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The equation , (P)/(x) = (1)/(k')+(P)/(k...

The equation , `(P)/(x) = (1)/(k')+(P)/(k")` is

A

Gibbs adsorption isotherm

B

Freundlich adsorption isotherm

C

Langmuir adsorption isotherm

D

BET equation

Text Solution

AI Generated Solution

The correct Answer is:
To determine which isotherm the equation \(\frac{P}{x} = \frac{1}{k'} + \frac{P}{k''}\) belongs to, we can analyze the equation step by step. ### Step 1: Identify the form of the equation The given equation can be rearranged to resemble a linear form. It can be expressed as: \[ \frac{P}{x} - \frac{P}{k''} = \frac{1}{k'} \] This suggests a relationship between the pressure \(P\) and the amount adsorbed \(x\). ### Step 2: Compare with known isotherm equations We need to compare this equation with the known adsorption isotherms: 1. **Langmuir Isotherm**: The Langmuir isotherm is given by the equation: \[ \frac{P}{x} = \frac{1}{k} + \frac{P}{k} \] This is similar to our equation, where \(k\) is a constant related to the adsorption capacity. 2. **Freundlich Isotherm**: The Freundlich isotherm is given by: \[ x = k P^{1/n} \] This does not resemble our equation. 3. **Gibbs Adsorption Isotherm**: This is a more complex relationship and does not fit our equation. 4. **BET Equation**: The BET equation is also more complex and does not match. ### Step 3: Conclusion From the analysis, it is clear that the equation \(\frac{P}{x} = \frac{1}{k'} + \frac{P}{k''}\) matches the form of the Langmuir isotherm equation. Therefore, the correct answer is that this equation belongs to the **Langmuir adsorption isotherm**. ### Final Answer The equation \(\frac{P}{x} = \frac{1}{k'} + \frac{P}{k''}\) belongs to the **Langmuir adsorption isotherm**. ---
To determine which isotherm the equation \(\frac{P}{x} = \frac{1}{k'} + \frac{P}{k''}\) belongs to, we can analyze the equation step by step. ### Step 1: Identify the form of the equation The given equation can be rearranged to resemble a linear form. It can be expressed as: \[ \frac{P}{x} - \frac{P}{k''} = \frac{1}{k'} \] ...
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