Thermochemistry

In our studies thus far we have written simple equations, predicted the product of simple reactions, balanced equations and performed quantitative calculations using balanced chemical equations. But there is one important characteristic of a chemical reaction which we have not yet included in a chemical reaction, the heat associated with the chemical reaction.

We have seen several reactions which we could classify as violent. Recall the reaction between magnesium and dry ice (carbon dioxide). Although the reaction was slow to start, once it began it proceeded rapidly. We saw how brightly the reaction became as the magnesium reacted with the carbon dioxide. The reaction of potassium in water was another violent reaction. Both of these reactions produced considerable heat. Heat is what we will focus on in Chapter 5.

Let's look at two reactions to set the stage for this discussion.

We will use the terms system and surroundings to help focus on how heat flows. System is that portion of the universe we single out for study and which is bounded by some boundary real or imaginary. The surrounding is everything else.

If in a chemical change or reaction, energy is released, the temperature of the system will get warmer than the surroundings, than heat will flow from the system to the surroundings. When we touch the system it feels hot. In the first experiment magnesium reacted with hydrochloric acid. Heat was produced in the reaction and it flows from the system (the reaction) to the surroundings. This is an example of an exothermic reaction.

Mg_(s) + 2HCl_(aq) ----> MgCl_2(aq) + H_2(g) + heat

In the second example the reaction occurred in the beaker. That was the system. Had we touched the reaction container (the system) is would have felt cool. Heat would be removed from our hand, which is at a higher temperature than the system. Heat must flow from the surrounding to the system. When an endothermic change or reaction occurs heat is absorbed by the system. In order for that to happen the temperature of the system is cooler than the surroundings and when we touch the system it feels cool. As the reaction occurred heat flowed from the surroundings to the system.

heat + Ba(OH)₂.8H₂O_(s) + 2NH₄SCN_(s) ---> Ba(SCN)_2(aq) + 2NH_3(g) + 10H₂O_(l)

So what have we discovered in these two examples? These two reactions were chosen because the particular change I wanted you to note was very evident. In the case of the reaction between magnesium and hydrochloric acid the reaction produced heat. Heat was released when the reaction began. In the case of the barium hydroxide and ammonium thiocyanate instead of getting hotter the reaction mixture became cooler.

The study of the energy changes when a reaction occurs is called thermochemistry. Thermochemistry is part of thermodynamics,the study of heat, energy, and work and and their transformations. To begin our study of thermodynamics (and we will encounter thermodynamics many different times during this year) we are going to begin by covering thermochemistry.

As an introduction to thermochemistry I need to define several important terms so that we might better understand the two reactions we observed earlier.

Those terms are energy, temperature, heat and work.

Because energy is not tangible, as are material objects, it become difficult to define it completely. Energy is the capacity to do work or to transfer heat.

When we discuss energy two forms of energy come to mind potential energy and kinetic energy. Potential energy

U = mgh: g = 9.8 m sec^-2

is energy stored in an object by virtue of its position. A book held above my head has more potential energy than a book held at my side near my waist. The amount of potential energy an object has depends on the mass of the object and its height above the earth's surface. If I drop the book the potential energy is converted to kinetic energy. Kinetic energy is energy of motion. The magnitude of the kinetic energy of an object depends on its mass and velocity.

E_k = 1/2 mv²

The heavier and faster an object is going the more work it can do on whatever. If we substitute the SI units for mass and velocity into the kinetic energy equation we have the correct units for energy. The SI unit for energy is the joule (J) (1 kg-m²s^-2 ). An object with a mass of 1 kg traveling at a velocity of 1 m sec^-1 has a kinetic energy of 1 J. A 100 watt light bulb produces 100 J of energy for every second it operates. (When the City of Stillwater sends a bill for the energy used at your house it includes an electrical bill for energy used in the form of electricity and the units used are kilowatt-hours. A single kilowatt-hour is equivalent to 1000 watts-3600 seconds or 3.6 x 10⁶ watt-sec or 3.6 x 10⁶ joules. A BTU is the amount of energy required to raise the temperature of one pound of water one degree Fahrenheit.)

