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Do these reactions always have to be paired with another energetically favorable reaction with a greater delta G magnitude, or is there a way to force reactions with a positive delta G to happen?

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  • $\begingroup$ Are you asking about $\Delta G$ or $\Delta G^0$? $\endgroup$ – Chet Miller Jun 4 '17 at 0:49
  • $\begingroup$ If it's redox, you can drive it with an external emf after constructing a cell. $\endgroup$ – Pritt says Reinstate Monica Jun 4 '17 at 5:09
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The change of the Free / Gibbs enthalpy $\Delta_{\text{R}}{}G$ consists of a contribution by reaction enthalphy $\Delta_{\text{R}}H$, and a contribution by reaction entropy, $\Delta_{\text{R}}S$:

$$ \Delta_{\text{R}}{}G = \Delta_{\text{R}}H - T \cdot \Delta_{\text{R}}S $$

Hence, the answer to your question is no. By variation of temperature $T$, for example, a reaction previously endergonic ($\Delta_{\text{R}}{}G > 0$) may become exergonic ($\Delta_{\text{R}}{}G < 0$), as summarized here.

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The two things to remember are: $\Delta G$ is a function of conditions and assumes an infinite amount of time. If a reaction has a positive $\Delta G$ it will not be thermodynamically driven. It can however be kinetically driven at leat in the short term. For example, the phase change in NiTinol alloys from cubic to monoclinic upon cooling can experience the formation of a metastable triclinic phase which is not thermodynamically favored but kinetically favored.

However if you want to drive the reaction, change the conditions. Just to demonstrate a few:

  1. For reactions with $\Delta S > 0$ you can change the temperature. (melting, boiling sublimation, and the reverse; see Figure 1 below)
  2. Change with electricity: $\Delta G = \Delta H - T\Delta S - nFE_{cell}^\circ $ (electrolysis)
  3. Change with pressure and/or volume: $\Delta G = \Delta H - T\Delta S - \int_{P_1}^{P_2} V\mathrm{d}P - \int_{V_1}^{V_2} P\mathrm{d}V $ [making diamonds; constant volume conditions are actually Helmholtz energy $(A)$]
  4. Change with concentration or partial pressure: $\Delta G = \Delta H - T\Delta S - RT\ln(Q)$ (Le Chatelier's principle)
  5. Change with magnetic field: $\Delta G = \Delta H - T\Delta S - \mu H_\mathrm{a} M $ (magnetic storage)
  6. Change with chemical potential: $\Delta G = \Delta H - T\Delta S - \mu \Delta N $ or more generally $\Delta G = \Delta H - T\Delta S - \sum^n_{i=1}\frac{\partial G}{\partial N_i} \mathrm d N_i $ (chemical potential for diffusion).
  7. Change with light: $\Delta G = \Delta H - T\Delta S - hf $ (radical formation)

and many more. So while you cannot make a reaction with a positive $\Delta G$ proceed spontaneously, you can change the environment to make it negative and thus "spontaneous".

enter image description here Figure 1: $\Delta G$ of water vapor with temperature.

Again remember a thermally spontaneous reaction is after infinite time will only proceed if the kinetic barrier is overcome otherwise the system will be meta-stable. for example the combustion of gasoline is a spontaneous reaction at room temperatrue and oxygen pressure, but is not pyrophoric (does not spontaneously ignite).

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