To determine whether the decomposition of red mercury(II) oxide (HgO) is spontaneous under standard state conditions and to find the temperature above which it becomes spontaneous, we need to consider the Gibbs free energy change (ΔG) for the reaction. Here's a step-by-step approach:
### Part (a): Determine if the Decomposition is Spontaneous Under Standard State Conditions
1. Gibbs Free Energy Change (ΔG):
The spontaneity of the reaction under standard state conditions (25°C or 298K) is determined by the Gibbs free energy change, which is given by the equation:
[tex]\[
\Delta G = \Delta H - T \Delta S
\][/tex]
where:
- ΔH is the enthalpy change of the reaction.
- ΔS is the entropy change of the reaction.
- T is the temperature in Kelvin.
2. Standard State Conditions:
Under standard state conditions (1 atm pressure, 298K), we need the standard enthalpy change (ΔH) and the standard entropy change (ΔS).
3. Calculating ΔG:
For the reaction to be spontaneous, ΔG must be negative (ΔG < 0).
4. Availability of ΔH and ΔS:
Without the specific values for ΔH and ΔS for the reaction, we cannot compute ΔG directly. Therefore, we cannot definitively determine the spontaneity of the reaction under standard state conditions.
Conclusion for Part (a):
We cannot determine if the decomposition of red mercury(II) oxide is spontaneous under standard state conditions without the values of ΔH and ΔS.
### Part (b): Determine the Temperature Above Which the Reaction Becomes Spontaneous
1. Condition for Spontaneity:
For the reaction to be spontaneous, the Gibbs free energy change must be negative:
[tex]\[
\Delta G < 0
\][/tex]
2. Gibbs Free Energy Equation:
Using the Gibbs free energy equation:
[tex]\[
\Delta G = \Delta H - T \Delta S
\][/tex]
we set ΔG < 0 for spontaneity:
[tex]\[
\Delta H - T \Delta S < 0
\][/tex]
3. Solving for Temperature (T):
Rearrange the inequality to solve for T:
[tex]\[
T > \frac{\Delta H}{\Delta S}
\][/tex]
4. Values Needed:
To find the specific temperature, we need the values of ΔH (enthalpy change) and ΔS (entropy change) for the reaction. Without these values, we cannot calculate the temperature explicitly.
Conclusion for Part (b):
We cannot determine the temperature above which the reaction becomes spontaneous without knowing the values of ΔH and ΔS.
### Final Summary:
- For part (a), we cannot determine if the decomposition of red mercury(II) oxide is spontaneous under standard state conditions due to the lack of ΔH and ΔS values.
- For part (b), we cannot find the temperature above which the reaction becomes spontaneous without the specific values of ΔH and ΔS.
