Chapter 5 - Thermochemistry

When a chemical reaction occurs, the answer involves stability. For a reaction to take place spontaneously, the final products of the reaction must be more stable than the reactants. But what is stability and what does it mean to say that one substance is more stable than the other? The key factor in determining the stability of a substance is energy. Less stable substances have higher energy and are generally converted into more stable substances with lower energy. But what, in turn, does it mean for a substance to have higher or lower energy? We will explore some different forms of energy in this chapter and look at the subject of thermochemistry - the release or absorption of heat energy that accompanies chemical reactions. So let's start by talking about energy. Energy is the ability to do work or transfer heat. Energy used to cause an object that has mass to move is called work. Energy used to cause the temperature of an object to rise is called heat. Now, this chapter is about thermodynamics, which is the study of energy transformations, and thermochemistry, which applies the field to chemical reactions specifically. Let's talk about kinetic and potential energy. Kinetic energy is energy an object possesses by virtue of its motion. So whenever something is moving, that is due to kinetic energy. The equation for kinetic energy is:[E_{\text{kinetic}} = \frac{1}{2} \cdot \text{mass} \cdot \text{velocity}^2] Here we have a girl with her bike at the top of the hill. At this point, there's zero kinetic energy - she's not moving. But she has potential energy; she has energy stored. Once she starts to move down the hill, she has kinetic energy. Potential energy is energy possessed by virtue of its position or chemical composition. We have some units for energy. The SI unit of energy is the Joule (J). One Joule is equal to (1 \: \text{kg} \cdot \text{m}^2/\text{s}^2). From this definition, we can obtain two conversion factors: (1 \: \text{J} = 1 \: \text{kg} \cdot \text{m}^2/\text{s}^2) and (1 \: \text{J} = 1 \: \text{N} \cdot \text{m}). Another non-SI unit, still in widespread use, is the calorie. One calorie is equal to 4.184 joules. It is important to understand that this calorie is not the same as a calorie of food. The food calorie is one kilocalorie (kcal), which means (1 \: \text{kcal} = 1000 \: \text{cal}). Now, let's talk about some definitions. The first ones that we need to understand are the system and the surroundings. The system includes the molecules we want to study. In this case, we have molecules of hydrogen (white spheres) and molecules of oxygen (red spheres). This is the system. The surroundings are everything else - the cylinder, the piston, etc. The system is basically the molecules of hydrogen and oxygen, while the surroundings are everything else. Work is energy used to move an object over some distance. Work is defined by force times distance, where F is for force and R is for distance. This is the definition of footwork. Energy is used to move an object over some distance. Work can also be transferred as heat, so energy can do work but can also be converted to heat. Heat flows from warmer objects to cooler objects. For example, if you put a piece of ice on your hand, the heat from your hand will be transferred to the ice, causing it to melt. Heat always flows from warmer objects to cooler objects. Now, let's consider the conversion of energy. Energy can be converted from one type to another. As we mentioned at the beginning of the lecture, the skier at the top of the hill has potential energy. As she starts to go down the hill, the potential energy is converted to kinetic energy. At the bottom, the energy is fully converted to kinetic energy, allowing for movement. This helps us understand the first law of thermodynamics, which states that energy is neither created nor destroyed. In other words, the total energy in the universe is constant. If a system loses energy, it must be gained by the surroundings, and vice versa. If the hand loses heat, it is because the ice absorbed that heat. This means that energy is simply being transformed, not created or destroyed. The internal energy of a system is the sum of all the kinetic and potential energy of its components, denoted as "e". So, "e" represents the internal energy of a system, including both kinetic and potential energy. As shown in the diagram, the internal energy of a system can change. For example, the system initially has a higher internal energy, but as time goes by, it starts to lose energy. Eventually, it finishes with a total energy less than the initial one, as the system absorbed energy from its surroundings. On the other hand, if the system gains energy from the surroundings, it will finish with a higher energy than the initial one, resulting in a positive change in energy. These are two examples of what can happen to a system. Sometimes, the system loses energy and it is gained by the surroundings. In other cases, the system gains energy from the surroundings. If the change in internal energy is greater than zero, it means the system absorbed energy from the surroundings. This change in energy is called endergonic. On the other hand, if the change in internal energy is lower or negative, it means the system released energy to the surroundings. This change in energy is called exergonic. In summary, energy can be transformed and converted, but not created or destroyed. The internal energy of a system is the sum of its kinetic and potential energy. Changes in internal energy can be positive or negative, representing energy absorbed or released by the system from its surroundings.The system because the surroundings are doing work on the system. Alternatively, the system can also use heat to affect the surroundings, and the system can do work on the surroundings. When energy is exchanged between the system and the surroundings, it is exchanged as either heat or work. Remember that we mentioned before that energy can be transformed into work or heat. In the case of energy from the system, it can be absorbed by heat or work, or lost by heat or work done on the surroundings. Therefore, the change in internal energy is equal to the heat plus the work. Here, we have a table that summarizes the possibilities for Q, the signs, and what those signs mean. For example, if Q is positive, it means that the system gains heat. If it's negative, it means that the system loses heat, which goes to the surroundings. Similarly, if work is positive, it means that work was done on the system by the surroundings. If it's