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For real gases, the relation between P, ...

For real gases, the relation between P, V and T is given by an van der Waals equation, `(P+(an^(2))/(V^(2)))(V-nb)=nRT`.
For the following gases `CH_(4),CO_(2), O_(2),H_(2)` which gas will have (i) highest value of 'a' and (ii) lowest value of 'b' respectively?

A

`(i) CO_(2), (ii) H_(2)`

B

`(i) CH_(4), (ii) CO_(2)`

C

`(i)H_(2), (ii) CO_(2)`

D

`(i) O_(2), (ii) H_(2)`

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To solve the problem, we need to analyze the van der Waals equation and the properties of the given gases (CH₄, CO₂, O₂, H₂) in relation to the parameters 'a' and 'b'. ### Step-by-step Solution: 1. **Understanding the Parameters 'a' and 'b':** - The parameter 'a' in the van der Waals equation represents the strength of the intermolecular forces of attraction between gas molecules. A higher value of 'a' indicates stronger intermolecular forces. - The parameter 'b' represents the volume occupied by one mole of the gas molecules, which is related to the size of the molecules. A lower value of 'b' indicates smaller-sized molecules. 2. **Analyzing Intermolecular Forces (Parameter 'a'):** - The strength of intermolecular forces generally increases with the number of electrons in the molecule and the complexity of the molecule. - For the given gases: - CO₂ (Carbon Dioxide) has a linear structure and significant polarizability due to its molecular weight and electron count. - CH₄ (Methane) has weaker intermolecular forces compared to CO₂ but stronger than O₂ and H₂. - O₂ (Oxygen) has weaker forces than CH₄ due to its diatomic nature. - H₂ (Hydrogen) has the weakest intermolecular forces among these gases. **Order of 'a':** CO₂ > CH₄ > O₂ > H₂ 3. **Analyzing Molecular Size (Parameter 'b'):** - The size of the gas molecules increases with molecular weight and complexity. - For the given gases: - H₂ (Hydrogen) is the smallest molecule. - O₂ (Oxygen) is larger than H₂. - CH₄ (Methane) is larger than O₂. - CO₂ (Carbon Dioxide) is the largest among these gases. **Order of 'b':** H₂ < O₂ < CH₄ < CO₂ 4. **Identifying the Highest 'a' and Lowest 'b':** - From the analysis: - The gas with the highest value of 'a' is **CO₂**. - The gas with the lowest value of 'b' is **H₂**. ### Final Answer: - (i) Highest value of 'a': **CO₂** - (ii) Lowest value of 'b': **H₂**
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