Question

Sulfur dioxide, and only sulfur dioxide, is contained in a stainless steel tank. The temperature and pressure inside the tank can be adjusted to any desired values. What is the maximal number of solid forms of sulfur dioxide that can exist inside the tank? If liquid sulfur dioxide is present, how many solid forms can exist? If instead of a liquid the vapor form of sulfur dioxide is present, how many solid forms can exist? Finally, suppose both a vapor and liquid are present. Again, how many forms of solid sulfur dioxide can coexist with the vapor and liquid? How would your answers change if water, rather than sulfur dioxide, was the contained material. (This is meant to be a straightforward application of the Gibbs phase rule).

Answer 1

Gibbs phase rule applies to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium.

The phase rule is given as:

F= C-P+2

F= Intensive degrees of freedom i.e. the number of intensive variables that can be changed independently without disturbing the number of phases in equilibrium

P= number of phases i.e. gas, homogeneous liquid phases, homogeneous solid phases

C= components i.e. minimum number of independent constituents

For a glass of liquid water,

F= 2 since, temperature and pressure are independant variables.

i.e. F= C-P+2

C=1, P=1

F= 1 -1 +2 =2

For a glass of boiling water in equilibrium with saturated steam.

F= C-P+2 = 1-2+2= 1

In this case, one of the independent intensive variables i.e. pressure is defined, for eg. 1 atm. At this pressure, the temperature has to be 100 degrees for water to boil. So, temperature cannot be chosen independently of pressure when iquid and vapor are present.

Vapor, solid and liquid state of water

At the triple point; vapor, liquid and solid states coexist. The triple point occurs only at one specific pair of temperature and pressure for any given substance. Once the triple point is stated, its values can be obtained from a graph. So, thermodynamic properties cannot be chosen independently.

i.e. F=  C-P+2 = 1-3+2 = 0

Solid forms of SO₂

F= 2, since it is given that temperature and pressure can be varied to any desired value

P=1

From phase rule,

F= C-P+2 i.e. C= F+P-2

So, C= 2+1-2=1

Solid and liquid SO₂ exist.

C= 2 +2-2= 2

Vapour and solid SO₂ exist.

C= 2+2-2= 2

Vapour and solid SO₂ exist.

C= 2+2-2= 2

Solid SO₂ coexit with vapour and liquid.

C= 2+3-2= 3