Question

2. For a process where ΔH⁰_sys < 0 and ΔS⁰_sys> 0, when is the sign on ΔG⁰_sys < 0?

a. ΔG⁰_sys is never less than zero

b. ΔG⁰_sys < 0 for all temperatures

c. ΔG⁰_sys < 0 for low temperatures

d. ΔG⁰_sys < 0 for high temperatures

3. For a process where ΔH⁰_sys < 0 and ΔS⁰_sys< 0, when is the sign on ΔG⁰_sys < 0?

a. ΔG⁰_sys < 0 for high temperatures

b. ΔG⁰_sys < 0 for all temperatures

c. ΔG⁰_sys is never less than zero

d. ΔG⁰_sys < 0 for low temperatures

Answer 1

2)

$\Delta$G⁰_sys = $\Delta$H⁰_sys - T$\Delta$S⁰_sys

If $\Delta$S⁰_sys > 0

$\Rightarrow$ T$\Delta$S⁰_sys > 0

$\Rightarrow$ -1 x T$\Delta$S⁰_sys < 0

$\Rightarrow$ -T$\Delta$S⁰_sys < 0

$\Delta$H⁰_sys < 0

If  -T$\Delta$S⁰_sys < 0 and $\Delta$H⁰_sys < 0

$\Rightarrow$$\Delta$H⁰_sys + ( -T$\Delta$S⁰_sys ) < 0

$\Rightarrow$$\Delta$H⁰_sys - T$\Delta$S⁰_sys < 0

$\Rightarrow$$\Delta$G⁰_sys < 0

Option B

3) If $\Delta$S⁰_sys < 0

$\Rightarrow$ T$\Delta$S⁰_sys < 0

$\Rightarrow$ -1 x T$\Delta$S⁰_sys > 0

$\Rightarrow$ -T$\Delta$S⁰_sys > 0

$\Delta$H⁰_sys < 0

$\Delta$G⁰_sys = $\Delta$H⁰_sys - T$\Delta$S⁰_sys

At high temperatures, -T$\Delta$S⁰_sys term becomes more positive than $\Delta$H⁰_sys , thus $\Delta$G⁰_sys becomes positive at high temperatures.

At low temperatures, -T$\Delta$S⁰_sys term is less positive than the $\Delta$H⁰_sys term, thus $\Delta$G⁰_sys is negative at low temperatures.

Option D