InterviewSolution
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InterviewSolution
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`Delta G` is energy availabe to do useful work and is thus a meaure of "Free energy". Show mathemactically that `Delta G` is a measure of free energy. Find the unit of `Delta G`. IF a reaction has positive enthalpy change and positive entropy change, under what condition will the reaction be spontaneous ? |
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Answer» Gibbs free energy is that thermodynamic quantity of a system, the decreases in whose value during a process is equal to the maximum possible useful work that can be obtained from the system. Mathematically, this results may be derived as follows The relationship between heat absorbed by a system q, the change in its internal energy, `Delta U` and the work done by the system is given by the equation of the first law of thermodynamics, therefore `q = Delta U + Q_("expansion") + W_("non-expansion")` ...(i) Under constant pressure condition, the expansions work is given by `p Delta V`. `:. q = Delta U+pDelta V + W_("non-expansion") " " (because Delta U+ p Delta V =Delta H)` `= Delta H + W_("non-expansion")` ...(ii) For a reversible change taking place at constant temperature, `Delta S = (q_("rev"))/(T)` or `q_("rev") = T Delta S` ...(iii) Substituting the value of q from Eq. (iii) in Eq. (ii) we get `T Delta S = Delta H + W_("non-expansion")` or `Delta H - T Delta S = -W_("non-expansion")` ...(iv) For a change taking place under conditions of constant temperature and pressure, `Delta G = Delta H - T Delta S` Substituting this value in equation (iv), we get `Delta G = -W_("non-expansion")` ...(v) Thus, free energy change can be taken as a measure of work other than the work of expansion. For most changes , the work of expansion can not be converted to other useful work, whereas the non-expansion work is convertible to useful work. Rearranging equation (v), it may write as `-Delta G = W_("non-expansion") = W_("useful")` As `-Delta G = W_("useful")` therefore, `Delta G` has the same units as those of work i.e., joule `Delta G = Delta H - T Delta S`. If `Delta H` = positive and `Delta S` = positive, then `Delta G` will be negative i.e., process will be spontaneous only when `T Delta S gt Delta H` in magnitude, which will be so when temperature is high. |
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