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GATE 2024 CY – Question 29

Physical Chemistry · Surfaces and Interfaces: Physisorption and chemisorption. Langmuir, Freundlich and Brunauer-Emmett-Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity, Self- assembly/ physical chemistry of colloids, micelles and macromolecules. · 1 mark · Multiple select

The non-dissociative adsorption of a gas on a given surface at a fixed temperature follows Langmuir isotherm. The plot(s) which give(s) a straight line is (are) [Given: V = volume of the adsorbed gas, P = pressure of the gas]

  1. $1/V$ versus $1/P$
  2. $P/V$ versus $P$
  3. $V$ versus $P$
  4. $V$ versus $1/P$

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Correct answer: (A) $1/V$ versus $1/P$; (B) $P/V$ versus $P$

Explanation

The **Langmuir isotherm** for non-dissociative adsorption is
$$V=\frac{V_mKP}{1+KP},$$
where $V_m$ is the monolayer volume and $K$ is the adsorption constant.

**Rearrange to get linear forms.**
- Take reciprocals: $\dfrac1V=\dfrac1{V_m}+\dfrac1{V_mK}\cdot\dfrac1P$. A plot of $1/V$ against $1/P$ is a **straight line**. ✓ (A)
- Multiply by $P$: $\dfrac PV=\dfrac1{V_mK}+\dfrac{P}{V_m}$. A plot of $P/V$ against $P$ is a **straight line**. ✓ (B)
- $V$ against $P$ is a curve that saturates at $V_m$. ✗
- $V$ against $1/P$ is also a curve. ✗

Answer **A and B**.