Question

If He(g) has an average kinetic energy of 7030 J/mol under certain conditions, what is the root mean square speed of F2(g) molecules under the same conditions? root mean square speed:

Answer 1

Answer = 606 m/s , explanation is shown below

the root mean square velocity may be given as

Vrms = √RT/M

Where,

Vrms = root mean square velocity of gas,

R=universal gas constant

T = absolute temperature and M= molar mass of the gas,

So, the average molar kinetic energy of the gas will be equal to,

E = 1/2 MV^2rms = 1/2 RT,

From above equation , We see that , the molar kinetic energy is not dependent on the nature of the gas. It depends only on temperature as the ideal behavior of the gas is concerned.

Therefore, we can conclude that both He(g) and F2(g) will have same average kinetic energy = 7030 J/mol. Under the same condition.

Now for F2(g),

Average kinetic energy = 1/2 Mf2 * V^2rms F2

1/2 * 18.99 *10^-3 kg/mol *2* V^2rms = 7030 J/mol

V^2rms = 7030 J/mol * 2/18.99*10^-3 kJ/mol*2

= 7030000/18.99 m/s

So, Vrms(F2) = √7030000/18.99 = ~608 m/s

please upvote