Valence in Molecular Bonding

Enthalpy

When an object is dropped from a high point (with high potential energy) and lands on a lower one, energy is released. For small objects, the most obvious form of that energy is sound - you hear the object hit the floor. However, while it is usually too small to notice, energy is also released in the form of heat - the floor is actually warmed a tiny bit by the impact of the object. This is easier to see when the object is larger and has much more potential energy, like when a satellite falls to earth. As the satellite falls through the atmosphere, its potential energy drops, and the excess energy is converted to heat, often causing the satellite to burn up. This is why space capsules require heat shields to protect them during their return to earth.

As we have seen in the previous section, chemical reactions also involve changes in potential potential energy. This means that they too can release (or absorb) heat.

You are probably well aware of this fact, as many reactions that release or absorb heat are common in our day-to-day lives. The combustion of candle wax (or natural gas, or diesel fuel) is an example of heat release; instant cold packs, used for treating sore muscles, are examples of heat absorption.

In this section, we will use our new tool, the reaction coordinate diagram, to analyze why a reaction releases or absorbs heat. We will then put some numbers to this analysis and do some useful calculations involving amounts of heat involved in a reaction.

Thermicity

Let's return to our reaction coordinate diagram from the previous section. Like all the diagrams we will see, it starts with potential energy rising to the transition state, after which it drops down to the products.

As you can see, though, in this case the rise is bigger than the fall. So, overall, we have a reaction where the products are in a higher potential energy state than the reactants.

As we have learned in prior lessons, energy can't be gotten for free. This increased potential energy had to come from somewhere. For this reaction to take place, heat must be absorbed from the surroundings.

Endothermic Reactions

In this reaction, the products have a higher potential energy than the reactants. You can think of this like moving a heavy book from a low shelf to a higher shelf. Moving a book this way takes energy. But instead of using energy from muscles, the energy to drive this reaction comes from the heat of the surroundings. Thus, as mentioned above, heat is absorbed.

We call reactions that absorb heat in this way endothermic because heat is taken in over the course of the reaction. When an endothermic reaction happens, the surroundings get cooler, because they are giving up heat to drive the reaction. The reaction inside an ice pack is an endothermic reaction.

The amount of heat absorbed is equal to the difference in potential energy between the products and reactants, as shown on the diagram above. We call this amount the enthalpy change of the reaction, which is given the symbol ΔH. The sign of ΔH is very important! We use a positive sign to represent heat coming into the reaction. Thus, endothermic reactions have positive values of ΔH.

Exothermic Reactions

Next, we will finally see a reaction coordinate diagram for a different reaction. In this case, you can see that the rise to the transition state is smaller than the fall to the products (or, put another way, the products have lower potential energy than the reactants). This lost potential energy has to go somewhere, and is released as heat to the surroundings.

Reactions that release heat are called exothermic because heat is flowing out over the course of the reaction. Exothermic reactions cause their surroundings to heat up. The combustion of candle wax, referenced above, is an example of an exothermic chemical reaction.

As before, the amount of heat released depends on the size of the gap between the reactants and products. We still refer to this amount as the enthalpy change of the reaction (ΔH). However, because we represent heat being released by the reaction with a negative sign, exothermic reactions have negative values of ΔH.

Comparing Reactions

You should be able to look at reaction coordinate diagrams and use them to draw conclusions about the reactions they represent. For example, by looking at the four diagrams at right, you should be able to conclude that all four are endothermic, because all four end up above where they start. Thus, they will have positive ΔH values.

Further, you should be able to see that Reaction B will have the largest value of ΔH, followed by Reaction A, then Reaction D, with Reaction C having the smallest value. This order can be determined by looking at the gap between the reactants and products in each case.

Enthalpy Calculations

We can usually measure the enthalpy change (ΔH) for a reaction, such as the one shown at right. This type of measurement uses calorimetry, which you learned about in prior lessons.

This value tells us that when one mole of the product is formed from one mole of each reactant, 134 kJ of heat are released. The negative sign tells us that this is an exothermic reaction.

As illustrated here, changing the substances involved in a reaction changes its ΔH value. Every reaction has a unique ΔH.

The exact value of ∆H depends on the relative strength of the bonds that are broken and the bonds that are made. Exothermic reactions typically involve breaking weaker bonds and forming stronger ones. Endothermic reactions involve breaking stronger bonds and forming weaker ones. Another factor that enters into the mix is the number of bonds being formed compared to the number being broken. Often it is possible to calculate the enthalpy change for a reaction from knowledge of the kind and number of bonds broken and formed.

We will now do some calculations involving ∆H values for a variety of reactions. These calculations are essentially the same as the ones you learned to do with ΔH_vap and ΔH_fus back in Lesson 2. In fact, this new concept of "reaction enthalpy" is just a broadening of those concepts. "Enthalpy of vaporization" and "enthalpy of fusion" can be thought of as examples of "reaction enthalpy," where the "reaction" is just a phase change. So, it may be useful for you to review your Lesson 2 notes before proceeding.

Say we want to know how much heat will be produced by reacting 100.0 g of C₂H₂ with an excess of chlorine. We can use the ΔH value for the reaction, -185 kJ/mol; because it is given in kJ/mol and we are given a reactant mass, we will need to convert the amount of C₂H₂ to moles. By now, this type of conversion should be almost second nature to you.

100.0 g C₂H₂/26.04 g/mol = 3.84 mol

Next, we can multiply this value by the reaction enthalpy (ΔH) to find the heat flow of the reaction.

q = -185 kJ/mol * 3.84 mol = -710 kJ

Note that we are returning to the convention we used earlier of using "q" to symbolize the absolute amount of heat absorbed or released by a process, and using a negative sign to indicate an outward flow of heat.

Consider a more practical example: say you need to burn some fuel to heat your tea kettle, and you know that doing so will require 45000.0 kJ of energy. Your fuel combusts with a reaction enthalpy of -6777 kJ/mol, and has a molar mass of 142.29 g/mol. How much fuel will you need to weigh out and burn?

To start, we will let q equal -45000.0 kJ, since we need the reaction to release heat. Then we will set this equal to the product of ΔH and n, the number of moles (since kJ/mol * mol gives kJ). Rearranging and solving, we can calculate n.

q = -45000.0 kJ = -6777 kJ/mol * n

n = -45000.0 kJ/-6777 kJ/mol

n = 6.64 mol

Then, we can convert from moles to grams by using the molar mass. We find that the mass of fuel needed for this reaction will be 945 g, or a bit less than a kilogram of fuel. These kinds of calculations are essential to engineers who need to design mechanisms that rely on fuel combustion to produce heat.

Practice:

a. The oxidation of 0.0700 moles of Al gives off 117.2 J of heat. Calculate ΔH for the oxidation of aluminum.

b. When 20.0 g of MgCl₂ is decomposed into chlorine and magnesium, it requires 135 kJ of heat. Calculate ΔH for this reaction.

c. Using your answer from (a), find the heat flow (with correct sign) when 26.2 g of Al are oxidized.

d. Using your answer from (b), find the heat flow when 2.5 mol of MgCl₂ are decomposed.

Answers:

a. -1674 kJ/mol

b. 643 kJ/mol

c. -1625 kJ

d. 1610 kJ

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