Question

Match the following parameters with description for spontaneity:

$\begin{array}{cccc}& \Delta \left(\text{Parameters}\right)& & \\ & {\Delta }_r{H}^o{\Delta }_r{S}^o{\Delta }_r{G}^o& & \text{Description}\\ i)& +-+& a)& \text{Non-spontaneous at high temperature}\\ ii)& --+& & \\ & athighT& b)& \text{Spontaneous at all temperatures}\\ iii)& -+-& c)& \text{Non-spontaneous at all temperatures}\end{array}$

Answer 1

${\Delta }_r{G}^o={\Delta }_r{H}^o-T{\Delta }_r{S}^o$

where ${\Delta }_r{G}^o=$ change in standard gibbs energy of the system

${\Delta }_r{H}^o=$ change in the enthalpy of the system
$T=$ temperature in kelvin
${\Delta }_r{S}^o=$ change in entropy of the system

Sign of Change in gibb’s free energy ${\Delta }_r{G}^o$ gives a criteria for spontaneity at constant pressure and temperature.

(i) If $\Delta G$ is negative $(<0)$, the process is spontaneous.

(ii) If $\Delta G$ is positive $(>0)$, the process is non-spontaneous.

Note : If a reaction has a negative enthalpy change and negative entropy change, it can be spontaneous when $\Delta H$ factor is large enough to outweigh $T\Delta S$ and for this temperature $\left(T\right)$ should be lower. If $T$ will be higher, $T\Delta S$ term will outweigh $\Delta H$ and we will observe $+ve$ value of $\Delta G$, which led to non- Spontaneous reaction at high temperature.

The spontaneity of reaction at different conditions can be given as following -

$\begin{array}{cccc}{\Delta }_r{H}^o& {\Delta }_r{S}^o& {\Delta }_r{G}^o& \text{Description}\\ -& +& -& \text{Reaction spontaneous at all temperatures}\\ -& -& -\left(\text{at low}T\right)& \text{Reaction spontaneous at low temperatures}\\ -& -& +\left(\text{at high}T\right)& \text{Reaction spontaneous at high temperatures}\\ +& +& +\left(\text{at low}T\right)& \text{Reaction spontaneous at low temperatures}\\ +& +& -\left(\text{at high}T\right)& \text{Reaction spontaneous at high hightemperatures}\\ +& -& +\left(\text{at all}T\right)& \text{Reaction spontaneous at all temperatures}\end{array}$

On basis of earlier observation, match the following will be


$\begin{array}{cccc}& \Delta \left(\text{Parameters}\right)& & \\ & {\Delta }_r{H}^o{\Delta }_r{S}^o{\Delta }_r{G}^o& & \text{Description}\\ i)& +-+& a)& \text{Non-spontaneous at high temperature}\\ ii)& --+& & \\ & athighT& b)& \text{Spontaneous at all temperatures}\\ iii)& -+-& c)& \text{Non-spontaneous at all temperatures}\end{array}$