Calculate Root Mean Square Speed of Oxygen Molecule in a Flask

[C-A-L]

I solved on my own the work below is incorrect.

Homework Statement

A sealed 500ml flask contains oxygen gas at a temperature of 27 degrees Celsius.
a) Calculate the root mean square speed of an oxygen molecule in the flask?
b) Calculate the average kinetic of an oxygen molecule in the flask?

Homework Equations

rms=square root (3r T/M)

The Attempt at a Solution

a) square root of (3*8.314)*(300/32)
=15.3 m/s
Is this the correct way to go about this question? b) KE average= 1/2 M (v)²
= 1/2*(32)*(15.3)²
=3.75*10³ N/m

I do have one more question but I would like to know if I did these two problems correctly.
Thank you for your time greatly appreciated.

 

[jbsteele]

No, these are not correct solutions. The first equation should be rms = square root (3RT/M) where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. For part a), you need to convert the temperature from Celsius to Kelvin (K = C + 273.15). Then solve for the root mean square speed of the oxygen molecule: rms = square root (3*8.314*(273.15 + 27)/32) = 15.5 m/sFor part b), the equation for average kinetic energy is KEaverage = 3/2 RT, where again R is the ideal gas constant and T is the temperature in Kelvin. Therefore, KEaverage = 3/2 * 8.314 * (273.15 + 27) = 3.78 * 103 N/m