Hess's law states that the enthalpy of the total reaction is equal to the enthalpy of the steps required to get to the total reaction, regardless of the path that is chosen. This means that we can combine the two half steps with known enthalpies in order to solve for the enthalpy of the main reaction.

Step 1.      

Step 2.    

Total:

Since step 1 results in two moles of liquid water, we need to use the second step twice in order to replace them with two moles of water vapor.

Combined:

Since the total reaction is created by step 1 occurring once and step 2 occurring twice, we can write the enthalpy as:

Use the given enthalpies of the steps to calculate the total change in enthalpy.

Use the following formula:

Plug in values:

Entropy is defined as the amount of disorder in a system and is favored in biological and chemical systems. Any system will prefer to have higher entropy, and spontaneous reactions will generally increase entropy in the system.

Gas particles move at higher velocity and with greater range than particles in liquids and solids. This contributes to their high level of entropy. Aqueous solutions gain entropy with the number of ions in solution, but do not reach the same level of entropy of gases. Colloids are homogenized mixtures, such as milk, and follow relatively the same principles as aqueous solutions.

Entropy can be thought of as the tendency for a system to favor disorder. This means that the least ordered scenario in a system is typically favored by probability. Entropy increases when disorder is increased. Examples include an ice cube melting into a puddle, a gas diffusing all throughout a room, and a mirror shattering. Each of these either increases the energy of the system or results in the creation of multiple pieces/particles from a single object.

When building a road, materials are placed in an ordered, specific manner. This gives it a negative entropy. 

Any reaction can be thought of as taking place in a system, while the surroundings are the rest of the universe. It helps to remember that the entropy of the universe is constantly increasing. This means that the entropy change in the universe increases following every reaction. A system can have a decrease in entropy, as long as the entropy of the surroundings increases by a greater value.

Spontaneity, or the likelihood that a reaction will occur, is determined by Gibbs free energy. The equation for Gibbs free energy is:

 is the term for entropy and a negative value for Gibbs free energy indiciates a spontaneous reaction. Thus, as temperature increases the effective value of the entropy term increases as well (since  is positive). Since the enthalpy,, remains constant, increasing the entropy term will have the total effect of decreasing the Gibbs free energy since entropy is subtracted from enthalpy. Decreasing the Gibbs free energy will result in a more spontaneous reaction.

The spontaneity of a reaction can be determined using the Gibb's free energy equation:

In this formula,  is enthalpy,  is entropy, and  is the temperature in Kelvin. In order for a reaction to be spontaneous, Gibb's free energy must be negative. Looking at the equation, we can see that the value for  will ALWAYS be negative if enthalpy is negative and entropy is positive.

These are the requirements for a reaction that is always spontaneous, regardless of temperature,

The first thing we need to do in order to solve this problem is determine at what temperature  is equal to zero. When  is equal to zero, the reaction is at equilibrium and will not go one way or the other. Using the Gibb's free energy equation, we can determine the temperature where the reaction is at equilibrium.

The question tells us the enthalpy and entropy values, allowing us to solve for the equilibrium temperature. Remember to convert the enthalpy from kilojoules to Joules.

At , the reaction is at equilibrium. In order to make the reaction spontaneous, do we need to raise or lower from this temperature? Notice how entropy in this case is positive. By increasing temperature, the negative portion of the equation will become larger, and will result in a negative value. This means that the above reaction is spontaneous at temperatures higher than . You can check you work by solving for the Gibb's free energy at a higher temperature.

Since the value is negative, the reaction is spontaneous at this higher temperature.

Given the above conditions, we can use the Gibb's free energy equation in order to determine the reaction's spontaneity.

Convert the temperature to Kelvin and the enthalpy to Joules.

Use the given values to solve for the Gibb's free energy.

Since  is positive at these conditions, we can conclude that the reaction is nonspontaneous and will not take place.

The sign of the change in Gibb's free energy,  tells us whether a reaction is spontaneous or not (whether the reaction requires the net input of energy or not). For a spontaneous reaction, the  value is always less than zero. This is because the free energy of the products is less than that of the reactants. This indicates that there is a net release of energy, as opposed to a net energy consumption. When the products are at a lower energy than the reactants, the reaction can proceed spontaneously, and is known as exothermic.