alleryStart learning →The root mean square speed of gas molecules is given by which expression?
ASquare root of RT divided by 3M
BSquare root of 3M divided by RT
CSquare root of 2RT divided by M
DSquare root of 3RT divided by M
Answer & Solution
Correct answer: D. Square root of 3RT divided by M
1. The average kinetic energy of a mole of gas can be written two ways, as one half M times the square of the root mean square speed, and as three halves RT.
2. Set the two equal and multiply both sides by two, giving M times the speed squared equals 3RT.
3. Divide by M and take the square root, giving the root mean square speed as the square root of 3RT divided by M.
4. Molar mass sits in the denominator, so heavier gases move more slowly at the same temperature.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 9 "Gases", section 9.5 The Kinetic-Molecular Theory_
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