If heat is transferred from the metal object to the water, that means that the temperature of the metal must be greater than that of the water. We must find the answer choice where this is the case. Since the temperatures are given in different units, they must be converted to the same unit for comparison purposes.

Only one answer option results in the metal having a greater temperature than the water:

In this problem, we need to track the transfer of heat from the aluminum to the water. Since the heat acquired by the water is equal to the heat given off by the aluminum, we can set their equations equal to each other; however, in order to avoid a negative number, aluminum's change in temperature will be set as the initial temperature minus the final temperature. This results in the equation below.

When a specific heat capacity is given, we typically use the equation . Since we know all of the factors except for the change in temperature, we can simply solve for .

The equation for enthalpy of reaction is:

Given our chemical reaction and the enthalpies of formation, we can find the enthalpy of reaction.

First, find the total enthalpy for the products.

Then, find the total enthalpy for the reactants.

Since the oxygen is elemental, its heat of formation is zero.

Return to the original equation to calculate the final enthalpy of reaction.

Hess's law states that the enthalpies of the steps in an overall reaction can be added in order to find the overall enthalpy. Since the overall enthalpy of the reaction is +68kJ, we can use the following equation to find step 2's enthalpy.

1) 

2) 

3) 

We need to add the given processes in such a way that leaves  on the left side, and  on the right. 

Since there are no  in the final equation, begin by combining processes 1 and 2 to eliminate.

First, reverse process 2 and multiply by two:

2a)

2a)

2a)

Add this result to process 1.

1)

2a)

1+2a) 

Now we need to combine with process 3 to eliminate the . Start by multiplying process 3 by two.

3a)

3a) 

Add this to the combined result from processes 1 and 2.

1+2a)

3a)

1+2a+3a) 

This gives our final combination. The elemental reaction is , and the enthalpy of the process is .

Scenarios 3 and 4 are presented as thought experiments because, common sense tells us, they will never happen. The fundamental reason they will never happen is because they do not lead to a total increase in entropy of the universe. In order for an event to proceed, this requirement must be satisfied.

Entropy describes the number of configurations a system can have or, alternatively, how much "order" it possesses.

When water freezes, it forms a crystal lattice, which is more ordered than liquid water. Likewise, collecting playing cards and stacking them in a deck involves a transformation from disorder (cards scattered around the floor) to order (a single deck). Chemically, the precipitation of  from aqueous ions comes from a decrease in entropy, as the free-flowing ions have been combined to form a solid, organized in a lattice. The combination of  and  to give  also results in a decrease in entropy, since the reactants have one mole of gas, and the products contain zero moles of gas.

The disproportionation of  to give two moles of  results in an increase in entropy, because the number of moles of gas increases in going from reactants to products.

The entropy change of the surroundings for an exothermic system must be positive. The release of heat by the exothermic reaction drives the increase in disorder of the environment surrounding the reaction vessel.

As the heat leaves the reaction system, it increases the entropy of the particles in the surroundings.

Entropy decreases when the number of moles of gas decreases during a reaction. In the case of the correct answer, the number of moles of gas decreases from two to one.

When a substance goes from a solid to a gas (sublimation) or from a liquid to a gas (evaporation), entropy increases. Likewise, when a solid dissolves in water, entropy increases. Entropy (i.e. the number of arrangements a system can have) is much greater in a gas than in a liquid or solid. It is also greater for ions solvated in solution than for an un-dissolved solid.

Note that, in general, the entropy of the universe increases. In order for a process to involve a decrease in entropy of the system, there is likely a consequent increase in entropy of the universe.