# Homework Help: Thermo: Lab vacuum

1. Sep 10, 2014

### kopinator

The best laboratory vacuum has a pressure of about 1.00 x 10-18 atm, or 1.01 x 10-13 Pa. How
many gas molecules are there per cubic centimeter in such a vacuum at 293K?

PV = nkT
P/kT = n/V = N (# of molecules per cm^3)

Since V is typically in units of m^3 or liters, should I make my volume .01V to account for the cm^3?

2. Sep 10, 2014

### Staff: Mentor

When making unit conversions, use the trick of multiplying by "1" to help you do the unit conversion.

So to convert from cm^3 to m^3 multiply by "1" like this:

$$1cm^3 * \frac{(1m)^3}{(100cm)^3}$$

The cm^3 unit terms in the numerator and denominator cancel (just like numbers cancel if they are identical in the numerator and denominator of a fraction), and you are left with what in units of m^3? Hint -- It's not 0.01 ...

3. Sep 10, 2014

### Staff: Mentor

4. Sep 10, 2014

### BvU

You are using the right equation. People are conditioned to see n as number of moles and N as number of molecules, so better use N.

Now try to work in a consistent set of units. SI units is what every reasonable person would use.
p in Pascal, Pa with 1Pa = 1 N/m[sup2[/sup]. Conversion: 1 atm = 101325 N/m[sup2[/sup].
k Boltzmann constant, J/K 1.3806488 10-23 J/K
T 293 K

The equation gives you n/V in molecules/m3.
Since the exercise asks for molecules/cm3, all you have to do is multiply by

( molecules/cm3 ) / (molecules/m3 ) = cm3 / m3 = (cm / m3) = (10-2)3

[I see berkeman beat me to it, well, good for you!

But I don't agree with him (/her?): pV = NkT is just fine. It's the same as pV = nRT since n = N/NA and R = kB*NA ]

5. Sep 10, 2014

### kopinator

Ok, sweet. Thank you!

6. Sep 10, 2014

### Staff: Mentor

Great post BvU. Thank you.