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What is the value of [tex]\Delta G[/tex] at [tex]500 \, K[/tex] if [tex]\Delta H = 27 \, \text{kJ/mol}[/tex] and [tex]\Delta S = 0.09 \, \text{kJ/(mol \cdot K)}[/tex]?

A. [tex]\Delta G = 0 \, \text{kJ/mol}[/tex]
B. [tex]\Delta G = 72 \, \text{kJ/mol}[/tex]
C. [tex]\Delta G = -18 \, \text{kJ/mol}[/tex]
D. [tex]\Delta G = 26.9 \, \text{kJ/mol}[/tex]



Answer :

GinnyAnswer
To find the value of [tex]\(\Delta G\)[/tex] at [tex]\(500 \, K\)[/tex] given [tex]\(\Delta H = 27 \, kJ / mol\)[/tex] and [tex]\(\Delta S = 0.09 \, kJ / ( mol \cdot K )\)[/tex], we use the Gibbs free energy equation:

[tex]\[ \Delta G = \Delta H - T \Delta S \][/tex]

1. Identify the given data:
- [tex]\(\Delta H = 27 \, kJ / mol\)[/tex]
- [tex]\(\Delta S = 0.09 \, kJ / ( mol \cdot K )\)[/tex]
- [tex]\(T = 500 \, K\)[/tex]

2. Substitute the values into the equation:

[tex]\[ \Delta G = 27 - 500 \times 0.09 \][/tex]

3. Calculate the product of [tex]\(T\)[/tex] and [tex]\(\Delta S\)[/tex]:

[tex]\[ 500 \times 0.09 = 45 \][/tex]

4. Subtract this product from [tex]\(\Delta H\)[/tex]:

[tex]\[ \Delta G = 27 - 45 \][/tex]

5. Perform the subtraction:

[tex]\[ \Delta G = -18 \, kJ / mol \][/tex]

So, the value of [tex]\(\Delta G\)[/tex] is [tex]\(-18 \, kJ / mol\)[/tex], which corresponds to option C:

C. [tex]\(\Delta G = -18 \, kJ / mol\)[/tex]

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