Question

At the same temperature, which of the following pair of gases have the same R.M.S velocity?
(A) $C{{l}_{2}},\text{ }{{O}_{2}}$
(B) ${{O}_{2}},\text{ }{{O}_{3}}$
(C) ${{C}_{3}}{{H}_{8}},\text{ }C{{O}_{2}}$
(D) $C{{O}_{2}},\text{ }CO$

Answer 1

Hint : We know that the atoms or molecules move at different speeds and in random directions. The root mean square (r.m.s) velocity is the average velocity of all the gas particles, and this can be calculated using the rms velocity.

Complete Step By Step Answer:
R.M.S velocity stands for root mean square velocity. It is defined as the square root of the average of the squares of different velocities of the gas molecules. The root mean square velocity (rms velocity) is directly proportional to the square root of temperature and inversely proportional to the square root molecular mass of the gas. Since temperature is constant, find the constant as velocity times the square root of molar mass. for clarity, observe that we do not require to convert the unit from $\,g/mol$ to $kg/mol$ . This is because we did not insert any of the values of the constant as their SI unit, and the value of the temperature was not exactly found. Just the constant relation as velocity time molar mass. The molar mass, hence the unit will cancel out if we insert into the hydrogen rms velocity equation:
$C\alpha \dfrac{1}{\sqrt{M}}$ and $M$ (molecular mass) of ${{C}_{3}}{{H}_{8}}$ and $C{{O}_{2}}$ are equal.
Therefore, the correct answer is option C.

Note :
Remember that for our clarity, observe that we do not require to convert the unit. This is because we did not insert any of the values of the constant as their SI unit, and the value of the temperature was not exactly found. Just the constant relation as velocity time molar mass. The molar mass, hence the unit will cancel out if we insert into the hydrogen rms velocity equation.