Ideal Gas Density: PV=mRT Explained

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Homework Help Overview

The discussion revolves around the ideal gas law, specifically the equations PV = mRT and PV = nRT. Participants are exploring the differences between these equations, particularly focusing on the constants involved and their units.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the use of different constants in the equations, noting that R varies depending on whether it is expressed per mole or per mass. Others suggest that the distinction between R and Rspecific should be clarified to avoid confusion.

Discussion Status

Participants are actively discussing the differences in the gas constant R and its implications for the equations. There is an emphasis on understanding the units and the context in which each form of the ideal gas law is applied. No consensus has been reached, but there are productive clarifications being made regarding the constants involved.

Contextual Notes

Some participants note that the original text may not clearly differentiate between the constants, leading to confusion about their application in the equations. The discussion also highlights the importance of understanding the specific gas constants in relation to their molar masses.

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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

 

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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=nRmT ... Rm in J/(mol⋅K) is constant (≈ 8.314)
 
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.
 
goldfish9776 said:

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 Rspecific T to make this distinction clear.

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

For example, Rspecific 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 Rspecific T, then ρ = m / V, and the equation becomes P = ρ Rspecific T
 
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