Question

question 14 (5 points)
listen
given that the enthalpy of reaction for a system at 298 k is -292 kj/mol and the entropy for that system is 224 j/mol*k, whats the free energy for the system?
a) -225 kj
b) -358 kj
c) -87,793 kj
d) -66,751 kj

Explanation:

Step1: Recall the Gibbs free energy formula

The formula for Gibbs free energy (\( \Delta G \)) is \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is enthalpy, \( T \) is temperature in Kelvin, and \( \Delta S \) is entropy.

Step2: Convert entropy units

Given \( \Delta S = 224 \, \text{J/mol·K} \), convert to kJ/mol·K: \( 224 \, \text{J/mol·K} = \frac{224}{1000} = 0.224 \, \text{kJ/mol·K} \).

Step3: Substitute values into the formula

\( \Delta H = -292 \, \text{kJ/mol} \), \( T = 298 \, \text{K} \), \( \Delta S = 0.224 \, \text{kJ/mol·K} \).
\( \Delta G = -292 - (298 \times 0.224) \)
First, calculate \( 298 \times 0.224 = 66.752 \)
Then, \( \Delta G = -292 - 66.752 = -358.752 \approx -358 \, \text{kJ/mol} \) (rounded to a reasonable value for the options).

Answer:

B) -358 kJ