. While in sedimentation causes the soil
to build up in areas such as streams, rivers, and surrounding
fields.
5. For controlling of pests and weeds in field to adopt the conventional
mothed or agronomical practices instead of chemical use.
6. livestock is raring in close conditions where they fed unnatural or
synthetic food and sent to slaughterhouses on a daily basis. As a
result, they add to the process of agricultural pollution.
7. Organic Contaminants manures and biosolids frequently
contain different types of nutrients, such as nitrogen, carbon,
and phosphorus etc. the excessive nutrients cause pollution.

8. The non-biodegradable materials should be avoided.

9. Avoid poor or improper land management leads to a permanent
loss of soil fertility or nutrient. It’s crucial for care agricultural
pollution to a minimum level. Therefore, the farmers should be
awareness of how their actions can influence the environmental
condition.
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