Calculating Pressure and Force from He Atoms Colliding with a Wall?

[higherme]

Homework Statement

A square box contain He at 25C. If the atoms collide with wall perpendicularly (90 degrees) at rate of 4.0E22 times/s, calculate pressure and force exerted on wall given area of wall 100cm^2 and speed of atoms =600 m/s

Homework Equations

PV=Nmv^2

The Attempt at a Solution

I'm not really sure what the N is... the question doesn't give the amount of He gas, so how do i know how many atoms there are? and the same for m...
otherwise, i can find V from area given; velocity also given, then i can find pressure

 

[higherme]

actually, for m, i can get from the molar mass and avogadro's number right?
but i still don't get what N is...

 

[Borek]

You don't need volume, gas density will be enough.

--
methods

 

[Dadface]

Homework Statement

A square box contain He at 25C. If the atoms collide with wall perpendicularly (90 degrees) at rate of 4.0E22 times/s, calculate pressure and force exerted on wall given area of wall 100cm^2 and speed of atoms =600 m/s

Homework Equations

PV=Nmv^2

The Attempt at a Solution

I'm not really sure what the N is... the question doesn't give the amount of He gas, so how do i know how many atoms there are? and the same for m...
otherwise, i can find V from area given; velocity also given, then i can find pressure

You could go to first principles:
.What is the momentum of one molecule on hitting the wall?
.What is the momentum when it bounces off?
.What is the momentum change?(remember momentum is a vector)
.Force is rate of change of momentum i.e.the total momentum change in 1 second so what is the force?

 

[higherme]

You could go to first principles:
.What is the momentum of one molecule on hitting the wall?
.What is the momentum when it bounces off?
.What is the momentum change?(remember momentum is a vector)
.Force is rate of change of momentum i.e.the total momentum change in 1 second so what is the force?

ok, so the momentum of 1 molecule hitting the wall is mv(mass x velocity)
when bounce off, the v is going to be in opposite direction so, change in momentum will be
mv - m(-v) = 2mv

so force = 2mv / time ? is this correct?
I have no idea what's next ...

 

[higherme]

So this is what i have:

F = change in momentum /time
F = 2mv /t

velocity is given in the question=600m/s , time is given = 4.0X10^22 times/s
m is I'm guessing the molar mass?

 

[Dadface]

So this is what i have:

F = change in momentum /time
F = 2mv /t

velocity is given in the question=600m/s , time is given = 4.0X10^22 times/s
m is I'm guessing the molar mass?

Your equation gives the change in momentum of a single molecule in one second i.e. the force exerted by the single molecule.If there were N molecules the total force would be
given by F=N2mv/t=2mv*N/t where N/t=number of collisions per second(4.0*10^22)

 

[higherme]

Your equation gives the change in momentum of a single molecule in one second i.e. the force exerted by the single molecule.If there were N molecules the total force would be
given by F=N2mv/t=2mv*N/t where N/t=number of collisions per second(4.0*10^22)

okay, that makes sense. But i still don't really get how to find the mass of He, which has to be in grams right...?

 

[higherme]

does the number of collision equals the number of molecules of He? If so, then i can get the # of moles from avogadro's number. Then with the moles, i can get grams of He using molar mass of He... can i do that?

m = 4.0X10^22 molecules * (1 mol/6.022E10^23 molecules) * (4.003 g/mol) He
=.266 g He
can someone double check.. thanks!

 

[Dadface]

m in the equation stands for the mass of a single helium atom which you can find from the mass of one mol of He divided by Avagadros number.To find F in N and P in N/m^2(Pa) you need to express m in Kg.