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What is the value of [tex]\(\Delta G\)[/tex] at [tex]\(300 \, \text{K}\)[/tex] if [tex]\(\Delta H = 27 \, \text{kJ/mol}\)[/tex] and [tex]\(\Delta S = 0.09 \, \text{kJ/(mol·K)}\)[/tex]?

A. [tex]\(\Delta G = 54 \, \text{kJ/mol}\)[/tex]
B. [tex]\(\Delta G = 0 \, \text{kJ/mol}\)[/tex]
C. [tex]\(\Delta G = 27 \, \text{kJ/mol}\)[/tex]
D. [tex]\(\Delta G = -18 \, \text{kJ/mol}\)[/tex]



Answer :

GinnyAnswer
To find the value of [tex]\(\Delta G\)[/tex] given that [tex]\(\Delta H = 27 \text{ kJ/mol}\)[/tex], [tex]\(\Delta S = 0.09 \text{ kJ/(mol·K)}\)[/tex], and the temperature [tex]\(T = 300 \text{ K}\)[/tex], we can use the Gibbs free energy equation:

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

Now, let's substitute the given values into this equation:

[tex]\[ \Delta G = 27 \text{ kJ/mol} - (300 \text{ K} \times 0.09 \text{ kJ/(mol·K)}) \][/tex]

First, calculate the product [tex]\(T\Delta S\)[/tex]:

[tex]\[ T\Delta S = 300 \text{ K} \times 0.09 \text{ kJ/(mol·K)} = 27 \text{ kJ/mol} \][/tex]

Now, substitute [tex]\(T \Delta S\)[/tex] back into the equation for [tex]\(\Delta G\)[/tex]:

[tex]\[ \Delta G = 27 \text{ kJ/mol} - 27 \text{ kJ/mol} = 0 \text{ kJ/mol} \][/tex]

Therefore, the value for [tex]\(\Delta G\)[/tex] is:

[tex]\[ \Delta G = 0 \text{ kJ/mol} \][/tex]

The correct answer is:

B. [tex]\(\Delta G = 0 \text{ kJ/mol}\)[/tex]

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