Cant determine vrms, even though equations are all correct.

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SUMMARY

The discussion centers on calculating the root mean square (rms) speed of oxygen molecules in a syringe using the equation vrms = √(3kT/m). The user initially calculated the temperature (T) as 445.9 K and the mass (m) of an oxygen molecule as 5.31 x 10-23 g. However, the calculation yielded an incorrect rms speed of 18.645 m/s due to unit inconsistency. The solution was found by converting the mass to kilograms, which resolved the issue and provided the correct result.

PREREQUISITES
  • Understanding of the ideal gas law (PV = NkT)
  • Familiarity with Boltzmann's constant (k = 1.38 x 10-23 J/K)
  • Knowledge of molecular mass calculations (m = molar mass / Avogadro's number)
  • Basic grasp of root mean square speed calculations (vrms = √(3kT/m))
NEXT STEPS
  • Learn about unit conversions in physics, particularly for mass and energy
  • Study the ideal gas law and its applications in thermodynamics
  • Explore the significance of Boltzmann's constant in statistical mechanics
  • Investigate the properties of gases, including molecular speeds and distributions
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Students in physics or chemistry, particularly those studying thermodynamics and gas laws, as well as educators seeking to clarify concepts related to molecular speed calculations.

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Homework Statement


A syringe of volume 20 ml has just been used and now lies empty on the doctor's desk. The pressure in the office is 100,000 Pa. Assume that the air is an ideal gas consisting of nitrogen N2 (80%) and oxygen O2 (20%) molecules. k=1.38×10-23 J/K and the molar mass of oxygen is 32 g/mol.

The syringe must be heated to high temperatures to sterilize it. When the syringe is at its maximum temperature, the number of oxygen molecules is 6.5 x 1019 (but the pressure, volume, and percent oxygen remain the same), what is the rms speed of the oxygen molecules?




Homework Equations


vrms = root 3kT/m


The Attempt at a Solution


i know its the equation above that gets me vrms, so i just need T and m
PV-=NkT
T is 445.9K (using T= PV/Nk)
and m is 5.31e-23g (from m = 32g/6.022e23)

so using vrms = root3kT/m i get 18.645m/s

but this is wrong for some reason.. plaease help thanks!
 
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For the value of Boltzmann's constant given, the mass needs to be in kilograms. That way the units on either side will be equal.
 
Thank you. That solved the problem. UNITS!
 

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