Ideal Gas Law

[shdw]

The density of a gas follows the Ideal Gas Law and varies inversely with temperature (measured in Kelvin) and directly with molar mass and pressure.

Ok so I am trying to make sense of scenarios:

1) Temperature is increased which results in a volumetric expansion of the gas and thus a decrease in density. It varies inversely. (Makes sense)

2) Pressure is increase, without a volumetric expansion, thus requiring more gas to increase that pressure or more matter. More matter with a constant volume equals more density. (Makes sense)

3) Take example 1 again. The temperature up and density down. According to the law, in this scenario, since the density went down the pressure should also go down.

P = nrt/v proves to me mathematically that the temperature going up should result in the pressure going up as well. But the wording of this passage makes it sound untrue. What am I missing?

 

[tgrayson]

P = nrt/v proves to me mathematically

since n = m/M, where M=molar mass, and m/V = ρ (density), the equation becomes

ρ = (MP)/(rT), which supports your quotation.

 

[charlie1017]

The statement you quote is a statement about how the pressure changes when you leave the other variables constant. In this case, for example, leaving the other variables constant and increasing only the temperature, the pressure increases.

The underlined statement is important, because the equation of state alone (the ideal gas law here) is not enough to determine the thermodynamic behavior of the gas. You must also know what kind of behavior you're dealing with (isothermal, adiabatic etc).

 

[shdw]

since n = m/M, where M=molar mass, and m/V = ρ (density), the equation becomes

ρ = (MP)/(rT), which supports your quotation.

Got it, thank you.