Question

For a chemical reaction, \[\Delta S\]=-0.035\[\dfrac{\text{kJ}}{K}\] and `\[\Delta H\]=\[-20KJ\] . At what temperature does the reaction turn spontaneous?
a.) <5.14 K
b.) <57.14 K
c.) <571.4 K
d.) <5714.0 K

Answer 1

Hint: To find out the value of temperature we should know about Gibbs free energy equation. We should know that if the value of Gibbs free energy is negative then only reaction will occur.


Complete step by step solution:
Let us first know about Gibbs free energy equation. If we know about the Gibbs free energy function then we can find the answer to this question.
We should know that Gibbs free energy is equal to the enthalpy of the system minus the product of the temperature and entropy. The equation is given as;
G = H – TS
In the above reaction we should know that:
G = Gibbs free energy
H = enthalpy
 T = temperature
S = entropy
And also we should know that Gibbs free energy is a state function hence it doesn’t depend on the path. So, we can say that change in Gibbs free energy is equal to the change in enthalpy minus the product of temperature and entropy change of the system.
\[\Delta \text{G}=\Delta \text{H}-T\Delta S\]
Now, we will calculate the above question. But, first we will write down the above values that are present in question.
\[\Delta S\]=-0.035\[\dfrac{\text{kJ}}{K}\]
\[\Delta H\]=\[-20KJ\]
For the reaction to be spontaneous, the value of \[\Delta \text{G}\]has to be negative.
So, we can write the Gibbs free energy equation as:
\[\begin{align}
  & \Delta \text{G}=\Delta \text{H}-T\Delta S \\
 & \Delta S=\dfrac{\Delta \text{H}}{\Delta T} \\
 & T=\dfrac{\Delta \text{H}}{\Delta S} \\
\end{align}\]
So, now we will put the values and find the temperature.
\[T=\dfrac{-20}{-0.0035}=571.42K\]
So, from the above calculation we can say that the correct option is C.

Note: If we focus on the second law of thermodynamics, it states that entropy of the universe always increases for a spontaneous process. And also we should know that all spontaneous processes are thermodynamically irreversible. We should know that \[\Delta G\] determines the direction and extent of chemical change.