Question #ba099

A reaction's change in Gibbs free energy, #DeltaG#, tells you whether or not that reaction is spontaneous or not at the specific temperature at which it takes place.

A chemical reaction's spontaneity refers to the reaction's ability to proceed without energetic input. In simple words, if a reaction is spontaneous at a given temperature, then it will not require energy to proceed.

If it's not spontaneous at a given temperature, then it will require energy to proceed.

Your bread and butter when it comes to assessing a reaction's spontaneity is this equation

#color(blue)(DeltaG = DeltaH - T * DeltaS)" "#, where

#DeltaG# - the change in Gibbs free energy
#DeltaH# - the enthalpy change of reaction
#T# - the temperature at which the reaction takes place, expressed 8n Kelvin
#DeltaS# - the entropy change of reaction

In order for a reaction to be spontaneous, you need #DeltaG<0#.

In your case, a positive enthalpy change of reaction and a negative entropy change of reaction will always, irrespective of the temperature at which the reaction takes place, result in #DeltaG>0#, which is what you get when the reaction is not spontaneous.

Plug in your values to get the actual value for #DeltaG# - do not forget to convert the temperature to Kelvin. Plus, notice that #DeltaH# is given is kilojoules and #DeltaS# in joules*, so an additional convertion will be needed here.

#DeltaG = "147 kJ" - (273.15 + 149) color(red)(cancel(color(black)("K"))) * (-67.0)"J"/color(red)(cancel(color(black)("K")))#

#DeltaG = "147 kJ" + overbrace("28,284.05 J")^(color(purple)("convert to kJ"))#

#DeltaG = "147 kJ" + "28.284 kJ" = color(green)(+"175 kJ")#

The answer is rounded to three sig figs.

So, #DeltaG>0#, which means that the reaction is not spontaneous.