For a reaction with ΔH = 100 kJ/mol and ΔS = 200 J/mol·K, at what temperature wi

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Question: For a reaction with ΔH = 100 kJ/mol and ΔS = 200 J/mol·K, at what temperature will the reaction become spontaneous?

Options:

Correct Answer: 500 K

Solution:

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = 100,000 J / 200 J/K = 500 K.

For a reaction with ΔH = 100 kJ/mol and ΔS = 200 J/mol·K, at what temperature will the reaction become spontaneous?

For a reaction with ΔH = 100 kJ/mol and ΔS = 200 J/mol·K, at what temperature will the reaction become spontaneous?

Step 1: Understand that for a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be less than or equal to zero (ΔG ≤ 0).
Step 2: Use the formula for Gibbs free energy: ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
Step 3: Set ΔG to 0 to find the temperature at which the reaction becomes spontaneous: 0 = ΔH - TΔS.
Step 4: Rearrange the equation to solve for T: T = ΔH / ΔS.
Step 5: Convert ΔH from kJ to J because ΔS is in J: ΔH = 100 kJ/mol = 100,000 J/mol.
Step 6: Substitute the values into the equation: T = 100,000 J/mol / 200 J/mol·K.
Step 7: Calculate the temperature: T = 500 K.

Gibbs Free Energy – Understanding the relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) in determining spontaneity of a reaction.
Thermodynamic Equations – Application of the equation ΔG = ΔH - TΔS to find the temperature at which a reaction becomes spontaneous.