When a reaction is spontaneous,  is less than 0. Since the reaction quotient (Q) is less than the equilibrium constant (K_eq), the reaction will proceed in the forward direction.

A positive cell potential means that the reaction is spontaneous, and is true of all galvanic cells. This is seen in the equation , where "" is the number of electrons in moles that are transferred in the balanced equation, "" is Faraday's constant, and "" is the cell potential. A positive cell potential results in a negative  meaning the reaction is spontaneous.

A negative  value means that the equilibrium constant for the reaction is greater than 1, while a positive value mean the equilibrium constant is less than 1.

 for this reaction is negative, because the reactants have nineteen moles of gas while the products have only twelve. Entropy will always decrease in the system if there is a decrease in the number of moles of gas; we know that entropy must be negative for this reaction.

To determine the  at low temperature, use the following formula for Gibbs free energy.

The reaction is exothermic because we are giver that the enthalpy is negative.

The entropy, , is also negative, as discussed above.

This makes our equation .

Remember that temperature is given in Kelvin, and will never be negative. At very low temperatures, the  term will be dominant, and will be less than zero, making negative. A negative value for indicates that the reaction will be spontaneous.

A reaction is spontaneous if the change of Gibbs free energy  is less than zero.

The total reaction is the change .

For this question, the change of enthalpy  is negative, since D is lower in energy than A. There is a net release of energy, making the reaction exothermic. The question states that the change of entropy  is positive, and temperature is always positive when measured in Kelvin. We can return to the Gibbs free energy equation to see the result of these characteristics.

Both terms on the right side are always negative, and  would always be negative. The reaction would be spontaneous at any temperature.

A chemical reaction will be spontaneous when its change in Gibbs free energy, or , is negative. This value can be represented numerically by the equation:

First, let's look at the value for . The equation is more likely to yield a negative  value if this variable is below zero, so we want a negative value for . , however, is being subtracted, so a positive  value will give us a more negative . In combination, these conditions give us a negative value minus a positive one, which will always yield a negative answer.

If a reaction with a negative and a positive is always spontaneous, we can reason that a reaction with a positive and negative can never be spontaneous. This combination will yield a positive value minus a negative value, always resulting in a positive solution.