Ideal Gas Density: PV=mRT Explained

[goldfish9776]

Homework Statement

in this notes , i was told that the PV=mRT , why ? shouldn't PV= NRT , N=number of moles ? it should be PV = m/M (RT) , right ?

Homework Equations

The Attempt at a Solution

 

[stockzahn]

The R is different in the two equations:

1) PV=mRT ... R in J/(kg⋅K) is variable and depends on the kind of gas (you find the values in tables)
2) PV=nR_mT ... R_m in J/(mol⋅K) is constant (≈ 8.314)

 

[BvU]

The text is perfectly clear. Read it carefully. They use R for a 'constant' that is different for each gas and $R_u$ for what we normally call the gas constant.

 

[SteamKing]

Homework Statement

in this notes , i was told that the PV=mRT , why ? shouldn't PV= NRT , N=number of moles ? it should be PV = m/M (RT) , right ?

Homework Equations

The Attempt at a Solution

What is not made clear in your text is that the R in PV = n RT and the R in PV = m RT have different values because they have different units.

In fact, the latter equation should be PV = m R_specific T to make this distinction clear.

R = 8.314 J / mol / °K, while R_specific = R / M, where M is the molar mass of a particular gas, in kg / mol

For example, R_specific for oxygen is 8.314 / 0.032 = 259.81 J / kg / °K, since M for oxygen is 0.032 kg / mol, approximately.

https://en.wikipedia.org/wiki/Gas_constant

If PV = m R_specific T, then ρ = m / V, and the equation becomes P = ρ R_specific T