Chemistry
Chapter 5: 6-8
WebLecture
Calorimetry and Enthalpy
Outline
Energy Considerations in Predicting Reaction Outcomes
Conservation of energy requires that the total energy in an isolate system before and after a transfer of energy among objects within the system remain constant. Obviously then, if we have many energy transfers, the total energy will remain unchanged throughout the sequence. We can use this principle to analyze complex chemical reactions with several steps, where the products of one reaction become the reactants of later reactions.
Hess's Law
An important chemical law is Hess's law, which states that the heats of reaction of individual steps in a chain of reactions can be added up to determine the overall heat of reaction of the final equation. This law is a direct result of the conservation of energy and the concept of a state function.
Don't confuse state functions for certain properties of a system with changes of state! A change of state is a change from one form of matter (solid, liquid, gas, plasma, Bose-Einstein condensate) to one of the other forms of matter. A state function is a property of a system that is independent of the manner of how it changes. With a state function, we only care about the initial and final states of the system, we don't care about internal steps.
You might look at it this way: your mother doesn't care about how long it takes, or whether you use levitation or pick everything up by hand, as long as your room goes from its current messy state to a pristine state that she can proudly show off to her mother. [You may care....in which case, this isn't a state function as far as you are concerned.]
In chemistry, because of the way the conservation of energy rules work, changes in enthalpy are state functions. Suppose that we have a particular endothermic reaction,
AB + CD + ΔE1 → AD + BC.
Let's say that there are several ways the reaction could occur, either directly (simply switching partners), or in multiple steps:
[1] AB + CD + ΔEa → [2] A+ + B- + C+ + D- + ΔEb → [3] AD + BC
The state function principle says that the overall energy expended will be the same whether we do it all in one step or broken down in two steps. In other words,
ΔEa + ΔEb = ΔE1.
If that doesn't make sense, think of it this way. You want a CocaCola out of the automat machine. It doesn't matter whether you put in 2 quarters and a dime (and get no change), or put in 3 quarters and get two nickels back, or put in a dollar bill and get a dime and a quarter back; the CocaCola still cost 65 cents. The state change is 65 cents out of your pocket and one CocaCola into your tummy.
The practical importance of Hess's law lies in its ability to show us which of several reactions will require the least amount of energy. We can break any reaction down and determine the enthalpy necessary to form the compound from the naturally occurring element. For example, we can experimentally determine the enthalpy changes required to form CO2 gas from naturally-occurring C and O2 gas. This is called the "enthalpy of formation" of CO2.
Because of the state function rules and Hess's law, we know that it doesn't matter whether we form CO2 from naturally occurring C and O2 gas, or as a by-product from a gas-forming acid-base reaction: the enthalpy of formation is the same in either case. So if we know the enthalpies of formation of all the products and reactants of a reaction from any source, we can determine the overall enthalpy change of a reaction as the differences between the energy necessary to form the products less the energy required to form the reactants:
ΔHreaction = sum of ΔHf(products) - sum of ΔHf(reactants)
By determining the heats of formation of common reactions, chemists can predict the heat required or released for reactions that use multiple steps, simply by totaling the heats of reaction of the individual steps. They can then determine which reactions are economically feasible, without actually having to perform them.
For example, C + O2 → CO2. It is sometimes necessary to produce CO2 commercially (as for the preparation of carbonated beverages), and so an energy efficient process is desirable to reduce costs of production. A chemist can look at several possible processes for isolating the C and O2 and forming CO2 from these basic elements, and estimate whether the process will be useful or merely theoretically interesting.
Calorimetry
The most common method of determining the heat of reaction is to run a reaction in an isolated system and measure the temperature change of the entire system. If the isolation is absolute (and the pressure doesn't change —that is, the system does no work on the outside environment —then the change in temperature must be entirely the result of the reaction and must be the entire result of the reaction as well!
To determine the enthalpy or heat change, we have to combine information about the temperature with information about the masses of components involved. We also need to know how fast the system absorbs or dissipates heat. In a water-based calorimeter, the reaction occurs in a chamber that transfers the heat energy to the surrounding water "heat sink". We can covert the temperature change of a given amount of water to energy by remembering that water absorbs heat according to its specific heat, 4.184 Joules/gram-Kelvin. In other words, to raise a gram of water one Kelvin, we must expend 4.184 Joules of energy. If a reaction causes 100grams of water to rise 5 Kelvin in temperature, then the water has absorbed
4.184 Joules/gram-Kelvin * 100 grams * 5 Kelvin = 2092 Joules of energy.
If we know the masses of the reactants involved, we can calculate the Joules per gram of substance or Joules per mole of substance involved.
