Using the Gibbs Phase Rule, determine the number of degrees of freedom and also

Question

Using the Gibbs Phase Rule, determine the number of degrees of freedom and also the variables that must be given for the system to be thermodynamically specified: (a) Air (assume N2, O2, Ar and CO2 only, in a fixed ratio) dissolved in the Schuykill River. (b) Air (assume N2, O2, Ar and CO2 only, in a fixed ratio) dissolved in the Schuykill River, which contains one organic pollutant that has been decomposing into H2O and CO2 for so long that the decomposition reactions have reached equilibrium. (c) Air dissolved in the Dead Sea (which is forming salt precipitates at the shore) (d) The gas from the outlet of a power plant furnace containing saturated water vapor, nitrogen, oxygen, CO2, and small particles of carbon. Assume the combustion reactions have reached equilibrium. (e) Molten steel (which is made of carbon and iron) in equilibrium with grains of the ledeburite and cementite phases of solid steel.

Explanation / Answer

Answer

a) Air (assume N2, O2, Ar and CO2 only, in a fixed ratio) dissolved in the Schuykill River

C=5 (including H2O) (all independent species or components)

P=2, liquid H2O and dissolved gases (phases are separated by no boundary)

F=C-P+2 (2 stands temperature and pressure)

F=5-2+2=5 (degrees of freedom ,no of independent intensive variables)

b) Air (assume N2, O2, Ar and CO2 only, in a fixed ratio) dissolved in the Schuykill River, which contains one organic pollutant that has been decomposing into H2O and CO2 for so long that the decomposition reactions have reached equilibrium

C=6 (pollutant also exists at eqm)

P=3 (solid=pollutant)

F=6-3+2=5

(c) Air dissolved in the Dead Sea (which is forming salt precipitates at the shore)

C=3 (air ,water ,ppt )

P=3

F=3-3+2=2

(d) The gas from the outlet of a power plant furnace containing saturated water vapor, nitrogen, oxygen, CO2, and small particles of carbon. Assume the combustion reactions have reached equilibrium.

C=5

P=2 (carbon =solid)

F=5-2+2=5

. (e) Molten steel (which is made of carbon and iron) in equilibrium with grains of the ledeburite and cementite phases of solid steel.

C=2 (carbon and iron)

P=3 (steel, the ledeburite and cementite)

F=2-3+2=1

Explanation= The gibbs rule applies only to non-reactive multi-component but heterogeneous systems present in thermodynamic equilibrium.

The rule is,

    F = C - P + 2

where F = number of degrees of freedom, C =number of components and P= number of phases in equilibrium with each other.(two liquids in equilibrium with each other, but having distinct boundary are two phases)

phases are solids, liquids and gases. Other F=, temperature and pressure)

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