Answer
Verified
393.3k+ views
Hint: It is the total entropy change \[\Delta H = \mathop { - T\Delta S}\nolimits_{surr} ........\left( 2 \right)\]$\mathop {\Delta S}\nolimits_{Total} $that decides the spontaneity of process but most of the chemical reactions fall into category of either closed system or open system. Therefore , for most of the chemical reactions there are changes in both enthalpy and entropy. The quantity that relates these two are called Gibbs energy and denoted by G. G is an extensive property .It is a state function. It has units of energy that are joules.
Complete answer:
\[\;G = H - TS\]
on differentiating \[\Delta G = \Delta H - T\left( {\Delta S} \right) - \left( {\Delta T} \right)S\]
the reaction occurs at constant temperature, ΔT=0
\[\Delta G = \Delta H - T\left( {\Delta S} \right)......\left( 1 \right)\]
We also know that entropy changes the surroundings.
\[\mathop {\Delta S}\nolimits_{surrounding} = T - \Delta H\]
\[\Delta H = \mathop { - T\Delta S}\nolimits_{surr} ......\left( 2 \right)\]
Substituting (2) in (1)
\[\Delta G = - T.\mathop {\Delta S}\nolimits_{Surr} - T\Delta S\Delta G = - T\left( {\mathop {\Delta S}\nolimits_{Surr} + \Delta S} \right)\]we know, \[\left( {\mathop {\Delta s}\nolimits_{Surr} + \Delta S} \right) = \mathop {\Delta S}\nolimits_{TOTAL} \]
⇒\[\Delta G = \mathop { - T(\Delta S)}\nolimits_{total} \]
Thus, the relationship \[\Delta G = \mathop { - T(\Delta S)}\nolimits_{total} \]is derived.
Note:
Knowledge of the sign and magnitude of free energy change of a chemical reactions allows:-
Prediction of the spontaneity of a chemical reaction
Prediction of the useful work that could be extracted from it.
If change in G is negative then the process is spontaneous .
If change in G is positive then the process is nonspontaneous
Entropy is defined as the degree of randomness in a state
Complete answer:
\[\;G = H - TS\]
on differentiating \[\Delta G = \Delta H - T\left( {\Delta S} \right) - \left( {\Delta T} \right)S\]
the reaction occurs at constant temperature, ΔT=0
\[\Delta G = \Delta H - T\left( {\Delta S} \right)......\left( 1 \right)\]
We also know that entropy changes the surroundings.
\[\mathop {\Delta S}\nolimits_{surrounding} = T - \Delta H\]
\[\Delta H = \mathop { - T\Delta S}\nolimits_{surr} ......\left( 2 \right)\]
Substituting (2) in (1)
\[\Delta G = - T.\mathop {\Delta S}\nolimits_{Surr} - T\Delta S\Delta G = - T\left( {\mathop {\Delta S}\nolimits_{Surr} + \Delta S} \right)\]we know, \[\left( {\mathop {\Delta s}\nolimits_{Surr} + \Delta S} \right) = \mathop {\Delta S}\nolimits_{TOTAL} \]
⇒\[\Delta G = \mathop { - T(\Delta S)}\nolimits_{total} \]
Thus, the relationship \[\Delta G = \mathop { - T(\Delta S)}\nolimits_{total} \]is derived.
Note:
Knowledge of the sign and magnitude of free energy change of a chemical reactions allows:-
Prediction of the spontaneity of a chemical reaction
Prediction of the useful work that could be extracted from it.
If change in G is negative then the process is spontaneous .
If change in G is positive then the process is nonspontaneous
Entropy is defined as the degree of randomness in a state
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE