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At a certain temperature T, the root-mean-square (rms) speed of N2 molecules is u. If the temperature is doubled to 2T and all the nitrogen molecules simultaneously dissociate completely into individual nitrogen atoms, what is the new rms speed?

1. u/2
2. 4u
3. 14u
4. 2u

Correct answer: 2u

Solution

v_rms = sqrt(3RT/M). New speed = sqrt(3R*2T/(M/2)) = sqrt(12RT/M) = 2*sqrt(3RT/M) = 2u. Doubling temperature and halving molar mass each contribute a factor of sqrt(2), giving a total factor of 2.

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