In the first reaction we saw, energy was given off in the form of heat. No work was done by the reaction, with the exception of pushing back the atmosphere. So no useful work. The appears to have been energy present in the reactants which is liberated when the products are formed, as heat when the reactants were combined.

In the second reaction energy was absorbed when the reaction occurred. Again no useful work was accomplished.

If we had the proper equipment we could have measured the temperature of both reactions. Temperature is a measure of the degree of hotness or coldness of an object. If I indicate the temperature of a sample of water is 95 degrees C we know the sample is very hot. If another sample of water has a temperature of 1 degrees C, we know the sample will feel cool when we touch it.

Heat is energy that is transferred as a result of a temperature difference. Heat always flows from a warmer object to a cooler object. Heat causes a change in temperature. So when we 'heat' an object it get hotter.

Lighting a bunsen burner and placing it beneath a beaker filled with water causes the temperature of the water to increase. Heat flows from the warmer flame of the bunsen burner to the cooler water. We can measure this temperature change using a thermometer. If we have two beakers, a 100 mL beaker and a 25 mL beaker each filled with water at the same initial temperature, and an equal amount of heat is added to each beaker we will find the water in the larger beaker to have a lower temperature compared to the temperature of the water in the small beaker. The temperature change depends on the amount of heat added to the water. Heat depends on the amount of matter present. When the bunsen burner is removed, the source of heat, the water in the beaker will cool, as heat flows from the warmer water in the beaker to the cooler air of the room, and return to room temperature. I have described heat as flowing or being transferred and this may be misleading. Heat is not matter, it is not contained in matter. Heat is a way to exchange energy. We will use the terms system and surroundings to help focus on how heat flows. System is that portion of the universe we single out for study and which is bounded by some boundary real or imaginary. The surrounding is everything else. If in a chemical change or reaction, energy is released and the temperature of the system will get warmer than the surroundings, than heat will flow from the system to the surroundings. When we touch the system it feels hot. In the first experiment potassium permanganate reacted with glycerine. Heat was produced in the reaction and it flows from the system (the reaction) to the surroundings. This is an example of an exothermic reaction.

Let's consider some experiments where we transfer some energy into water by heating.

Amount and Temperature:

Suppose we have two containers of water are at 25 ¾C initially. One contains 50 mLs and the other 100 mLs.

The beaker on the left has 25 mLs of water and the beaker on the right has 50 mLs of water. Both have the same initial temperature. If I add the same amount of heat to both beakers, using a bunsen burner, the beaker with the smaller amount of liquid reaches a higher temperature. This suggests that there is a relationship between the final temperature of a substance and its mass when a constant amount of heat is transferred. In this case the smaller the mass of the substance the higher the final temperature. This is an inverse relationship.

change in temperature is inversely proportional to the mass of substance

Amount and Heat:

If we consider another example suppose the two beakers above are each heated with the same source of heat for the same amount of time. If the final temperature of the 50 mLs sample is 50 ¾C than the final temperature would be 37.5 ¾C.

Consider the two beakers containing water, both at the same initial temperature, say 25 degrees Celsius.

If the final temperature of the water in both beakers is the same to which was the greater amount of heat added? This is a variation on the previous example approached in a slightly different way. In this case the final temperature (the change in temperature) is the same. For this to happen more heat will have to be added to the beaker with 100 mLs of water. This establishes another relationship, the amount of heat required to increase the temperature of a sample of a substance is directly related to the amount of that substance.

amount of heat is directly proportional to the mass of substance

Check out the class DCI for more discussion.

