Ideal Gas Law: "Can I Use the Ideal Gas Equation of State?" Professor Amanda D

Home , Compressibility, Compressibility factor, Equation of state, Ideal gas, Specific volume, Weight

Ideal Gas Law: "Can I use the ideal gas equation of state?" Professor Amanda D. Smith

1 Is the substance in the gas phase? Formulations of the ideal gas equation

You’d be surprised where people try to use this. ME style:

2 Do you even need this equation? P v = RT

You may be able to calculate what you need from the problem PV = mRT statement. (e.g. Given the mass of a closed system and its initial ChemE style: volume, vi = Vi/m)

P v = RuT And if your problem statement says to treat the ﬂuid as an ideal gas, go right ahead. PV = NRuT

3 Can you find the values you need in the Formulations of the ideal gas equation thermodynamic tables? with compressibility factor correction

If so, just do that. Using these values is both straightforward and ME style: accurate.

P v = ZRT 4 Is this equation appropriate?

PV = mZRT Your options, in order of preference: ChemE style: 1. Calculate the compressibility factor Z if you have enough data. Use the correction factor in your ideal gas equation. P v = ZRuT

2. Estimate Z value using reduced pressure PR and reduced PV = ZNRuT temperature TR, and reading the compressibility chart. Use the correction factor in your ideal gas equation. Notation:

3. Compare your pressure with Pcr. Is it much, much smaller? m Mass N Number of moles 4. Compare your temperature with Tcr. Is it twice as big? P Pressure 5 What else can you do? PR Reduced pressure (relative to critical pressure), given by P/P cr

R Gas constant, unique to the substance 1. Use another, more accurate equation of state, such as: Ru Gas constant, universal

The gas constant R is the universal constant Ru divided by the molar mass • Beattie-Bridgeman (also called molecular mass or, unfortunately, molecular "weight"), which is just mass per unit mole. • Benedict-Webb-Rubin T ABSOLUTE temperature • Lee-Kesler TR Reduced temperature (relative to critical temperature), T/T cr

• van der Waals v Speciﬁc volume (per unit mass) v Molar speciﬁc volume (per unit mole) • virial expansion

Z Compressibility factor, given by P v/RT 2. Make the assumption that the gas behaves as ideal using This represents the ratio of the speciﬁc volume of your gas to the speciﬁc volume of your engineering judgment. an ideal gas.