Concentration of Molecules in the Air

[MysticDude]

Homework Statement

At a height of 300km above the Earth's surface, an astronaut finds that the atmospheric pressure is about 10^-8 mmHg and the temperature 500 K. How many molecules are there per milliliter at this altitude?

Homework Equations

The Attempt at a Solution

I first thought that I had to calculate the amount of moles in area then multiply that by Avogadro's number. But then I realized that there is no amount of volume given here, only the height, as I was thinking about using the Ideal Gas Law. All I need is the volume, but I don't know how to get it. Was I even on the right track here?

 

[Coto]

$PV = nRT \implies V/n = RT/P \implies n/V = P/RT$. To simplify your calculation, take the universal gas constant to be: $R = 0.08206 \frac{\textrm{atm}\cdot\textrm{L}}{\textrm{K}\cdot\textrm{mol}}$.

 

[MysticDude]

$PV = nRT \implies V/n = RT/P \implies n/V = P/RT$. To simplify your calculation, take the universal gas constant to be: $R = 0.08206 \frac{\textrm{atm}\cdot\textrm{L}}{\textrm{K}\cdot\textrm{mol}}$.

Yes, but I'm missing the volume. I only have the 300 km in the air for information.

 

[Coto]

They're looking for mols/mL ... so no, you don't need a volume, you need an n/V ... which only requires knowledge of P and T. (Liter is a measure of volume).

 

[Borek]

You are given volume. They ask for number of molecules per milliliter.

 

[MysticDude]

Okay, so by using Coto's equation, I get 3.207 x 10^-13$$\frac{mol}{L}$$.
So to get $\frac{molecules}{milliliter}$, I would have to do this:
$$3.207 x 10^{-13}\frac{mol}{L} x \frac{1 L}{1000 mL} x 6.022x10^{23}\frac{molecules}{mol}$$...in order to get my answer, right?

 

[Coto]

Exactly... except $N_A = 6.022 \cdot 10^{23}\frac{\textrm{moleculues}}{\textrm{mol}}$. Not -23 :).

 

[MysticDude]

Exactly... except $N_A = 6.022 \cdot 10^{23}\frac{\textrm{moleculues}}{\textrm{mol}}$. Not -23 :).

I changed that a minute after I saw the negative. I guess the picture didn't update o.o

Anyway, I got something like 192764220 molecules/milliliter. Can you compare?

 

[Borek]

Close enough to what I get. Watch significant figures.

 

[MysticDude]

Close enough to what I get. Watch significant figures.

I know that I should watch significant numbers. I just plugged in everything directly into my calculator. Thanks a bunch for checking!