Root Mean Square Speed

Increasing the temperature allows a gas to absorb thermal energy and convert into kinetic energy. Kinetic energy allows the gas to move and the speed at which it moves gives us the root mean square speed

Root Mean Square Speed & Kinetic Energy

Concept: Understanding kinetic energy & Root Mean Square Speed

Video Transcript

Welcome back guys. In this new video, we're going to take a look at the kinetic energy of gases. We've talked about kinetic energy really quickly in previous videos. We say that when we increase the temperature of any type of container, the gas particles in there will absorb that thermal energy and convert it to kinetic energy. This is the energy that they're going to use in order to push themselves around inside of this container.
We're going to say in order to measure the average kinetic energy of a gas molecule or particle, we must employ the root mean square equation. The root mean square equation is U, which stands for velocity, equals square root of 3RT over M. When I say velocity, I mean speed. The units for velocity or speed are meters per second.
Here this R is not the same R we're used to seeing. Because we're talking about speed or energy, R is now 8.314 joules over moles times K. Remember when do I use this R? I use this R anytime we're talking about speed, velocity, kinetic energy. Energy is the key word here. The three keywords we look out for are energy speed or velocity. That's when we use this R. The other R is associated with the Ideal Gas Law. It's different.
Here, T represents temperature in Kelvin. Here, capital M means molar mass or molecular mass. But here it's different. We're used to seeing molecular mass or molar mass in grams per mole, but in this case, in this equation, it's going to be in kilograms per mole. You have to remember that. It's in kilograms per mole.
Now the R we're going to look at it a little bit closer. We're going to say here joules is just a form of energy. We're going to say joules are kilograms times meters squared over seconds squared. That's what joules mean. That means that our R is really 8.314 kilograms times meters squared over moles times K times seconds squared. Because the second squared is on the bottom here, we would have to put it on the bottom here. Just remember the units that are involved with joules. This is going to help us in our calculations to see what we isolate when we find our answer.

Example: A 1.56 x 1013 pg gaseous particle travels at 6.21 . Determine its kinetic energy. 


The kinetic energy (in J or kJ) of a gas molecule is directly proportional to its absolute temperature in Kelvins. 

Problem: Calculate the molar mass, in g/mol, of a gaseous compound with an average root mean velocity of 652 m/s at a temperature of 30 degrees Celsius.


Remember that using the root mean square speed equation deals with molar mass in g/mol, so further conversion may sometimes be needed. 

Root Mean Square Speed Additional Practice Problems

Which of the following statements is/are true? Check all that apply.

a) There are gas molecules that move slower than the average speed.

b) There are gas molecules that move faster than the average speed.

c) All the gas molecules in a sample have the same kinetic energy.

d) The average kinetic energy of gas molecules increases with temperature.

f) The average speed of gas molecules increases with temperature.

Watch Solution

A 0.81 mole sample of CO2 is confined in a 20 L container. The volume of the gas sample is decreased to 10L while holding temperature constant. The average molecular speed will.

a. increase
b. decrease
c. remain the same
d. insufficient information to answer

Watch Solution

A gas or vapor may be liquefied only at temperatures

(A) equal to the normal boiling point.

(B) above the normal boiling point.

(C) above the critical temperature.

(D) at or below the critical temperature.

Watch Solution

What is the root mean square speed (in m/s) of hydrogen molecules at 25.0°C?                  

( R= 8.3145 kg m2 s-2 mol -1 k-1)


a) no given answer is close

b) 3.72 x 106

c) 6.10 x 101

d) 1.93 x 103

e) 3.72 x 103


Watch Solution

Which of the following statements about gases is true?

  1. Heavier gas particles effuse faster than lighter gas particles.
  2. Particles of different masses have the same average speed at a given temperature.
  3. The higher the temperature, the lower the average kinetic energy of a gas sample.
  4. At very high pressures, a gas will occupy a larger volume than predicted by the ideal gas law.
  5. Particles of lighter masses have a lower average speed then particles of a higher mass at a given temperature
Watch Solution