What is the root-mean-square speed of chlorine gas molecules at a temperature of 346 K? (R = 8.31 J/mol⋅K, NA = 6.02 × 1023, and the molecular mass of Cl2 = 71)

Root mean square velocity is the square root of the averages of squares of molecular velocity. This is calculated to take into account the random motion of gaseous molecules in the various direction.

The formula for root mean square velocity is following:

[tex]RMS=\sqrt{3RT/M}[/tex]

so we are having the following values that are given:

T=346K

R=8.31J/mol.K

Molecular mass of Cl₂=71

So putting the values in equation of root mean square velocity

[tex]RMS=\sqrt{3RT/M} \\RMS=\sqrt{[3\times8.314\times346]/71} \\RMS=\sqrt{121.54}\\RMS=11.02m/s[/tex]

adioabiola adioabiola · Answer 2 · 2021-11-03T17:55:40+01:00

The root mean square speed of chlorine molecules at 346K is: 11.02 m/s.

According to the question;

We are required to determine the root-mean-square speed of chlorine gas molecules at a temperature of 346 K.

The r.m.s speed of gas molecules is given mathematically as;

[tex]r.m.s = \sqrt{ \frac{3rt}{m} }

[/tex]

where: r = gas constant
T = temperature and m = molar mass

The r.m.s speed =

[tex] \sqrt{{3 × 8.31 × 346}/71}[/tex]

The RMS speed =√ 121.5

= 11.02 m/s

Ultimately, the root mean square speed of chlorine molecules at 346K is: 11.02 m/s.