Question

How many reactions are non-spontaneous at 300 K. For independent reaction ΔH & ΔS values are given.

• A. $ΔH = –25 kJ/mol, ΔS = –80 J/mol$
• B. $ΔH = +25 kJ/mol, ΔS = –50 J/mol$
• C. $ΔH = -22 kJ/mol, ΔS = +50 J/mol$
• D. $ΔH = –22 kJ/mol, ΔS = 80 J/mol$

Answer 1

Answer: (B)

$ΔH = +25 kJ/mol, ΔS = –50 J/mol$

Answer 2

A reaction is considered spontaneous at a particular temperature when it exhibits a positive change in Gibbs free energy, denoted as $\Delta G$. The formula for calculating $\Delta G$ is $\Delta G = \Delta H - T\Delta S$, where $\Delta H$ represents the change in enthalpy, and $\Delta S$ represents the change in entropy. A negative $\Delta G$ value indicates a spontaneous reaction, while a positive $\Delta G$ value indicates a non-spontaneous reaction.

$\mathbf{\triangle H}$	$\mathbf{\triangle S}$	$\mathbf{\triangle G}$	$\mathbf{Spontaneity \,of \,reaction}$
Negative (exothermic)	Positive	Negative	Reactions are spontaneous at all temperatures.
Negative (exothermic)	Negative	Negative or Positive	Reactions become spontaneous at low temperatures.
when $	T.\triangle S	<	\triangle H
Positive (endothermic)	Positive	Negative or Positive	Reactions become spontaneous at low temperatures.
when $	T.\triangle S	<	\triangle H
Positive (endothermic)	Negative	Positive	Reactions are non-spontaneous at all temperatures.

Now, let's examine the Gibbs free energy changes for each reaction at a temperature of 300 K:

**(A) ** $ΔH = –25 kJ/mol, \,ΔS = –80 J/mol$

$\triangle G\,=\triangle H - T\triangle S$
$\triangle G = -25 -300\times (\frac{-80}{1000})$
$= -25 -300 \times (-0.08)$
$= -25 - (-24)$
$= -25 +24$
$\triangle G = -1$
⇒$ΔG \text{ is negative, the reaction is spontaneous.}$

**(B) **$ΔH =+25 \,kJ/mol, ΔS = +50 \,J/mol$

$\triangle G\,=\triangle H - T\triangle S$
$\triangle G = +25 -300\times (\frac{-50}{1000})$
$= +25 -300\times (-0.05)$
$= +25 -(-15)$
$= +25 +15$
$\triangle G = +40$
⇒$ΔG \text{ is positive, the reaction is non-spontaneous.}$

**(C) **$ΔH = -22\, kJ/mol, ΔS = +50 \,J/mol$

$\triangle G\,=\triangle H - T\triangle S$
$\triangle G= -22 -300\times (\frac{50}{1000})$
$=- 22 -300\times (0.05)$
$= -22 -(15)$
$\triangle G= -37$
⇒$ΔG \text{ is negative, the reaction is spontaneous.}$

**(D) **$ΔH = –22 \,kJ/mol, ΔS = 80\, J/mol$

$\triangle G\,=\triangle H - T\triangle S$
$\triangle G= -22 -300\times (\frac{80}{1000})$
$= -22 -300 \times (0.08)$
$= -22 -24$
$\triangle G = -46$
⇒$ΔG \text{ is negative, the reaction is spontaneous.}$

$\text{So, The Correct answer is only option (B)}$ $ΔH = +25 kJ/mol, ΔS = –50 J/mol$.