Certainly! Let's solve the problem step by step to find [tex]\(\Delta G\)[/tex] for the given reaction:
Given data:
- [tex]\(\Delta H = -56.13 \, \text{kJ}\)[/tex]
- [tex]\(\Delta S = 87.1 \, \text{J/K}\)[/tex]
- [tex]\(T = 303 \, \text{K}\)[/tex]
We need to use the formula:
[tex]\[ \Delta G = \Delta H - T \Delta S \][/tex]
First, let's convert the entropy change ([tex]\(\Delta S\)[/tex]) from J/K to kJ/K, because the enthalpy change ([tex]\(\Delta H\)[/tex]) is given in kJ.
1. Converting [tex]\(\Delta S\)[/tex] from J/K to kJ/K:
[tex]\[ \Delta S = 87.1 \, \text{J/K} \][/tex]
Since [tex]\(1 \, \text{kJ} = 1000 \, \text{J}\)[/tex], we can convert:
[tex]\[ \Delta S = \frac{87.1 \, \text{J/K}}{1000} = 0.0871 \, \text{kJ/K} \][/tex]
Now, let's substitute the values into the [tex]\(\Delta G\)[/tex] formula:
2. Using the formula [tex]\(\Delta G = \Delta H - T \Delta S\)[/tex]:
[tex]\[ \Delta G = -56.13 \, \text{kJ} - 303 \, \text{K} \times 0.0871 \, \text{kJ/K} \][/tex]
3. Calculate the product [tex]\(T \Delta S\)[/tex]:
[tex]\[ 303 \, \text{K} \times 0.0871 \, \text{kJ/K} = 26.3913 \, \text{kJ} \][/tex]
4. Finally, calculate [tex]\(\Delta G\)[/tex]:
[tex]\[ \Delta G = -56.13 \, \text{kJ} - 26.3913 \, \text{kJ} \][/tex]
[tex]\[ \Delta G = -82.5213 \, \text{kJ} \][/tex]
So, the Gibbs free energy change [tex]\(\Delta G\)[/tex] for the reaction is [tex]\(-82.5213 \, \text{kJ}\)[/tex], which is approximately [tex]\(-82.5 \, \text{kJ}\)[/tex].
Among the given options, the correct one is:
- [tex]\(-82.5 \, \text{kJ}\)[/tex]
