Solving Interstellar Gas Pressure: A Daunting Task

[chineseman1]

I have been trying to do this questions for about 30 minutes right now and its a one dot questions. I think I am converting the atoms wrong. Could someone help me?

A typical region of interstellar space may contain 10^6 atoms per cubic meter (primarily hydrogen) at a temp of 100 K. What is the pressure of the gas?

>Okay, what I have done was use PV=nrT, but I am having trouble converting it. Do I take the atoms and divide by avogadros?

Thank You.

 

[Integral]

It depends on what value of r you are using. Your units need to match.

 

[chineseman1]

I am using 8.31.

 

[LeonhardEuler]

For future reference you should post homework problems in the homework section-where this thread will probably be moved to in a minute anyway.

Anyway, you have 10⁶ atoms in 1 m³. 10⁶ atoms is:
$$10^6 atoms\times\frac{1mol}{6.02\times 10^{23} atoms}\approx1.66mol$$
in one m³. Convert m³ to L by multiplying by 1,000 then you can use the ideal gas law.

 

[LeonhardEuler]

I am using 8.31.

Always keep in mid what units you are using. $R=8.31\frac{J}{K\cdot mol}$ so you better not convert to liters after all because $1J=1\frac{kg\cdot m^2}{s^2}$, so the unit of volume is the m³

 

[chineseman1]

Okay. So I was doing it right!
But when I do use the Ideal Gas Law I get 1.37E-19, while the answer in my book is 10^-15. So I really don't know what I am doing wrong here. I as doing P= nRT/V, so I just plugged in all my variables and still not getting right answer.

 

[Bystander]

Okay. So I was doing it right!
But when I do use the Ideal Gas Law I get

1.37E-19,

while the answer in my book is 10^-15. So I really don't know what I am doing wrong here. I as doing P= nRT/V, so I just plugged in all my variables and still not getting right answer.

Take another look at your bookkeeping on exponents.

And, review comments on significant figures.

 

[LeonhardEuler]

Okay. So I was doing it right!
But when I do use the Ideal Gas Law I get 1.37E-19, while the answer in my book is 10^-15. So I really don't know what I am doing wrong here. I as doing P= nRT/V, so I just plugged in all my variables and still not getting right answer.

What units is your answer in?
What are the units of the answer in the book?
Are you sure you didn't convert your volume to liters? You should keep it as 1m³

 

[chineseman1]

I got in! It was sig figs, the killer of me. Thanks to all you guy physics gurus!