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Initially, the root mean square (rms) velocity of N2 molecules at certain temperature is u.
If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :
If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :
- a)u/2
- b)2u
- c)4u
- d)14u
Correct answer is option 'B'. Can you explain this answer?
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Initially, the root mean square (rms) velocity of N2 molecules at cert...
Given:
The initial root mean square (rms) velocity of N2 molecules at a certain temperature is u.
To find:
The new rms velocity when the temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms.
Solution:
Concept:
The root mean square (rms) velocity of a gas molecule is given by the formula:
u = √(3RT/M)
where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Explanation:
When the temperature is doubled, the new temperature becomes 2T.
1. Initial rms velocity of N2 molecules:
The initial rms velocity of N2 molecules at a certain temperature is u.
Using the formula, u = √(3RT/M)
2. Final rms velocity of N atoms:
When the N2 molecules dissociate into N atoms, the molar mass M becomes half of the initial value.
Therefore, the molar mass of N atoms is M/2.
Using the formula, v = √(3R(2T)/(M/2))
3. Simplifying the equation:
v = √(3R(2T)/(M/2))
v = √(12RT/M)
v = √(12u^2)
v = 2u
Conclusion:
Therefore, the new rms velocity when the temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms is 2u. Hence, the correct answer is option 'B'.
The initial root mean square (rms) velocity of N2 molecules at a certain temperature is u.
To find:
The new rms velocity when the temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms.
Solution:
Concept:
The root mean square (rms) velocity of a gas molecule is given by the formula:
u = √(3RT/M)
where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Explanation:
When the temperature is doubled, the new temperature becomes 2T.
1. Initial rms velocity of N2 molecules:
The initial rms velocity of N2 molecules at a certain temperature is u.
Using the formula, u = √(3RT/M)
2. Final rms velocity of N atoms:
When the N2 molecules dissociate into N atoms, the molar mass M becomes half of the initial value.
Therefore, the molar mass of N atoms is M/2.
Using the formula, v = √(3R(2T)/(M/2))
3. Simplifying the equation:
v = √(3R(2T)/(M/2))
v = √(12RT/M)
v = √(12u^2)
v = 2u
Conclusion:
Therefore, the new rms velocity when the temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms is 2u. Hence, the correct answer is option 'B'.
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Initially, the root mean square (rms) velocity of N2 molecules at certain temperature is u.If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be:a)u/2b)2uc)4ud)14uCorrect answer is option 'B'. Can you explain this answer?
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