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At constant temperature and pressure, co...

At constant temperature and pressure, correct order of entropy of gases for their equal moles is

A

He < Ne < Ar < Kr

B

`H lt O_2 lt CO_2 lt PCI_3`

C

`He = Ne = O_2lt Ar lt Kr = Xe`

D

`O_2 = 0_3 lt N_2 lt Cl_2`

Text Solution

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The correct Answer is:
To determine the correct order of entropy of gases at constant temperature and pressure with equal moles, we need to consider the nature of the gases involved. Entropy is a measure of randomness or disorder in a system, and it generally increases with the complexity of the molecules involved (i.e., the number of atoms in the molecule). ### Step-by-Step Solution: 1. **Understanding Entropy**: - Entropy (S) is a measure of disorder in a system. The more complex a molecule (more atoms), the higher the entropy. 2. **Factors Affecting Entropy**: - At constant temperature and pressure, the entropy of gases is influenced by the number of atoms in the gas molecules. More atoms generally mean higher entropy due to increased degrees of freedom and complexity. 3. **Analyzing the Options**: - **Option 1**: Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr) - All are monoatomic noble gases. Since they have the same number of moles and are monoatomic, they will have similar entropy values. This option is not correct for a distinct order. - **Option 2**: Hydrogen (H2), Oxygen (O2), Carbon Dioxide (CO2), Phosphorus Trichloride (PCl3) - Here, we have: - H2 (diatomic) - O2 (diatomic) - CO2 (triatomic) - PCl3 (polyatomic) - The order of increasing complexity (and thus increasing entropy) is: H2 < O2 < CO2 < PCl3. This is a valid order. - **Option 3**: O2, O3 (ozone), N2, Cl2 - Ozone (O3) is triatomic, while O2 is diatomic. Since O3 has higher entropy than O2, this order is incorrect. - **Option 4**: O2, O3, N2, Cl2 - Similar reasoning as above applies here, making this order incorrect as well. 4. **Conclusion**: - The correct order of entropy for the gases at constant temperature and pressure with equal moles is: **H2 < O2 < CO2 < PCl3**. ### Final Answer: The correct order of entropy of gases for their equal moles at constant temperature and pressure is: **H2 < O2 < CO2 < PCl3**.
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