Le Chatelier's Principle
If a system at equilibrium is subjected to a change of any one of the factors such as concentration, pressure or temperature, the system adjusts itself in such a way as to nullify the effect of that change.
Change of pressure : If a system consists of gases, then the concentration of all the components can be alterd by changing the pressure. To increase the pressure on the system,the volume has to be decreased proportionally. The total number of mols per unit volume will now be more and the equilibrium will shift in the direction in which there is a decrease in number of moles i,e. towards the direction in which there can be decrease in pressure.
Effect of pressure on melting point : There are two types of solids:
(a) Solids whose volume decreases on melting e.g., ice,diamond carborundum magnesium nitride and quratz.
Solids (higher volume)`hArr`Liquid (lower volume) The process of melting is facilitated at high pressure, thus, melting point is lowerd.
(b) Solids whose volume increase on melting e.g.,Fe,Cu,Ag,Au,etc.
Solid (lower volume)`hArr` Liquid (higher volume) In this case the process of melting become difficult at high pressure, thus melting point becomes high.
(c) Solubility of substances : When solid substances are dissolved in water, either heat is evolved (exothermic) or heat is absorbed (endothermic).
`KCI+aqhArrKCI(aq)-heat`
In such cases, solubility increase with increase in temperature. Consider the case of KOH, when this is dissolved,heat is evolved.
`KOH+aqhArrKOH(aq)+heat`
In such cases, solubility decrease with increase in temperature.
(d) Solubility of gases in liquids : When a gas dissolves in liquid,there is decrease in volume. Thus increase of pressure will favour the dissolution of gas in liquid.
Au(s)`hArr`Au(l)
Above equsilibrium is favoured at :

Options

A. High pressure low temperature
B. High pressure high temperature
C. Low pressure, high temperature
D. Low pressure, low temperature

Answer

To determine the conditions under which the equilibrium of the reaction \( \text{Au(s)} \rightleftharpoons \text{Au(l)} \) is favored, we can analyze the effects of temperature and pressure based on Le Chatelier's Principle.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
- The reaction involves the conversion of solid gold (Au) to liquid gold (Au). This is a phase change from solid to liquid.

2. **Determine the Enthalpy Change**:
- The melting of gold is an endothermic process, meaning it requires heat. Therefore, the enthalpy change (\( \Delta H \)) for this reaction is positive.

3. **Apply Le Chatelier's Principle for Temperature**:
- According to Le Chatelier's Principle, if we increase the temperature of an endothermic reaction, the equilibrium will shift to the right (towards the products) to absorb the added heat.
- Thus, higher temperatures will favor the formation of liquid gold.

4. **Consider the Volume Change**:
- When solid gold melts into liquid gold, the volume of the liquid is greater than that of the solid.
- According to the ideal gas law and the principles of pressure, increasing the volume of a system at equilibrium will favor the side with more moles of gas or, in this case, the side with greater volume (liquid).

5. **Apply Le Chatelier's Principle for Pressure**:
- Since the volume of the liquid is greater than that of the solid, increasing pressure will favor the side with fewer moles or lower volume. Therefore, to favor the equilibrium towards the liquid state, we need to decrease the pressure.

6. **Conclusion**:
- The conditions that favor the equilibrium of the reaction \( \text{Au(s)} \rightleftharpoons \text{Au(l)} \) are:
- **High Temperature** (to favor the endothermic melting process)
- **Low Pressure** (to favor the formation of the liquid state which has a higher volume)

### Final Answer:
The equilibrium is favored at **high temperature and low pressure**.