Find the Root-Mean-Square of the gas

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In summary, to find the molar mass of a gas at a given temperature and pressure, one can use the equation M = D(RT/P) where D is the density of the gas. This density can be found using the ideal gas law, PV = nRT, where n is the number of moles. Once the molar mass is found, it can be plugged into the equation Vrms = sqrt(3RT/M) to calculate the root-mean-square velocity of the gas molecules.
  • #1
VitaX
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Homework Statement



At 329 K and 1.37 x 10-2 atm, the density of a gas is 1.39 x 10-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas.

Homework Equations



PV = nRT
Vrms = sqrt(3RT/M)

The Attempt at a Solution



I could do this problem right now if there was a molar mass given in the question. How does the density help with finding the answer to the problem? I don't see any examples utilizing it so I'm not sure what to do.
 
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  • #2
Hint:
Try to find a relation between density and molar mass from the equation PV=nRT
n=m/M , where m is the mass of the gas and M the molar mass
 
  • #3
All I can see is that density = mass/volume. So you are saying to replace n with m/m? And then set the equation equal to M? So it would be M = mRT/PV and substitite it in for M in the Vrms equation? So then it would be M = D(RT/P) and substitute that in for M in the Vrms equation? Or I guess I could find M right then and there and that gives me answer to part b then just plug M into the Vrms equation and that finds Vrms. Is that basically the solution to this problem?

Pressure in Pascals, density in kg/m^3 right?
 
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  • #4
VitaX said:
Or I guess I could find M right then and there and that gives me answer to part b then just plug M into the Vrms equation and that finds Vrms. Is that basically the solution to this problem?

Its better this way. Use R=0.0821 Lit atm K-1mol-1 because pressure is given in atm. Substitute the 'D' as it is and you will get 'M' in g units

VitaX said:
Pressure in Pascals, density in kg/m^3 right?

Once you find out M in g units, convert it in kg units and plug it in your equation for Vrms. Use R in SI units here.
 
  • #5
I was always told to conver to Pascals for pressure and use 8.31 J/mol*K for R. But I'm sure either works. I believe what I got is correct. I got M = .027 Kg/mol and Vrms = 497 m/s roughly.
 
  • #6
VitaX said:
I was always told to conver to Pascals for pressure and use 8.31 J/mol*K for R. But I'm sure either works. I believe what I got is correct. I got M = .027 Kg/mol and Vrms = 497 m/s roughly.
The first value looks good.

Please show your work on the second.
 
  • #7
M = D(RT/P) = .0127(8.31*268/1030.2) = .027 Kg/mol

Vrms = sqrt(3RT/M) = sqrt(3*8.31*268/.027) = 497.47 m/s
 

What is the root-mean-square (RMS) of a gas?

The root-mean-square (RMS) of a gas is a mathematical term that represents the average speed of the gas molecules in a sample. It is calculated by taking the square root of the average squared speed of the molecules.

Why is calculating the RMS of a gas important?

Calculating the RMS of a gas is important because it gives us an understanding of the kinetic energy and velocity of the gas molecules, which are crucial in various scientific fields such as thermodynamics, fluid dynamics, and chemistry.

How do you find the RMS of a gas?

To find the RMS of a gas, you need to first determine the average squared speed of the gas molecules by taking the sum of the squared speeds of each molecule and dividing it by the total number of molecules. Then, take the square root of this value to get the RMS.

What units is the RMS of a gas measured in?

The RMS of a gas is typically measured in meters per second (m/s) or centimeters per second (cm/s), depending on the unit system used. It can also be expressed in other units such as miles per hour (mph) or kilometers per hour (km/h).

Is the RMS of a gas the same as its average speed?

No, the RMS of a gas is not the same as its average speed. The RMS represents the average speed of the gas molecules, but it takes into account the squared speeds of each molecule, while the average speed only considers the individual speeds of the molecules. Therefore, the RMS is usually higher than the average speed.

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