As you study this chapter, keep in mind that the techniques outlined here are used daily by industrial chemists to bring you all the chemicals on which you depend--from nylon to ceran stove tops to the soap you use to wash your face to the fertilizer you put on the garden. Without the dedication of all those chemists who put together the kind of information in heats of formation tables, many of the goods and services you enjoy would be much more expensive.
The Bottom line: Enthalpy of Formation
We can put all this together by realizing the the formation of different molecules from the elements in their natural state are all examples of chemical reactions that follow Hess's law and the laws of thermodynamics. Since enthalpy is a state value, we are only concerned with differences between states, not absolute values at a given state. We can chose any convenient point as a "zero" point from which to measure, so by convention, the enthalpy needed to form an element in its natural state is 0. The enthalpy of formation for Be(s) is zero. The enthalpy of most gases (found in diatomic states), such as H2(g) is zero.
To determine the enthalpy of formation of a compound, we must perform an experiment that produces the compound as a result of combining the elements in their natural form. Suppose we use electrolysis of water to split the elements H2 gas and O2 gas. We can determine the amount of energy we put into the system from the temperature change of the water and the amount of electricity used.
H2O (l) → H2 (g) + ½O2 (g) ΔH = +285.83 kJ/mole
The formation of water requires the reaction to run the other way:
H2 (g) + ½ O2 (g) → H2O (l) ΔH = -285.83 kJ/mole
We can do a similar experiment to determine the formation of CO2 from C(s) and O2. The results of this experiment show that the formation of CO2 releases energy as well:
C (s) + O2 (g) → CO2 (g) ΔH = -393.509
And we can do the same thing for the formation of methane from C(s) and H2:
C (s) + H2 (g) → CH4 ΔH = -74.87
Now we can use Hess's law to predict the outcome of a reaction such as burning methane in oxygen:
CH2 + 1½ O2 → CO2 + H2O
We add up the enthalpies of formation for products:
-285.83 Formation of ONE mole H2O (g)
-393.509 Formation of ONE mole of CO2 (g)
------------
-679.339 kJ
We add up the enthalpies of formation for the reactants
-74.87 Formation of ONE mole of CH4 (g)
0 Formation of ONE mole of O2 (g) (its natural state)
--------------
-74.87kJ
We subtract the initial state (reactant enthalpy of formation) from the final state (product enthalpy of formation) to get the change in enthalpy for the reaction:
-679.339kJ - (-74.87kJ) = -679.339kJ + 74.87kJ = -604.469kJ
The reaction should produce (assuming the reaction is complete and there are other energy losses) about 604.5 kiloJoules of energy for each mole of CH4 burned.
Product Favored or Reactant Favored?
Since energy tends to move to a lower state whenever the system will allow it, reactions that produce energy (exothermic or exergonic reactions) are more likely to occur than actions that require energy input (endothermic or endergonic reactions). Take a look at the compounds and energies of formation listed in Appendix L of the text. The compounds commonly found in nature, like CO2, methane, water, iron oxide (rust), and ammonia gas (NH3 all form during exothermic reactions from their constituent elements. Compounds not found in nature, such as ethene (C2H4 (g) have to be manufactured. Elemental forms that are not the normal "room temperature" form of the element, such as iodine gas (I2 (g)) also require energy input to form. The laws of thermodynamics require that energy move to the lowest state possible within a system, and so determine whether an element appears in nature as a gas, liquid, or solid, and whether a compound (which might form in other conditions) will form within the local climate temperature ranges.
We are now prepared to evaluate reaction systems, sets of reactions that will produce a desired product from available materials. By calculating different reaction steps leading to the same products, we can determine which will be most effective or cost the most (in terms of energy input) if there are endothermic steps involved.
Practice with the Concepts
Enthalpy is an extensive quantity!
Discussion Questions
- What does it mean to say that the heat of formation for a given elemental form is zero?
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