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

Options

A. `He gt Ne gt Ar gt Kr gt Xe`
B. `H lt O_2 lt CO_2 lt PCI_3`
C. `He = Ne = 0,_2lt Ar lt Kr = Xe`
D. `O_2 = 0_3 lt N_2 lt Cl_2`

Answer

To determine the correct order of entropy of gases at constant temperature and pressure for equal moles, we need to consider the molecular weights of the gases involved. Entropy is a measure of the randomness or disorder of a system, and for gases, lighter gases tend to have higher entropy than heavier gases when the number of moles is constant.

### Step-by-Step Solution:

1. **Identify the Gases**: Let's consider a few common gases: Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), and Xenon (Xe).

2. **Determine Molecular Weights**:
- Helium (He) = 4 g/mol
- Neon (Ne) = 20 g/mol
- Argon (Ar) = 40 g/mol
- Krypton (Kr) = 84 g/mol
- Xenon (Xe) = 131 g/mol

3. **Analyze the Molecular Weights**:
- From the molecular weights, we can see that Helium has the lowest molecular weight, followed by Neon, Argon, Krypton, and Xenon.

4. **Order of Entropy Based on Molecular Weight**:
- Since entropy increases with decreasing molecular weight (at constant temperature and pressure), we can arrange the gases in order of increasing molecular weight and thus decreasing entropy:
- He (4 g/mol) > Ne (20 g/mol) > Ar (40 g/mol) > Kr (84 g/mol) > Xe (131 g/mol)

5. **Final Order of Entropy**:
- Therefore, the correct order of entropy for equal moles of these gases at constant temperature and pressure is:
- \( S_{He} > S_{Ne} > S_{Ar} > S_{Kr} > S_{Xe} \)