What's the rms speed of the molecules?

In summary, the conversation is discussing the calculation of the root mean square speed of molecules in a canister containing an ideal gas. The volume, pressure, and mass of the gas are known, and the temperature is not needed in the calculation. The formula v = square root of(3kT/m) is used, where k is Boltzmann's constant and m is the mass of the molecule. Eventually, the solution will include the term "nm", which represents the number of moles times the molar mass.
  • #1
cdymdcool
10
0
1. A canister containing 150kg of an ideal gas has a volume of 8 m^3. If the gas exerts a pressure of 5*10^5 Pa, what's the rms speed of the modecules?



I can't get the temperature of the canister...
 
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  • #2
You don't need it. You have PV=nRT, so T=PV/nR. Leave it as that and continue solving the problem. Eventually, you should get a "nm" in your solution. What's this equal to?
 
  • #3
so nm equals the #of moles times its mass, what isn't the #of moles still unknow?
 
  • #4
nm is the #of moles times the molar mass (mass per mole). What's # of moles times the mass per mole?
 
  • #5
ideasrule said:
nm is the #of moles times the molar mass (mass per mole). What's # of moles times the mass per mole?

I use the formula v = square root of(3kT/m), which k stands for boltzmann's constant and m stants for the mass of molecule.
 

Related to What's the rms speed of the molecules?

What is the significance of the root-mean-square (rms) speed of molecules?

The rms speed of molecules is a measure of the average speed of all of the molecules in a gas. It helps us understand the kinetic energy and temperature of a gas, as well as how it behaves under certain conditions.

How is the rms speed of molecules related to temperature?

The rms speed of molecules is directly proportional to the temperature of a gas. As the temperature increases, the molecules move faster and the rms speed increases. This is because temperature is a measure of the average kinetic energy of molecules.

What factors affect the rms speed of molecules?

The rms speed of molecules is affected by the temperature, mass, and size of the molecules. Heavier molecules move slower than lighter molecules at the same temperature, and larger molecules also tend to move slower than smaller ones.

Can the rms speed of molecules be calculated?

Yes, the rms speed of molecules can be calculated using the root-mean-square formula: vrms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole.

How does the rms speed of molecules differ from the average speed of molecules?

The rms speed of molecules takes into account the speed of all molecules in a gas, while the average speed only considers the average of all the speeds. The rms speed is always slightly higher than the average speed, as it includes the faster-moving molecules in the calculation.

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