Fora particular reaction, ΔH = 120.5 kJ and ΔS = 758.2 J/K. What is ΔG for this reaction at 298 K?
As you know, the change in Gibbs free energy for a given chemical reaction tells you whether or not that reaction is spontaneous at a given temperature or not.
#color(blue)(DeltaG = DeltaH - T * DeltaS)#
At standard state conditions, i.e. at a pressure of
Now, what does the sign of
In order for a reaction to be spontaneous at a given temperature, you must have
If you break this down by looking at the equation for
This means that you can have
#DeltaH<0#, #DeltaS>0 ->#spontaneous at any temperature #DeltaH>0#, #DeltaS<0 ->#non-spontaneous regardless of temperature #DeltaH>0#, #DeltaS>0 ->#spontaneous at a certain temperature range #DeltaH<0#, #DeltaS<0 ->#spontaneous at a certain temperature range
In your case, you have a positive change in enthalpy and a positive change in entropy. This means that the spontaneity of the reaction will depend on the temperature
More specifically, if
If not, then
So, plug in your values and solve for
#DeltaG = "120.5 kJ" - 298 color(red)(cancel(color(black)("K"))) * 758.2 * 10^(-3)"kJ"/color(red)(cancel(color(black)("K")))#
#DeltaG = color(green)(-"105.4 kJ")#
I'll leave the answer rounded to four sig figs.
So, this particular reaction is spontaneous at