A rxn has delta H ^0 rxn=-112kj and delta S^0 rxn =354 J/K. at what temp is the change in entropy for the rxn equal to the change in entropy for the surroundings?
Isn't dS surr = -dH/T and you want dS surr to = 354 J.
354 = -(-112000)/T
No. dS=-dH/T... solve for T
316K
To determine the temperature at which the change in entropy for the reaction is equal to the change in entropy for the surroundings, we can use the relationship:
ΔSuniverse = ΔSsystem + ΔSsurroundings
Given that ΔH^0rxn = -112 kJ and ΔS^0rxn = 354 J/K, we need to convert ΔH^0rxn to ΔS^0rxn in order to have consistent units for ΔS.
First, let's convert ΔH^0rxn from kJ to J:
ΔH^0rxn = -112 kJ = -112,000 J
We know that ΔS^0rxn is given as 354 J/K.
Now, we need to calculate ΔS^0surroundings. Using the equation:
ΔSuniverse = ΔSsystem + ΔSsurroundings
We can rearrange the equation to solve for ΔSsurroundings:
ΔSsurroundings = ΔSuniverse - ΔSsystem
Since we want ΔSsurroundings to be equal to ΔSsystem, the equation becomes:
ΔSsurroundings = 0
Therefore, ΔSuniverse = ΔSsystem.
Now, let's substitute the values into the equation:
0 = ΔSsystem + ΔSsurroundings
0 = ΔSrxn + ΔSsurroundings
0 = ΔS^0rxn + ΔSsurroundings
0 = 354 J/K + ΔSsurroundings
Solving for ΔSsurroundings:
ΔSsurroundings = -354 J/K
Now, we have ΔSsurroundings. Let's convert this value to kJ/K:
ΔSsurroundings = -354 J/K = -0.354 kJ/K
Since we have the values for ΔH^0rxn, ΔS^0rxn, and ΔSsurroundings, we can use the equation:
ΔH^0rxn = T * ΔS^0rxn - T * ΔSsurroundings
Rearranging the equation to solve for T:
T = ΔH^0rxn / (ΔS^0rxn - ΔSsurroundings)
Substituting the values:
T = (-112,000 J) / (354 J/K - (-0.354 kJ/K))
Simplifying:
T = (-112,000 J) / (354 J/K + 0.354 kJ/K)
T = (-112,000 J) / (354 J/K + 0.354 kJ/K)
T = (-112,000 J) / (354 J/K + 0.354 kJ/K)
T = (-112,000 J) / (354 J/K + 0.354 kJ/K)
T = (-112,000 J) / (354.354 J/K)
T = - 316.065 K
Since temperature cannot be negative, we can conclude that the change in entropy for the reaction is never equal to the change in entropy for the surroundings.