Question
What is an adsorption isotherm? Describe Freundlich adsorption isotherm.
✓
Answer
Adsorption isotherm: A graph between extent of adsorption (x/m) and the pressure 'p' of the gas at constant temperature is called adsorption isotherm.
Freundlich Isotherm: The relationship between $\frac{\text{x}}{\text{m}}$ and pressure of the gas at constant temperature is called adsorption isotherm and given
as by $\frac{\text{x}}{\text{m}}=\text{k}\text{p}^{1/\text{n}}(\text{n}>1)$ k and n depend upon the nature of gas and the solid.
$\frac{\text{x}}{\text{m}}$ first increase with increase in pressure at low pressure but becomes independent of pressure at high pressure.
Thus three cases arise from the graph
At low pressure, extent of adsorption is directly proportional to pressure (raised to power one).
$\frac{\text{x}}{\text{m}}\propto\text{P}^1$
At high pressure, extent of adsorption is independent of pressure (raised to power zero).
$\frac{\text{x}}{\text{m}}\propto\text{P}^0$
Therefore at intermediate value of pressure, adsorption is directly proportional to pressure raised to power 1/n .Here n is a variable whose value is greater than one.
$\therefore\ \frac{\text{x}}{\text{m}}\propto\text{P}^{\frac{1}{\text{n}}}$
Using constant of proportionality, k, also known as adsorption constant we get
$\frac{\text{x}}{\text{m}}\propto\text{k}\text{P}^{\frac{1}{\text{n}}}$
Taking logarithm on both sides, we get
$\log\frac{\text{x}}{\text{m}}=\log\text{k}+\frac{1}{\text{n}}\log\text{p}$
Here x is the weight of the gas absorbed by m mass of the adsorbent at a pressure p, k and n are constant (at a particular temperature) and for a particular adsorbate-adsorbent pair.
The equation above equation is comparable with comparable with equation of straight line,
y = mx + c where, m represents slope of the line and c represents intercept on y axis.
Plotting a graph between log(x/m) and log p, we will get a straight line with value of slope equal to 1/n and log k as y-axis intercept.
log(x/m) vs. log p graph.
Freundlich Isotherm: The relationship between $\frac{\text{x}}{\text{m}}$ and pressure of the gas at constant temperature is called adsorption isotherm and given
as by $\frac{\text{x}}{\text{m}}=\text{k}\text{p}^{1/\text{n}}(\text{n}>1)$ k and n depend upon the nature of gas and the solid.
$\frac{\text{x}}{\text{m}}$ first increase with increase in pressure at low pressure but becomes independent of pressure at high pressure.
Thus three cases arise from the graph
At low pressure, extent of adsorption is directly proportional to pressure (raised to power one).
$\frac{\text{x}}{\text{m}}\propto\text{P}^1$
At high pressure, extent of adsorption is independent of pressure (raised to power zero).
$\frac{\text{x}}{\text{m}}\propto\text{P}^0$
Therefore at intermediate value of pressure, adsorption is directly proportional to pressure raised to power 1/n .Here n is a variable whose value is greater than one.
$\therefore\ \frac{\text{x}}{\text{m}}\propto\text{P}^{\frac{1}{\text{n}}}$
Using constant of proportionality, k, also known as adsorption constant we get
$\frac{\text{x}}{\text{m}}\propto\text{k}\text{P}^{\frac{1}{\text{n}}}$
Taking logarithm on both sides, we get
$\log\frac{\text{x}}{\text{m}}=\log\text{k}+\frac{1}{\text{n}}\log\text{p}$
Here x is the weight of the gas absorbed by m mass of the adsorbent at a pressure p, k and n are constant (at a particular temperature) and for a particular adsorbate-adsorbent pair.
The equation above equation is comparable with comparable with equation of straight line,
y = mx + c where, m represents slope of the line and c represents intercept on y axis.
Plotting a graph between log(x/m) and log p, we will get a straight line with value of slope equal to 1/n and log k as y-axis intercept.
log(x/m) vs. log p graph.
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