At a certain temperature, the root-mean-square-speed of the molecules of hydrogen in a sample of gas is 1055 m/s. Compute the root-mean square speed of molecules of nitrogen at the same temperature. Show calculations and unit conversions. (10 points)

The Kinetic Molecular Theory postulates that gaseous particles are in a state of continuous random motion, whereby they move at varying speeds while reversing directions and colliding with one another. We consider both speed and direction when using velocity to describe the motion of gas particles.

The distribution of velocities remains constant even though the velocity of gaseous particles changes constantly. Since we are unable to determine each particle's velocity individually, we frequently make decisions using the behavior of the particles as a whole. The velocities of particles traveling in opposing directions have opposite signs.

Given:

root mean square speed of hydrogen = 1055 m/s

root mean square speed of nitrogen = ?

Formula used :

Vrms = ( 3RT/M) ^ (1/2)

where,

Vrms = root mean square speed

R = Universal gas constant

M = molar mass

T = temperature

Solution:

for hydrogen ,

1055 = ( 3 RT / M ) ^( 1/2)

= > 1055 = ( 8.3145 x 3 x T / 0.01) ^(1/2)

= > 1055 ^2 = 8.3145 x 3x T / 0.01

= > 1338 K = T

for nitrogen,

Vrms = ( 3 x 8.3145 x 1338 / 0.28)^ (1/2) = 345.24 m/s

Therefore, root means square speed of nitrogen is 345.24 m/s.

To learn more about root mean square speed :

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