Question

The root mean square(rms) speed of X2 gas is x m/s at a given temperature. When the temperature is doubled, the X2 molecules dissociated completely into atoms. The root mean square speed of the sample of gas then becomes (in m/s)

• A. $\frac{x}{2}$
• B. x
• C. 2x
• D. 4x

Answer 1

Answer: (C)

2x

Answer 2

The root mean square (rms) speed of gas molecules is directly proportional to the square root of the temperature. Mathematically, it can be expressed as:

v rms​=√(3 kT/m) ​​

Where:

• v rms​ is the rms speed of the gas molecules.
• k is the Boltzmann constant.
• T is the temperature in Kelvin.
• m is the mass of a gas molecule.

Given that the rms speed of X2 gas is m/s x m/s at a given temperature, let's consider the situation when the temperature is doubled. If the X2 molecules dissociate completely into atoms, the mass m in the formula will change, as X2 molecules become two X atoms.

Now, let's analyze the relationship: v rms1​ v rms2​​=T 1​ T 2​​​

Since T 2​ is double of T 1​, we have: rms2rms1=2 v rms1​ v rms2​​=2​

Therefore, vrms2=2×rms1 v rms2​=2​× v rms1​.

Given that vrms1=m/s v rms1​=x m/s, we have: rms2=2×=2m/s v rms2​=2​× x =2 x m/s.

Hence, when the temperature is doubled and X2 molecules dissociate into atoms, the root mean square speed of the sample of gas becomes 2m/s2 x m/s.

The correct option is(C): 2x