The root mean square speed of molecules of nitrogen gas is v at a certain temperature. When the temperature is doubled, the molecules dissociate into individual atoms. The new rms speed of the atom is:
Correct answer: B. 2v
- A. √2v
- B. 2v
- C. v
- D. 4v
Explanation
When the temperature of nitrogen gas (N₂) is doubled, the root mean square (rms) speed for the N₂ molecules increases by a factor of √2, due to the formula: v rms = √(3kT/m). However, when the molecules dissociate into individual nitrogen atoms, the mass of each atom is half that of an N₂ molecule. Because the rms speed is inversely proportional to the square root of mass, the speed further increases. Thus, the new rms speed of the nitrogen atoms is 2v. Option A (√2v) only accounts for the temperature change, not the dissociation. Option C (v) suggests no change, which is incorrect due to the temperature increase. Option D (4v) exaggerates the effect of temperature and dissociation.
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Gas behaviour is explained through the kinetic molecular theory and the relationships among pressure, volume and temperature. Work includes STP, Boyle's and Charles's laws, absolute zero, the ideal gas equation, and the distinction between ideal and real gases, especially the effects of intermolecular forces and molecular volume.
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