Answered

From science to arts, IDNLearn.com has the answers to all your questions. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

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

A. [tex]\Delta G = 27\, kJ/mol[/tex]

B. [tex]\Delta G = 54\, kJ/mol[/tex]

C. [tex]\Delta G = 0\, kJ/mol[/tex]

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

Sagot :

GinnyAnsweridn
To solve for the Gibbs free energy change ([tex]\(\Delta G\)[/tex]), we can use the Gibbs free energy equation:

[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:
- [tex]\(\Delta H = 27 \, \text{kJ/mol}\)[/tex],
- [tex]\(\Delta S = 0.09 \, \text{kJ/(mol \cdot K)}\)[/tex],
- [tex]\(T = 300 \, \text{K}\)[/tex].

First, we substitute these values into the equation:

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

Next, perform the multiplication:

[tex]\[ 300 \, \text{K} \times 0.09 \, \text{kJ/(mol \cdot K)} = 27 \, \text{kJ/mol} \][/tex]

Then, subtract this result from the enthalpy change:

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

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

Thus, the value for [tex]\(\Delta G\)[/tex] at [tex]\(300 \, \text{K}\)[/tex] is:

C. [tex]\(\Delta G = 0 \, \text{kJ/mol}\)[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.