The following reation has the following standard thermodynamic parameters: delta H= -33.6 kJ/mol delta S= -59.8 J/(mol*K). C(g) + D(g) --> E(g)
Calculate the temperature at which the reaction becomes nonspontaneous.
dG = dH - TdS
Set dG = 0 and solve for T
T = dH/dS = -33.6/-0.0598 = ?
To determine the temperature at which the reaction becomes nonspontaneous, we can use the equation:
ΔG = ΔH - TΔS
Where:
ΔG = Gibbs free energy
ΔH = enthalpy change
T = temperature
ΔS = entropy change
At the nonspontaneous condition, ΔG will be equal to zero:
0 = ΔH - TΔS
Rearranging the equation, we can solve for T:
T = ΔH / ΔS
Substituting the given values:
T = (-33.6 kJ/mol) / (-59.8 J/(mol*K))
Converting the units to have consistent kilojoules and joules:
T = -33.6 kJ/mol / (-59.8 kJ/(mol*K))
T = 0.561 K
Therefore, the reaction becomes nonspontaneous at a temperature of approximately 0.561 K.
To calculate the temperature at which the reaction becomes nonspontaneous, you can use the equation:
ΔG = ΔH - TΔS,
where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
Since the reaction becomes nonspontaneous when ΔG is positive, we can set ΔG equal to zero and solve for T:
0 = ΔH - TΔS.
Rearranging the equation, we get:
T = ΔH / ΔS.
Now, let's substitute the values given in the problem:
ΔH = -33.6 kJ/mol,
ΔS = -59.8 J/(mol*K).
First, we need to convert ΔH from kJ to J:
ΔH = -33.6 kJ/mol * 1000 J/1 kJ = -33,600 J/mol.
Now, we can substitute these values back into the equation to calculate the temperature:
T = (-33,600 J/mol) / (-59.8 J/(mol*K)).
Calculating this gives us:
T ≈ 562.9 K.
Therefore, the temperature at which the reaction becomes nonspontaneous is approximately 562.9 Kelvin.