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

The Correct Option is B

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

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

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