Answer:
Both reaction A and reaction B are non spontaneous.
Explanation:
For a spontaneous reaction, change in gibbs free energy ([tex]\Delta G[/tex]) should be negative.
We know, [tex]\Delta G=\Delta H-T\Delta S[/tex], where T is temperature in Kelvin scale.
Reaction A: [tex]\Delta G=(10.5\times 10^{3})-(298\times 30)J/mol=1560J/mol[/tex]
As [tex]\Delta G[/tex] is positive therefore the reaction is non-spontaneous.
If at a temperature T K , the reaction is spontaneous then-
[tex]\Delta H-T\Delta S< 0[/tex]
or, [tex]T> \frac{\Delta H}{\Delta S}[/tex]
or, [tex]T> \frac{10.5\times 10^{3}}{30}[/tex]
or, [tex]T> 350[/tex]
So at a temperature greater than 350 K, the reaction is spontaneous.
Reaction B: [tex]\Delta G=(1.8\times 10^{3})-(-113\times 298)J/mol=35474J/mol[/tex]
As [tex]\Delta G[/tex] is positive therefore the reaction is non-spontaneous.
If at a temperature T K , the reaction is spontaneous then-
[tex]\Delta H-T\Delta S< 0[/tex]
or, [tex]T> \frac{\Delta H}{\Delta S}[/tex]
or, [tex]T> \frac{1.8\times 10^{3}}{-113}[/tex]
or, [tex]T> -16[/tex]
So at a temperature greater than -16 K, the reaction is spontaneous.
