Each of the following statements is false. Rewrite each so that it makes a correct statement about free energy.
a. ΔGuniverse > 0 for any spontaneous process.
b. ΔH = ΔG TΔS.
a. ΔGuniverse < 0 for any spontaneous process.
To rewrite the statement, we need to understand the concept of free energy (G). Free energy is a thermodynamic potential that measures the maximum amount of work that can be extracted from a system at constant temperature and pressure. For a spontaneous process, the change in free energy of the universe (ΔGuniverse) must be negative.
To determine whether a process is spontaneous, we can use the equation ΔGuniverse = ΔGsystem + ΔGsurr, where ΔGsystem is the change in free energy of the system and ΔGsurr is the change in free energy of the surroundings. For a spontaneous process, the overall change in free energy of the universe must be negative, indicating that the process can occur without requiring external energy.
Therefore, we rewrite the statement as ΔGuniverse < 0 for any spontaneous process, which correctly reflects the concept of free energy.
b. ΔH = TΔS - ΔG
To rewrite the statement, we can use the Gibbs-Helmholtz equation, which relates the change in enthalpy (ΔH) to the changes in temperature (T), entropy (ΔS), and free energy (ΔG). The correct equation is:
ΔH = TΔS - ΔG
This equation shows that the change in enthalpy is related to the changes in temperature and entropy, with the addition of the negative value of the change in free energy. This equation is commonly used to calculate the change in enthalpy when the temperature and entropy changes are known.