To find the Gibbs free energy change ([tex]\(\Delta G\)[/tex]) of the reaction, we will use the following formula:
[tex]\[
\Delta G = \Delta H - T \Delta S
\][/tex]
Where:
- [tex]\(\Delta H\)[/tex] is the change in enthalpy,
- [tex]\(T\)[/tex] is the temperature in Kelvin,
- [tex]\(\Delta S\)[/tex] is the change in entropy.
Given values:
- [tex]\(\Delta H = -1652 \ \text{kJ/mol}\)[/tex]
- [tex]\(\Delta S = 0.097 \ \text{kJ/(K·mol)}\)[/tex]
- [tex]\(T = 298 \ \text{K}\)[/tex]
Step-by-step solution:
1. First, write down the formula and insert the known values:
[tex]\[
\Delta G = -1652 - (298 \times 0.097)
\][/tex]
2. Calculate the term [tex]\(T \Delta S\)[/tex]:
[tex]\[
T \Delta S = 298 \times 0.097 = 28.906
\][/tex]
3. Substitute this value back into the equation for [tex]\(\Delta G\)[/tex]:
[tex]\[
\Delta G = -1652 - 28.906
\][/tex]
4. Perform the subtraction to find [tex]\(\Delta G\)[/tex]:
[tex]\[
\Delta G = -1652 - 28.906 = -1680.906
\][/tex]
Thus, the Gibbs free energy change [tex]\(\Delta G\)[/tex] for the reaction is [tex]\(-1680.906 \ \text{kJ/mol}\)[/tex].
Given the provided options, none of them correspond directly to [tex]\(-1680.906 \ \text{kJ/mol}\)[/tex]. However, our calculated result is the accurate representation of the Gibbs free energy change based on the provided data.
