Thermodynamics - Review and summary

The first law of thermodynamics says" energy is conserved.

Definitions:

The system is the sample, or object, or apparatus we are interested in.

The surroundings is everything else.

We can add energy to our system either in the from of heat, q, or work, w.

By convention, when q > 0 heat is added to the system (the energy of the system increased).

Likewise, when w > 0 work has been done on the system (the energy of the system increased).

Define the Internal Energy, E, of a system as the sum the kinetic and potential energies of all the particles in the system. We will only be interested in the change in E, which we will call DE, as the system undergoes some process or change.

DE = E_final- E_initial.

If q > 0 then E is increased and vice versa.

If w > 0 then E is increased and vice versa.

The first law of thermodynamics an be written in the form of an equation:

DE = q + w.

One of the ways that we can do work on the system is to compress it. Or, if the system expands against some kind of pressure, the system will do work on the surroundings.

(We will not consider electrical work in 103A.)

Most of the time we are working in a laboratory open to atmospheric pressure. So our expansion work comes from our system (sample) expanding against the atmospheric pressure or contracting under the atmospheric pressure.

For example, when we cool a sample open to the atmosphere the sample contracts. in this contraction the atmosphere pushes on the sample so that we have done work on the system.

Call the work done on the system in an expansion or a contraction process, w_exp. If the sample contracts w_exp > 0; if the sample expands, then, w_exp < 0.

If we do not have electrical work, or any other work other than expansion and contraction, then the first law can be rewritten as:

DE = q + w_exp.

Our most common experience is that our experiments are done on a laboratory bench open to atmospheric pressure. In this case the pressure, p, on the system is constant. Using a subscript, p, to indicate that pressure is being held constant, we can rewrite the first law as,

DE_p = q_p + w_exp.

In the laboratory we usually measure the heat absorbed by or released from our system. In this case the w_exp seems to get in the way.

Accordingly we define a new quantity, H, called the enthalpy. Enthalpy has units of Joules. Enthalpy was referred to as the "heat content" in the early days of thermodynamics, but that name is no longer used. Enthalpy is defined such that,

DH_p = DE_p- w_exp.

From this definition we see that

DH_p = q_p.

(It is necessary that pressure be held constant for this relationship to be true. If pressure is not constant this relationship does not hold. You can still define enthalpy and DH, but the relationships of these quantities to E and DE is more complicated.)

All of the phase changes we discussed above take place at constant pressure. Thus the heats involved are heats at constant pressure. That is, they can be called q_p.

It is customary to use DH rather than q for situations like these. The various heats involved in the phase changes are called DH_fus, DH_vap, DH_sub, and so on. It is understood that in these cases the pressure is held constant.

Let's do one more example of a phase change using the correct language.

What is the enthalpy change in melting 500. g of Ag at 1234 K? From the tables we find that DH_fus = 11.3 kJ/mol for Ag at 1234 K (which is the normal melting point of silver).

Moles Ag = 500. g/(107.9 g/mol)

DH = 11.3 kJ/mol ´ mol Ag.
 
 

Heats of Chemical Reactions

Chemical reactions almost always give off heat or absorb heat. In this course we will refer to the heat of reaction as DH. Before we discuss heats of reaction we need to define more carefully what we mean when we write the equations for chemical reactions.

Recall that a chemical reaction equation always has the form,

reactants ® products.

Then

DH = H_products- H_reactants,

even though we will never look at an individual H for any substance.

Here's what we didn't tell you. The chemical reactions we will do calculations on always have the form

reactants(isolated, pure, at temperature, T, and pressure, p)

®

products(isolated, pure, at temperature, T, and pressure, p).

The temperature, T, is usually 25^oC and the pressure, p, is usually 1 atmosphere.

Even if the temperature is not 25^oC and/or the pressure is not 1 atmosphere, p and T still have be the same on both sides of the arrow.

Example, consider the reaction

2 HCl(g) + Na₂CO₃(s) ® 2 NaCl(s) + CO₂(g) + H₂O(l).

According to what we have just said, this reaction equation describes a process which

begins with 2 moles of pure, isolated HCl(g) at 25^oC and 1 atmosphere pressure and one mole of pure, isolated Na₂CO₃(s) at 25^oC and 1 atmosphere and

ends with 2 moles of pure, isolated NaCl(s) at 25^oC and 1 atmosphere, 1 mole of CO₂(g) at 25^oC and 1 atmosphere, and one mole of H₂O(l) at 25^oC and 1 atmosphere.

This reaction will get hot. How do we deal with that?

Let's rewrite the equation for the reaction in a way that is instructive even if it is not strictly proper:

2 HCl(g) + Na₂CO₃(s) ® 2 NaCl(s) + CO₂(g) + H₂O(l) + heat.

Here's how we are to understand this equation. The reaction mixture got hot, so we cooled the products back down to the initial temperature, usually 25^oC. However, we measured the amount of heat as we removed it. Then we separated the products into their own containers and measured any heat involved in that process.

So we end up with our products separated and isolated and pure at 25^oC and 1 atmosphere pressure. And we have obtained an amount of heat out of the reaction, q_p. In our case heat went out into the surroundings so that it left the system. That is, q_p < 0.

(That may sound strange at first - that the system got hot, but q_p < 0. But the reason the system got hot, so that heat had to be removed, was because the system gave up some of its energy in the form of heat.)

A reaction that gives up heat to the surroundings (gets hot) is called an exothermic reaction.

In exothermic reactions, q_p < 0. But we want to use some of our new terminology. Since

DH_p = q_p,

it is clear that DH_p < 0 for an exothermic reaction.

Since we agree that all chemical reactions are going to be constant pressure processes we usually leave off the subscript, p, and just carry with us the knowledge that the reaction is at constant pressure.

The changes in enthalpy for chemical reactions are usually written as simply DH, or DH_react, or sometimes D_rH.

For some reactions, DH > 0, or we could say, q_p > 0. In this case heat went INTO the system. The system gained heat. Reactions where DH > 0 are called endothermic reactions. (In endothermic reactions the reaction mixture would get cold. Endothermic reactions are not as common as exothermic reactions, but they do exist.)

Chemical energy provides most of the energy that we use in life and industry, including keeping all animals alive. (Note: Plants convert solar energy into stored chemical energy which animals then convert into heat and work, etc.)

Therefore, it is important to understand the heat and energy involved in chemical reactions.

How To Measure Heats of Chemical Reactions

A common way to measure heats of chemical reactions is to use a "bomb calorimeter." A bomb calorimeter is a sealed metal container in which the reaction is carried out and the container (with its reaction mixture) are immersed in a large insulated water bath.

The reaction is allowed to run in the sealed container and any heat involved goes into (our out of) the water in the water bath.

Since we know the specific heat of the water in the water bath and we know how much water is in the water bath. We can find out how much heat the reaction generated or used by measuring the temperature change in the water bath.

(We would like the water bath to be large so that the temperature change is small. Recall that ideally we want the final temperature of the products to be the same as the initial temperature of the reactants.)

Here's an example of such an experiment.

We have a bomb calorimeter apparatus with heat capacity 3576 J/K. (This means that it takes 3575 J to raise the temperature of the apparatus by 1.00 K.)

We place 0.4539 g of glucose in the apparatus with an excess of O₂ in order to run the reaction:

C₆H₁₂O₆(s) + 6 O₂(g) ® 6 CO₂(g) + 6 H₂O(l).

We find that the temperature of the apparatus increases by 2.37 K. What is the DH for the above reaction in kJ/mol? (FW of glucose is 180.16 g/mol.)