Ideal Gas Density: PV=mRT Explained

In summary, the equations PV=mRT and PV=nRT have different values for R because they have different units. The latter equation should be written as PV = mRspecific T to make this distinction clear. Rspecific is equal to R divided by the molar mass of the gas, making it more convenient for relating pressure to density.
  • #1
goldfish9776
310
1

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

 

Attachments

  • 0049.jpg
    0049.jpg
    58.1 KB · Views: 346
Physics news on Phys.org
  • #2
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)
 
  • #3
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.
 
  • #4
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
 
  • Like
Likes goldfish9776

1. What is the ideal gas law and how does it relate to gas density?

The ideal gas law, PV = nRT, is a fundamental equation in thermodynamics that describes the relationship between the pressure (P), volume (V), temperature (T), and amount (n) of a gas. When rearranged, this equation can be used to calculate the density (m/V) of an ideal gas.

2. What does the variable 'R' represent in the ideal gas law equation?

The variable 'R' represents the ideal gas constant, which is a universal constant that relates the properties of an ideal gas. Its value is 0.0821 L·atm/mol·K at standard temperature and pressure (STP).

3. What is the significance of the ideal gas law in scientific research?

The ideal gas law is a crucial tool in many scientific fields, including chemistry, physics, and engineering. It allows researchers to predict and understand the behavior of gases under different conditions, which is essential in various experiments and industrial processes.

4. How does temperature affect the density of an ideal gas?

According to the ideal gas law, as temperature increases, the volume of an ideal gas also increases. This means that the density of the gas decreases because the same amount of gas is occupying a larger volume. Therefore, temperature has an inverse relationship with gas density.

5. Can the ideal gas law be applied to real gases?

The ideal gas law is a simplified model that applies to hypothetical ideal gases that have no intermolecular forces and occupy no volume. In reality, most gases deviate from this ideal behavior at high pressures and low temperatures. However, for most practical purposes, the ideal gas law is a good approximation for real gases under normal conditions.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
663
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
953
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
8K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top