How Do You Calculate Molecules Per Unit Volume from Pressure and Temperature?

[MetalCut]

Hi.

Can someone maybe give me an equation to determine the number of molecules per unit volume (N/V) when the pressure(P) and the temperature(T) is given. The pressure is in PA and the temperature is in Kelvin.

Thanx

 

[dav2008]

The ideal gas law says that for an ideal gas: PV=NkT where P, V, and T are pressure (Pascals), volume(m^-3), and temperature(K) respectively, N is the number of molecules, and k is Boltzmann's constant of 1.381 × 10⁻²³ J/K

 

[MetalCut]

I know that one. But the volume is not given, so how can i get the N/V, the number of molecules per volume?

 

[dav2008]

Can you solve the ideal gas law for N/V?

 

[MetalCut]

Yeah, so I must determine the volume first before I can determine the number of molecules. Let me give you the question. Maybe you can point out what I am misssing.

On the sunlit surface of Venus, the atmospheric pressure is 9.0 x 10 6Pa, and the temperature is 740K. On the Earth's surface the atmospheric pressure is 1.0 x 10 5Pa, while the surface temp can reach 320K. These data imply that Venus has a "thicker" atmosphere at its surface than does the earth, which means that the number of molecules per unit volume (N/V) is greater on the surface of Venus than on Earth. Find the ratio (N/V)venus / (N/V)earth.

Thanx

 

[dav2008]

Why do you want to solve for the number of molecules?

You are trying to solve for N/V. Solve for N/V in the ideal gas law and see what it is dependent on.

 

[MetalCut]

Ok but isn't N the number of molecules?

 

[Hootenanny]

Ok but isn't N the number of molecules?

Yes, N is the number of molecules, so as dav2008 says, solve for N/V and you will have your answer.

-Hoot

 

[MetalCut]

Ok Thanx man.