How Many Molecules in 1 mL of a Vacuum at 27.0 degrees Celsius?

[maceng7]

Homework Statement

A vacuum pump on Earth can produce a vacuum with a pressure as low as 1.00*10^-8 torr. How many molecules are present in each mL at a temperature of 27.0 degrees Celsius?

V = 1mL = 10^-3 L <-- How many sig figs should I use here? Should I make it 1.00*10^-3L or keep it 10^-3L?
P = 1.315789 atm
T = 300.15 K
n = ?

Homework Equations

Pv = nRT

The Attempt at a Solution

PV =nRT

n = PV / RT

= (1.315789atm)(1.00*10^-3L) / (0.08206 Latm / Kmol)(300.15K)

= 5.342156*10^-16mol * 6.022*10^23 molecules

= 3.22*10^8 molecules / L <--- How do I change my answer back to how many molecules/mL and how many sig figs should my answer reflect? 1 or 3?

 

[jedishrfu]

isnt a liter = 1000 mL

 

[maceng7]

Yeah so would I just multiply my answer by 1000?

 

[jedishrfu]

okay so think a liter is 1000 times bigger than a mL right? so that means it can hold 1000
times the # of molecules that an mL would have? so do you multiply or divide?

 

[maceng7]

my mistake, yeah I'd definitely divide my answer by 1000. Also for sig figs, since the question says "one milliliter" how many digits should I interpret that as? Should I let the volume = 1mL, which would give me one sig fig in my answer or should I just make it 1.00mL and include 3 sig figs in my answer?

 

[jedishrfu]

there's rules for how to treat sig figures usually the value with the least # of sig figures dictates what you can say.

here's the rules from wikipedia:

http://en.wikipedia.org/wiki/Significant_figures

 

[Borek]

Your answer was already correct - you used 10^-3L as a volume, so you calculated number of moles in 1 mL. You added L at the very end of the calculation out of nothing, confusing yourself.

Question says "in each mL" which probably means "exactly mL" - so there is as many significant digits as you want. Sure, it doesn't make sense to report all digits your calculator displays - I would go with three.