1. The first law states that the energy that is extractable from a system is the same as the energy originally put into it, so you cannot 'win', i.e. make an energy profit. This is where most perpetual motion machines fall down. The second law states that conversion of heat into useful energy is only 100% efficient if you have a heat sink at absolute zero. Equivalently, all energy conversions that produce heat (and that's pretty much all of them), are transferring a certain amount of useful energy into a form that cannot be easily recovered. This is where all the other perpetual motion machines fall down. The third law states that it's impossible to get a heat sink to absolute zero, so you cannot even break even, since some of your energy will be forever lost as worthless, degraded heat, that can never be efficiently converted back into a useful form.
  2. Living things are open systems because they are able to exchange both energy (e.g heat) and matter (e.g. oxygen and carbon dioxide) with their surroundings. However, modelling open systems is extremely difficult, so they are usually modelled as (energy exchanging, but not matter exchanging) closed systems, which to a good approximation, they (and particularly cell cultures) are.
  3. The endothermic reaction between sodium bicarbonate (baking soda) and hydrochloric acid, must produce a large increase in the entropy of the system under standard conditions. A large positive entropy change will be sufficient to make the Gibb's free energy change negative, and therefore make the reaction spontaneous. This is in fact the case (∆G0 is +28.5 kJ mol−1, and therefore ∆S = 230 J mol−1 K−1. Intuitively, this is sensible, since one of the products is a highly disordered gas.
  4. ∆G0 = ∆H0 − T∆S = −91.8 × 103 − 298 x ( −199 ) = −32.5 kJ mol−1 (note units). This indicates that the reaction is spontaneous under standard conditions. The value we got is twice the free energy change associated with the formation of a single mole of ammonia from its constituent elements in their standard states. Consequently, the value 16.25 kJ mol−1 is termed the free energy change of formation, ∆G0f, of ammonia.
  5. The Gibb's free energy only states which reactions are thermodynamically feasible, not at what rate they will occur. The conversion of diamond to graphite is energetically favoured, but the reaction path has such a huge activation energy, that diamonds do not convert to graphite at any appreciable rate.
  6. For potassium ions, ∆E = − ( R T ⁄ z F ) ln ( [X]in ⁄ [X]out ) = − ( 8.314472 × 298 ⁄ 1 × 96485.34 ) * ln ( 150 ⁄ 15 ) = −59 mV. This is consistent (give or take 10 mV) with the membrane potential being due entirely to free movement of potassium ions and nothing else. Sodium ions would give the same answer, but the opposite sign (+59 mV).
  7. The redox potential of the NAD/NADH couple is −0.32. For the reaction

    NADH + H+ → NAD + UQH2

    we calculate the free-energy change, we need to reverse the sign of the NADH/NAD couple, and add them together, giving 0.10 + 0.32 = +0.42V. Using the equation ∆G0 = − n F ∆E0, we can see this is spontaneous (∆G has a negative value). We can show the same for all the other couples in the redox chain: UQH2 coupled to cyt-c has a redox potential of 0.22 − 0.10 = + 0.12 V; that of cyt-c coupled to iron in Complex IV is 0.77 − 0.22 = +0.55 V; that of iron in Complex IV coupled to oxygen is 0.82 − 0.77 = +0.05 V.