Below is a plot of what happens to the temperature of a sample of water as heat was added at a constant rate. The heating curve is summarized in the graph below;

We notice the obvious, as heat is added (along the x-axis) the temperature of the sample, in general, increases. Looking at the plot more closely we actually see there are two plateaus where the temperature remains constant as heat is added. The sample is water so it is interesting that the two plateaus are at 0 degrees Celsius and 100 degrees Celsius. One plateau (#2) corresponds to the melting/freezing point of water, the other plateau (#4) corresponds to the boiling/condensing point of water. Besides the two plateaus there are three regions where the temperature increases linearly with added heat.

The five label regions can be characterized by specifying the temperature change (if any) and the phase(s) present.

At #1 the temperature changes from -10 degrees Celsius to 0 degrees Celsius; the phase is H₂O(s). We are referring to the line with a positive slope between - 10 deg Celsius and 0 deg Celsius. So as heat is added the temperature of the sample of water increases linearly. That the line has a constant slope over the temperature range suggests uniform behavior. That is there is a relationship between the amount of heat added and the temperature change. It turns out that how much heat is required to change the temperature of solid water also depends on the amount of water. The characteristic property that relates the amount of heat required to change the temperature of 1 gram of a substance by 1 degree Celsius is called specific heat. The specific heat of water in the solid phase has a value of 2.09 J g^-1 C^-1.

At #2 the temperature does not change, but heat is added. The added heat is absorbed by the solid converting the solid to the liquid. So at the left most point on the horizontal line the sample is all solid and the temperature is 0 degrees Celsius. As heat is added the solid melts, recall it takes energy to over come the attractive forces holding the particles together in the solid phase, forming the liquid. The amount of intermolecular attractive forces broken in this phase change is small since the particles are very close to each other in each phase. So at the right most point of the horizontal line the sample is all liquid at 0 degrees Celsius. The heat required to convert water from the solid phase to the liquid phase;

H₂O(s) ---> H₂O(l)

is called the heat (enthalpy) of fusion (heat of solidification). For water the heat of fusion has a value of 6.01 kJ mol^-1.

At #3 the temperature changes from 0 degrees Celsius to 100 degrees Celsius. The phase is liquid. Again notice the linear behavior. In this temperature range, given the amount of water remains constant, the addition of a given amount of heat causes the temperature of the water to change by the same amount. The specific heat of liquid water is 4.184 J g^-1 C^-1. Comparing liquid water to solid water it takes more than twice the amount of heat to change the temperature of liquid water by the same amount compared to solid water.

At #4 the temperatrue does not change as the heat is added. At this plateau the heat added is absorbed by the liquid as it is converted to the gas(vapor) phase. The heat absorbed is used to overcome the attractive forces between the particles in the liquid phase. Notice the amount of energy required to convert a liquid to its gas is much greater compared to the energy required to convert a solid to its liquid. At the left-most point on this line the sample is all liquid at 100 degrees Celsius. Moving to the right the amount of water in the liquid and vapor change, and the temperature remains constant. At the extreme right the sample is all vapor at 100 degrees Celsius.The heat required to convert water from the liquid phase to the gas phase;

H₂O(l) ---> H₂O(g)

is called the heat (enthalpy) of vaporization (heat of condensation). For water the heat of vaporization has a value of 40.67 kJ mol^-1.

At #5 the temperature changes from 100 degrees Celsius to 110 degrees celsius. The phase is gas(vapor). In the vapor phase the specific heat of water is 1.84 J g^-1 C^-1.

Here is a summary table of the specific heats and enthalpy of phase changes for water;

Let's look at several sample problems;

How much heat is required to change 36.0 g of H₂O(l) at 100 deg C to 36.0 g of H₂O(g) at 100 deg C? Answer

How much heat is required to convert 30.0 g of H₂O(s) at -10 deg C to 30.0 g of H₂O(g) at 110 degC. Answer

The specific heat of iron is 0.433 J g^-1 C^-1. What is the final temperature if 45.0 g of iron, initially at 95 deg C, is added to 100.0 g of water at 23.0 deg C? Answer.

Some other useful specific heats are;