The spontaneity of a reaction is determined by the equation for Gibbs free energy. 

Here, H is a positive number and S is negative, meaning that G will always be a positive value. T will be given in Kelvin, and cannot be negative. Reactions with positive Gibbs free energy values are never spontaneous.

A positive value for ΔG (Gibbs free energy) will guarantee a nonspontaneous reaction. When ΔH (enthalpy) is postive and ΔS (entropy) is negative, the change in Gibbs free energy must be positive and, therefore, nonspontaneous.

Because T (temperature) will always have a positive value, a negative entropy and positive enthalpy will always result in a positive Gibbs free energy.

All of the following scenarios would lead to spontaneous reaction, since each scenario would result in a negative Gibbs free energy (-ΔG).

Negative enthalpy, positive entropy:

Positive enthalpy and entropy with high temperature:

Negative enthalpy and entropy with low temperature:

According to the Gibbs free energy equation, a system is at equilibrium when  is equal to 0.

Since , a system is in equilibrium when               . A negative Gibbs free energy means that the reaction will be spontaneous. At equilibrium, the forward reaction rate equals the reverse reaction rate, though the net rate is zero.

The rate law can be determined by comparing changes in reactant concentration to changes in rate. In this reaction, doubling XY doubles the reaction rate; the reaction is first-order for XY. Doubling Z increases the rate by a factor of eight, so the reaction is third-order for Z (2³ = 8).

Knowing that Rate = k[XY] [Z]³, we can solve for k by using data from one of the trials. Plugging in data from trial 1, we can calculate the value of k.

0.16 = k[100][200]³

k = 2 * 10^-10

Let's look at each of the three reactants individually.

Compare trials 1 and 3. Doubling  without changing the other reactants doubles the rate from to ; therefore  has a superscript of 1.

Compare trials 3 and 4. Doubling  without changing the other reactants results in a rate that is four times faster, increasing from to . The rate increases with the square of concentration of , 

Compare trials 1 and 2. Doubling without changing the other reactants has no effect on the rate, which remains at , so  is not part of the final rate equation.

The final rate law will be .

Comparing trials 2 and 3, we see that when P_XY is constant and P_Z doubles, the rate increases by a factor of 8, or 2³. Rate is therefore proportional to [Z]³.

Comparing trials 1 and 2, we see that when P_Z is held constant and P_XY doubles, the rate doubles. Rate is therefore proportional to [XY].

Remember that in these problems, you are looking for the value of n in the function . When doubling the concentration does not affect the reaction rate, n = 0. When doubling the concentration doubles the reaction rate, n = 1. When doubling the concentration quadruples the reaction rate, n = 2.

The order of a reaction or rate law is given by the sum of the exponents in the rate expression. Rate = k[A]¹[B]¹ is the only second-order rate law. This is the case since the reaction order is determined by the number of reactants involved. Rate = k[A]¹[B]² is not second-order; since it has one A reactant and two B reactants, this is a third-order reaction.

The coefficients in front of the reactants simply show the balanced equation, and do NOT give any information on the order of the reactants. The order of the reactants must be determined experimentally by comparing how reaction rates change when the reactant's concentration is altered.

Only the reactant in question must have an altered concentration between two trials; all others must be kept constant. When a reaction rate is doubled and the initial reaction rate is quadrupled, we determine that the reaction is second order with respect to the reactant. If the concentration of a reactant is altered but the reaction rate is unaffected, the order of the reactant is zero. Finally, if the reaction rate and reactant are multiplied by the same factor between two trials, the reactant is first order.

In the table, we can compare trial 1 and 4 to see the effect of doubling A, with constant B and C. This does not affect the rate, to A must be zeroth order. Comparing trials 2 and 3 shows that doubling B, with A and C held constant, will quadruple the rate. The reaction must be second order for B. Finally, comparing trials 1 and 2 shows us that tripling C, with A and B held constant, will triple the reaction rate. The reaction must be first order for C. This yields the rate law .

If the concentration of a reactant is doubled, . The relationship between this change and the change in rate is, therefore, , where n is the order of the reaction with respect to X. This can be reduced to , allowing us to find the reaction order from the experimental rate.

The reaction order is equal to the sum of the exponents of the concentration variables in the rate law.

Because reactant B has an exponent of two and reactant C has an exponent of one, the total sum is three, and the reaction is therefore third order.