Question

(10 points) Question 2 Why is “generalized compressibility chart” used? Explain the purpose. (10 points) Question 3 Explain the difference between R and Ru. How are these two related?

Answer 1

1) The generalized compressibility chart is a useful tool for predicting the properties of gases or gas mixtures with acceptable accuracy for most enginering purpose.

it shows the p-v-T relation for gases .

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.

The accuracy of PV = nRT can be judged is by comparing the actual volume of 1 mole of gas (its molar volume, V_m) to the molar volume of an ideal gas at the same temperature and pressure. This ratio is called the compressibility factor (Z) with:

  

Z= molar volume of gat at same T and P molar volume of idean gas at same T and P = (PVm/RT) measured

Ideal gas behavior is therefore indicated when this ratio is equal to 1, and any deviation from 1 is an indication of non-ideal behavior.

2.0 1.5 z (kPa) N2 CHA H2 Ideal gas 1.0 02 CO2 0.5 0 0 200 400 800 1000 600 P (atm)

A graph of the compressibility factor (Z) vs. pressure shows that gases can exhibit significant deviations from the behavior predicted by the ideal gas law. from the above chart, at very low values of pressure, all the gases show Z ≈ 1 and behave almost ideally. At high pressure, on the other hand, all the gases have Z > 1 which makes them more difficult to compress than an ideal gas. as pVm > RT.

In such cases, repulsive forces become predominant. At intermediate values of pressure, the majority of gases displays Z < 1, which indicates that attractive forces are predominant and, therefore, compression turns out to be favoured.

2) Specific gas constant(R): which is associated with each gas and have units of (Jole│kelvin.mole) and it is different for each gas.

Universal gas constant(Ru):which is Boltzmann constant times Avogadro number and it is approximately equal to 8.31446(Jole│kelvin.mole) and it is constant for all gases.

They are related as R=Ru/M.
Where M is the molar constant of the gas or molecular weight be of the gas.