Question

Compute the root-mean-square speed of Nemolecules in a sample of neongas at a temperature of 71°C.

Answer 1

According to Kinetic Molecular Theory, gaseous particles are in a state of constant random motion; individual particles move at different speeds, constantly colliding and changing directions. We use velocity to describe the movement of gas particles, thereby taking into account both speed and direction. Although the velocity of gaseous particles is constantly changing, the distribution of velocities does not change. We cannot gauge the velocity of each individual particle, so we often reason in terms of the particles' average behavior. Particles moving in opposite directions have velocities of opposite signs. Since a gas' particles are in random motion, it is plausible that there will be about as many moving in one direction as in the opposite direction, meaning that the average velocity for a collection of gas particles equals zero; as this value is unhelpful, the average of velocities can be determined using an alternative method.

By squaring the velocities and taking the square root, we overcome the directional component of velocity and simultaneously acquire the particles' average velocity. Since the value excludes the particles' direction, we now refer to the value as the average speed. The root-mean-square speed is the "measure of the speed of particles in a gas", defined as the square root of the average velocity-squared of the molecules in a gas.

It is represented by the equation: V_rms= 3RT / M_Ne ................................(1)

Where,

V_rms is the root-mean-square of the velocity,

M_Ne is the molar mass of the gas in kilograms per mole = 0.0201797 kg,

R is the molar gas constant = 8.314 J / (K * mol), and

T is the temperature in Kelvin = 344 K

Put the value in equestion 1 we get,

V_rms= 3RT / M_Ne

V_rms =3 x 8.314 x 344 / 0.0201797

= 425182.13

= 652.05 m/s

Root mean square velocity of Ne molecule at 71⁰C =  652.05 m/s