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What is the value of [tex]\Delta G[/tex] at [tex]1000 \, K[/tex] if [tex]\Delta H = -220 \, kJ / mol[/tex] and [tex]S = -0.05 \, kJ / ( mol \cdot K )[/tex]?

A. [tex]780 \, kJ[/tex]
B. [tex]-270 \, kJ[/tex]
C. [tex]-220 \, kJ[/tex]
D. [tex]-170 \, kJ[/tex]

Sagot :

GinnyAnswer
To find the Gibbs free energy change ([tex]\(\Delta G\)[/tex]) at a given temperature ([tex]\(T\)[/tex]), we can use the following formula:

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

Where:
- [tex]\(\Delta H\)[/tex] is the enthalpy change.
- [tex]\(T\)[/tex] is the temperature in Kelvin.
- [tex]\(\Delta S\)[/tex] is the entropy change.

We are given the following values:
- [tex]\(\Delta H = -220 \text{ kJ/mol}\)[/tex]
- [tex]\(T = 1000 \text{ K}\)[/tex]
- [tex]\(\Delta S = -0.05 \text{ kJ/(mol K)}\)[/tex]

Let's substitute these values into the formula step-by-step:

Step 1: Write down the formula and substitute the values:
[tex]\[ \Delta G = -220 \text{ kJ/mol} - (1000 \text{ K} \times -0.05 \text{ kJ/(mol K)}) \][/tex]

Step 2: Calculate the term [tex]\(T \Delta S\)[/tex]:
[tex]\[ 1000 \text{ K} \times -0.05 \text{ kJ/(mol K)} = -50 \text{ kJ/mol} \][/tex]

Step 3: Substitute this result back into the formula:
[tex]\[ \Delta G = -220 \text{ kJ/mol} - (-50 \text{ kJ/mol}) \][/tex]

Step 4: Simplify the expression:
[tex]\[ \Delta G = -220 \text{ kJ/mol} + 50 \text{ kJ/mol} = -170 \text{ kJ/mol} \][/tex]

Therefore, the value of [tex]\(\Delta G\)[/tex] at [tex]\(1000\)[/tex] K is [tex]\(-170 \text{ kJ/mol}\)[/tex].

The correct answer is:

D. [tex]\(-170 \text{ kJ}\)[/tex]
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