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What is the change in temperature in K if the change in entropy is [tex]150 \, \text{J} \, \text{K}^{-1} \, \text{mol}^{-1}[/tex], the change in enthalpy is [tex]-99.3 \, \text{kJ/mol}[/tex], and the change in Gibbs free energy is [tex]-105 \, \text{kJ/mol}[/tex]?

Answer :

The change in temperature, given the changes in entropy, enthalpy, and Gibbs free energy, Gibbs free energy resulting in a temperature change of 780 Kelvin.

Calculating the Change in Temperature Using Thermodynamic Quantities

To determine the change in temperature given the change in entropy ( centropy), change in enthalpy (enthalpy), and change in Gibbs free energy (Gibbs free energy), we use the following formula derived from the Gibbs free energy equation:

delta G = delta H - T delta S

Where delta G is the change in Gibbs free energy, delta H is the change in enthalpy, T is the temperature in Kelvin, and delta S is the change in entropy. We rearrange this equation to solve for the temperature change (T):

T = ( delta H - delta G) / delta S

Given:

Change in entropy delta S = 150 J K⁻¹ mol⁻¹

Change in enthalpy delta H = -99.3 kJ/mol = -99300 J/mol

Change in Gibbs free energy delta G = -105 kJ/mol = -105000 J/mol

Substitute the values into the temperature equation:

T = ( (-99300 J/mol) - (-105000 J/mol) ) / (150 J K⁻¹ mol⁻¹)

T = 780 K

The change in temperature, in this case, is 780 Kelvin.

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