under what conditions could the decomposition of Ag2O(s) into Ag(s) and O2(g) proceed spontaneously at 298 K?
2Ag2O(s)---->4Ag(s)+O2(g) dG=22.42 Kj
answer= 0.000118 atm.
To determine the conditions under which the decomposition of Ag2O(s) into Ag(s) and O2(g) could proceed spontaneously at 298 K, we need to assess the Gibbs free energy change (∆G) of the reaction.
∆G represents the maximum amount of non-expansion work that can be obtained from a system, and it is an indicator of the spontaneity of a reaction. If ∆G is negative (∆G < 0), the reaction is spontaneous under the given conditions.
In this case, you've provided the ∆G value for the reaction, which is 22.42 kJ. However, to determine the pressure of O2(g) at which the reaction becomes spontaneous, we need to use the following equation that relates ∆G, temperature (T), and the equilibrium constant (K):
∆G = -RT ln(K)
Where:
∆G: Gibbs free energy change (-RT ln(K))
R: Gas constant (8.314 J/(mol·K))
T: Temperature in Kelvin (298 K)
ln: Natural logarithm
K: Equilibrium constant
We can rearrange the equation to solve for the equilibrium constant:
K = e^(-∆G / RT)
Now, we can substitute the given values into the equation:
K = e^(-22.42 × 10^3 J / (8.314 J/(mol·K) × 298 K))
After evaluating this, we obtain the equilibrium constant (K) for the reaction. Since this reaction involves the decomposition of Ag2O(s), the equilibrium constant is related to the partial pressure of O2(g). To determine the pressure of O2(g) at which the reaction becomes spontaneous, we need to solve for the partial pressure of O2(g) in the equilibrium expression.
Let's assume the partial pressure of O2(g) is P. According to the balanced equation, for every two moles of Ag2O(s) decomposed, we obtain one mole of O2(g). Therefore, the equilibrium constant expression for the reaction can be written as:
K = [P(O2)] ^ 1
Since the coefficient for O2(g) is 1, the partial pressure of O2(g) is equal to K. Hence, we need to solve for K:
K = 0.000118 atm.
Therefore, the partial pressure of O2(g) at which the decomposition of Ag2O(s) into Ag(s) and O2(g) proceeds spontaneously at 298 K is 0.000118 atm.