Homework Help: Where's my particle?

1. Feb 23, 2015

Jilly

A. Given that the average diameter of all particles in a sample is 16 nm, te density of all particles is 1.25 x 10^-4 g/cm^3, and the density of the sample of air is 100 microgram/cm^3, how many particles are in 1 L of this air sample?

V(particle) =2.14x10^-18 cm^3
x density = 2.675x10^-22 g

1 L = 1000cm^3
1000cm^3x100microgram/cm^3 = 100000 microgram= 0.1g

0.1g/2.675x10^-22 = 3.74x10^20 particles

B. In what layer of the atmosphere was this sample of air likely taken from (you can assume a sea level temperature of 15C)?

3.74x10^20 particles/ 6.02x10^23 particales/mol = 6.21 moles

P = [(6.21 mol)(0.08206L•atm/mol•K)(288K)]/1L = 0.015 atm ... Aaaaand that's where I get stuck,

I'm pretty sure I'm supposed to use the equation:
P(h) = P(0) x e^-Mgh/RT

Where:
P(h) = pressure at any given height
P(0) =pressure at sea level
M = 28.97 g/mol
g = 9.81 m/s^2
R = 0.08206 L•atm/K•mol

And solve for h to determine the height my particle is at and then reference atmospheric layers but... I have too many extra variables....

2. Feb 23, 2015

SteamKing

Staff Emeritus
How do your get 6.21 moles from 3.74*1020 particles / 6.02*1023 particles/mol?

An order of magnitude calculation suggests n = 1020 / 1023, which is nowhere close to 6.

3. Feb 23, 2015

Jilly

The Calc for pressure is still 0.015.
Number of moles should equal 0.000621

4. Feb 23, 2015

SteamKing

Staff Emeritus
Which extra variables do you have which are preventing you from finding the altitude?

5. Feb 23, 2015

Jilly

Well, in order to calculate for 'h' I'd need P(h), and Temperature at P(h) ...

6. Feb 23, 2015

Jilly

I just don't understand what I'm not seeing to solve this... What am I missing? =\

7. Feb 24, 2015

SteamKing

Staff Emeritus
8. Feb 24, 2015

Jilly

The equation I posted is equation 2 on that page.

9. Feb 24, 2015

SteamKing

Staff Emeritus
Then, if you read that page carefully and check the definition of the variables for equation 2, you'll find that you know all that you need in order to find the altitude where the sample could have been taken.

Remember, the pressure of 0.015 atm. is the pressure at altitude. If you carefully list all of the variables and their values, you'll find that altitude is the only one which is unknown.

10. Feb 24, 2015

Jilly

Hmmmm
0.015 is pressure at sea level...

so 0.015 should be P(0)

Is it that I'm simply misunderstanding the question and I should assume that temperature of 15C is constant? But how would I find pressure at the height the particle is at? And if I'm not assuming the temperature is constant (since in real life it obviously wouldn't be) how do I calculate that? I'm pretty sure I'm just not understanding the information given...

11. Feb 24, 2015

SteamKing

Staff Emeritus
Really? I thought the pressure at sea level on earth was, you know, 1 atmosphere. It's kinda like a definition, or something.

Read Post #9 more carefully, especially the last two sentences.

From the Wiki article on the Barometric Formula:

Read the quoted section above carefully. You should have enough information now to solve your problem.