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)
- x
- 2x
- 4x
The Correct Option is C
Solution and Explanation
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:
vrms=√(3kT/m)
Where:
- vrms 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/sxm/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: vrms1vrms2=T1T2
Since T2 is double of T1, we have: rms2rms1=2vrms1vrms2=2
Therefore, vrms2=2×rms1vrms2=2×vrms1.
Given that vrms1=m/svrms1=xm/s, we have: rms2=2×=2m/svrms2=2×x=2xm/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/s2xm/s.
The correct option is(C): 2x
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Concepts Used:
States of Matter
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
There are three States of Matter:
The three states of matter are as follows:
Solid State:
- The solid-state is one of the fundamental states of matter.
- Solids differ from liquids and gases by the characteristic of rigidity.
- The molecules of solids are tightly packed because of strong intermolecular forces; they only oscillate about their mean positions.
Liquid State:
- The molecules in a liquid are closely packed due to weak intermolecular forces.
- These forces are weaker than solids but stronger than that of gases.
- There is much space in between the molecules of liquids which makes their flowing ability easy.
Gaseous State:
- In this state of matter, distances between the molecules are large (intermolecular distance is in the range of 10-7-10-5 cm.
- The intermolecular forces experienced between them are negligible.
- Thus, translatory, rotatory and vibratory motions are observed prominently in gases.