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At 298 K, [tex]\(\Delta H^0 = -1652 \text{ kJ/mol}\)[/tex] and [tex]\(\Delta S^0 = 0.097 \text{ kJ/(K·mol)}\)[/tex]. What is the Gibbs free energy of the reaction?

A. [tex]\(67,000 \text{ kJ}\)[/tex]
B. [tex]\(-907 \text{ kJ}\)[/tex]
C. [tex]\(-745 \text{ kJ}\)[/tex]
D. [tex]\(225 \text{ kJ}\)[/tex]


Sagot :

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.