Question

Question #ba099

Answer 1

`DeltaG = +"175 kJ"`

Explanation:

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.