Question

At 400K, the root mean square (r.m.s) speed of gas X (molecular weight=40) is equal to the most probable speed of gas Y at 60K. The molecular weight of the gas Y is:
A. 3
B. 4
C. 10
D. 2

Answer 1

This question is very easy if we know the formulas. Root mean square speed is the mean velocity of all the molecules of gas and most probable speed is the velocity which most of the molecules have.
- Formula Used: Root mean square speed =$\sqrt {3RT/M}$,
where R- Rydberg constant,
T- Temperature,
M-molecular mass
Most probable speed = $\sqrt {2RT/M}$

Complete Step by step solution: Given: T1=400K, Molecular mass of gas X =40, Molecular mass of gas Y=60, T2=60K
RMS speed of gas X= Most probable speed of gas Y
$\sqrt {\dfrac{{3 \times R \times T1}}{{MX}}} = \sqrt {\dfrac{{2 \times R \times T2}}{{MY}}}$
On squaring both sides, we get $\dfrac{{3 \times R \times 400}}{{40}}$=$\dfrac{{2 \times R \times 60}}{{MY}}$

Dividing by R both sides,$30MY = 120$
We get, $MY = 4$
So our correct option is B.

Additional Information:
There is one more type of speed which is average speed of the gas.
Average speed=$\sqrt {\dfrac{{8 \times R \times T}}{{\pi \times M}}}$

Note:
Remember temperature is different for both of the gases. Also remember the speeds formulae like most probable speed, root mean square speed, and average speed.