Recollection: Units can be a real bitch in Physical Chemistry
I've recently encoutered a physical chemistry problem which reminded me of just how messy a simple problem can become when it came to sorting out the units. My P. Chem. professor was Dr. Lionel Carreira, he was highly involved with the development of CARS, however he was pretty easy on us in his tests and quizzes. The sorting out of the equations wasn't so much of a factor in those exams, a lot of points could have been deducted by simply not keeping track of units.
The root mean square velocity of oxygen molecules is 480m/s while the pressure is 20kPa.
What is the concentration (particles/volume) of oxygen?
Sourced from
http://www.physicsforums.com/showthread.php?p=1216079#post1216079
The equations that were utilized to solve the problem can be found in the page that is hyperlinked to the above text.
The equation to plug in the numbers are pretty simple, however, one has to incorporate the right units for the gas constant, here are just some of them (Figure 1)....... the same goes for the value of k.
| Values of R |
|---|
| 8.314472 J · K-1 · mol-1 |
| 0.0820574587 L · atm · K-1 · mol-1 |
| 8.20574587 x 10-5 m³ · atm · K-1 · mol-1 |
| 8.314472 cm3 · MPa · K-1 · mol-1 |
| 8.314472 L · kPa · K-1 · mol-1 |
| 8.314472 m3 · Pa · K-1 · mol-1 |
| 62.3637 L · mmHg · K-1 · mol-1 |
| 62.3637 L · Torr · K-1 · mol-1 |
| 83.14472 L · mbar · K-1 · mol-1 |
| 1.987 cal · K-1 · mol-1 |
| 6.132439833 lbf · ft · K-1 · g · mol-1 |
| 10.7316 ft³ · psi · °R-1 · lb · mol-1 |
You won't find problems like this anywhere in your undergraduate courses besides in Physical Chemistry. Unless you're of a different major.
(n/v)=20 kPa(1000 Pa/1 kPa)(1.3806503 × 10-23 m2 kg s-2 K-1)3/[8.314472 m^3 · Pa · K-1 · mol-1(16 grams of Oxygen/mole of Oxygen)(1 mole/6.022 x 10^23 atoms)(1 kilogram/1000 grams)(2 atoms of Oxygen/1 diatomic molecule)(480 m/s)^2]= 0.00813782909722 moles/m^3
(0.00813782909722 moles Oxygen/L)(6.022x10^23 molecules Oxygen/mole)= 4.900600682 x 10^24 molecules/m^3
It can get substantially worse....I'm sure you grad students remember.
Figure 1 Gas constant values obtained
from Wikipedia
http://en.wikipedia.org/wiki/Gas_constant
