Thermodynamics- Mixtures

Question 1

Molar analysis

Answer 1

Specifying the number of moles of each component in the mixture

Question 2

Gravimetric analysis

Answer 2

Specifying the mass of each component in the mixture

Question 3

In the topic of mixtures, what do the symbols: m, k, N, y, mf, M, R and the subscripts: m, i and u mean?

Answer 3

m means mass. k is number of components. N is number of moles. y is mole fraction. mf is mass fraction. M means molar mass. R is gas constant. Subscripts- m is mixture, i is specific component, u is universal.

Question 4

What is the mass and mole fraction of a component in a mixture?

Answer 4

The ratio of the mass/mole number of the component to the mass/mole number of the mixture

Question 5

Ways of calculating apparent or average molar mass of mixture, Mm

Answer 5

Equal to mm/Nm and Σmi/Nm and Σ(NiMi)/Nm and ΣyiMi from 1 to k.

Question 6

Formula for gas constant if the mixture

Answer 6

Rm=Ru/Mm

Question 7

What is Dalton’s law of additive pressures in words and formula and when does it hold?

Answer 7

The pressure of a gas mixture is equal to the sum of the pressures each gas would exert if it existed alone at the mixture temperature and volume. Formula
Pm=ΣPi(Tm,Vm) from 1 to k
Holds exactly for ideal gas mixtures but only approximately for real ones

Question 8

What is Amagat’s law of additive volumes in words and formula and when does it hold?

Answer 8

The volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed alone at the mixture temperature and pressure. Formula
Vm=ΣVi(Tm,Pm) from 1 to k
Holds exactly for ideal gas mixtures but only approximately for real ones.

Question 9

What is the pressure and volume fraction of a component in a gas mixture?

Answer 9

Pi/Pm

Vi/Vm

Question 10

Which fractions are equivalent to the mole fraction of a component in an ideal-gas mixture?

Answer 10

Pressure fraction, volume fraction

Question 11

Formula for partial pressure and volume of a component in a mixture

Answer 11

Partial pressure yiPm

Partial volume yiVm

Question 12

Ways of finding compressibility factor of a mixture and when to use each method

Answer 12

Use formula Zm=ΣyiZi from 1 to k
Each Zi can be determined either at Tm and Vm for Dalton’s law or Tm and Pm for Amagat’s law. You use these values to find Z on the individual gas’s compressibility chart. Amagat’s law uses mixture pressure Pm which accounts for the influence of intermolecular forces between the molecules of different gases unlike for Dalton’s law. Therefore Amagat’s law is more appropriate for high pressures and Dalton’s law more appropriate for low pressures.

Question 13

How can internal energy, enthalpy and entropy of a mixture be calculated using summations of its components?

Answer 13

The sum of each of these properties for the individual components. The sum of the mass of times the specific of these properties for the individual components. The sum of the moles of times the per mole of these properties for the individual components. All summations from 1 to k.

Question 14

How can specific internal energy, enthalpy and entropy of a mixture be calculated using summations of its components?

Answer 14

Sum from 1 to k of the mass fraction of each component times it’s specific property. Same works for properties per unit mole if you use mole fraction instead of mass fraction.

Question 15

How can the specific heats of a mixture be calculated using summations of its components?

Answer 15

Same way as specific internal energy, enthalpy and entropy where you use the mass or mole fraction as appropriate.

Question 16

Gibbs-Dalton law

Answer 16

Under the ideal-gas approximation, each gas component in the mixture behaves as if it exists alone at the mixture temperature Tm and mixture volume Vm.