# Question ba099

Jan 1, 2016

$\Delta G = + \text{175 kJ}$

#### Explanation:

A reaction's change in Gibbs free energy, $\Delta G$, 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

$\textcolor{b l u e}{\Delta G = \Delta H - T \cdot \Delta S} \text{ }$, where

$\Delta G$ - the change in Gibbs free energy
$\Delta H$ - the enthalpy change of reaction
$T$ - the temperature at which the reaction takes place, expressed 8n Kelvin
$\Delta S$ - the entropy change of reaction

In order for a reaction to be spontaneous, you need $\Delta G < 0$.

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 $\Delta G > 0$, which is what you get when the reaction is not spontaneous.

Plug in your values to get the actual value for $\Delta G$ - do not forget to convert the temperature to Kelvin. Plus, notice that $\Delta H$ is given is kilojoules and $\Delta S$ 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, $\Delta G > 0$, which means that the reaction is not spontaneous.