Question

The degree of freedom for the system \[H{{O}_{\left( s \right)}}\rightleftharpoons \text{ }H{{O}_{\left( l \right)}}\] is-
A.1
B.0
C.2
D.-1

Answer 1

Hint: Degree of freedom for a system is dependent on the Phase rule. According to the law, the system is in thermodynamic equilibrium between two or more same or different components. It relates the existing number of constituents, phases and degrees of freedom present in a chemical system.

Complete answer:
We have to find the degree of freedom for the system,
\[H{{O}_{\left( s \right)}}\rightleftharpoons \text{ }H{{O}_{\left( l \right)}}\]
Here, there is equilibrium between solid state and liquid state of water. The component is same and the phases are different.
Using the formula for the Gibbs Phase rule,
\[F\text{ }=\text{ }C\text{ }\text{ }P\text{ }+\text{ 2}\]
So,
$F=$Degree of freedom
$C=$Number of components
$P=$Number of Phases
For the given system-
$C=1$ and $P=2$
Substituting the values of $C$ and$P$in the Gibbs Phase formula
\[\begin{align}
  & F\text{ }=\text{ }C\text{ }\text{ }P\text{ }+\text{ }2 \\
 & F=\text{ 1- 2 + 2} \\
 & \text{F = -1 + 2} \\
 & \therefore \text{ F = 1} \\
\end{align}\]
Thus, the degree of freedom for the system \[H{{O}_{\left( s \right)}}\rightleftharpoons \text{ }H{{O}_{\left( l \right)}}\] is 1.

Note:
There will be three phases that represent states of matter- solid, liquid and vapour/steam/gas. They have different physical and chemical properties, as the phases are distinct. In the phase diagram, when all the three phases exist in equilibrium it is called the triple point or the invariant point. At this point the temperature and pressure are unique and the degree of freedom is zero. Also, F i.e. degree of freedom is also referred to as “variance of the system”.
With two phases and one component, for example- solid and liquid- there is only one degree of freedom and the pressure is different at particular temperature. While with two phases and two components the pressure is the same at different temperatures.