For a reaction with ΔH = 50 kJ/mol and ΔS = 100 J/mol·K, at what temperature will the reaction become spontaneous?
Practice Questions
1 question
Q1
For a reaction with ΔH = 50 kJ/mol and ΔS = 100 J/mol·K, at what temperature will the reaction become spontaneous?
500 K
250 K
1000 K
200 K
To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = (50,000 J/mol) / (100 J/mol·K) = 500 K.
Questions & Step-by-step Solutions
1 item
Q
Q: For a reaction with ΔH = 50 kJ/mol and ΔS = 100 J/mol·K, at what temperature will the reaction become spontaneous?
Solution: To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = (50,000 J/mol) / (100 J/mol·K) = 500 K.
Steps: 8
Step 1: Understand that for a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be less than or equal to zero.
Step 2: Recall 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: ΔH = 50 kJ/mol = 50,000 J/mol.
Step 6: Use the given ΔS value: ΔS = 100 J/mol·K.
Step 7: Substitute the values into the equation: T = 50,000 J/mol / 100 J/mol·K.
