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Answer :
Final answer:
The root mean square velocity of I₂(g) at 373 K is calculated using the formula Urms = √(3kT/M), where k is Boltzmann's constant, T is the temperature, and M is the molar mass. After converting the molar mass of I₂ to kg/mol and substituting the values, the Urms is found to be approximately 191 m/s, which is option b). Therefore the correct answer is b) 191 m/s.
Explanation:
To calculate the root mean square velocity (Urms) of I2(g) at 373 K, we use the formula:
Urms = √(3kT/M)
where:
- k is Boltzmann's constant (1.38 × 10-23 J/K)
- T is the temperature in kelvin
- M is the molar mass of the gas in kg/mol
We also need to convert the molar mass of I2 from g/mol to kg/mol by dividing by 1000 since the atomic mass unit is approximately 127 g/mol for iodine, and I2 would have a molar mass of 2 × 127 g/mol = 254 g/mol or 0.254 kg/mol.
Thus:
Urms = √((3 × 1.38 × 10-23 J/K × 373 K) / 0.254 kg/mol)
After calculating the above expression, we find that the Urms is approximately 191 m/s, which corresponds to option b).
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