negative, it means that work was done by the system to the surroundings. The change in internal energy (ΔE) can be positive or negative, indicating a net gain or loss of energy by the system. Now, let's discuss the exchange of heat between the system and the surroundings. When heat is absorbed by the system from the surroundings, the process is called endothermic. In this case, the system gains heat from the surroundings. Conversely, the system may release heat to the surroundings, which is known as an exothermic process. For example, in a reaction, the reactants may produce energy that the system absorbs, making it an endothermic reaction. Now, let's talk about state functions. Usually, we have no way of knowing the internal energy of a system. Finding that value is simply too complex. However, we do know that the internal energy of a system is independent of the path by which the system achieves that state. In the example below, the water could have reached room temperature from either direction. It doesn't matter if it started at 100 degrees Celsius and cooled down or if it started as ice at 0 degrees Celsius and warmed up. The important thing is that it reaches the same temperature, indicating a state function. The internal energy of a system depends only on its present state, not on the path taken to reach that state. Therefore, the change in internal energy depends only on the initial and final internal energy. It doesn't matter how the system arrived at that point, as long as it had an initial and final internal energy. Here, we have an example of how a battery can be discharged. In this case, it releases energy, which is transformed into heat. The energy is released from the battery and is transformed into work and heat. The change in energy for both examples is the same, indicating a loss of internal energy. However, work and heat are not state functions. Whether the battery is shorted out or discharged by running a fan, the change in internal energy may be the same, but the distribution between work and heat may differ. Heat and work are different in the two cases, so heat and work are not state functions. However, ΔE is a state function. So, work, which we mentioned before, is a type of energy usually seen in an open container. The only work done is by a gas pushing on the surroundings. For example, we have a gas in a container with a piston and a cylinder, representing the initial state. As the gas starts to move the piston up, we have a change in volume. This change in volume represents the work done by the gas. In this case, the gas is the system, and the piston and cylinder are the surroundings. We can measure the work done by the gas if the reaction is done in a vessel fitted with a piston. For instance, in the reaction where HCl produces hydrogen, the gas starts to move the piston, creating work. The work done is equal to -PΔV, where P is the pressure and ΔV is the change in volume. If a process takes place at constant pressure and the only work done is the pressure-volume work, we can account for heat flow by measuring the enthalpy of the system. Enthalpy (H) is the internal energy (E) plus the product of pressure and volume. Therefore, ΔH = ΔE + PΔV. When a system changes at constant pressure, the change in enthalpy (ΔH) is equal to the heat transfer (q). So, ΔH = q. Enthalpy is associated with the heat interchange in the system. In an endothermic reaction, the system absorbs heat. In an exothermic reaction, the system releases heat to the surroundings. This is determined by the sign of ΔH. If ΔH is positive, it is an endothermic reaction. If ΔH is negative, it is an exothermic reaction. The enthalpy of a reaction (ΔH) is calculated by subtracting the enthalpy of the reactants from the enthalpy of the products. ΔH = H(products) - H(reactants). This quantity, ΔH, is called the enthalpy of reaction or the heat of reaction. In the example given, the enthalpy is lower in the final state compared to the initial state, indicating a negative ΔH. This means that the reaction is exothermic. Enthalpy is an extensive property, which means it depends on the amount of substance present. It's going to depend on the amount of reactants that we have. Changing the LTV for our reaction in the forward direction is equal in size but opposite in sign to the change in enthalpy for the reverse reaction. So sometimes we're going to have a reaction that goes from left to right and also from right to left. Okay, so these are basically in a cleave. These are known as equilibrium reactions. So the enthalpy in the forward direction will be equal in size to the opposite but will have the opposite sign for the reverse reaction. So if, for example, the reaction is 104, the opposite will be -100 joules, for example. Thus, Delta H for a reaction depends on the state of the products and the state of the reactant. Also, if the products are solid or liquid, if you produce water as ice or water as a gas, you're going to have different enthalpies because the enthalpy depends on the state of the products. One way that we can calculate and determine the enthalpy is by using a system known as calorimetry. Since we cannot know the exact enthalpy of the reactants and products, we measure the change in enthalpy through calorimetry, the measurement of heat flow. Okay, so we're going to have a reaction and we're going to measure the change in temperature that will result from that reaction. The instrument used to measure heat flow is called a calorimeter. We need to introduce two concepts that are part of calorimetry. The amount of energy required to raise the temperature of a system by one Kelvin is the heat capacity, usually given for one mole of substance. Here, we have some different values. For this case, our specific heat. The specific heat is defined as the amount of energy required to raise the temperature of one gram of a substance by one Kelvin or one degree Celsius. The difference between heat capacity and specific heat is that specific heat is erasure for a temperature for 1 gram of substance. Here, we have one gram of water, and to go from 14.5 to 50.5, we need like 4.184 joules, or one calorie, to increase the temperature by one degree. So there's basically an equation that we can use a lot to determine, for example, specific heat. Here, we're going to put the heat transfer as Q, the mass as M, and the temperature change as delta T. So this is an equation, and we have here four variables. And remember that this kind of equation is not just to determine specific heat. We can also determine the heat transfer, for example, if we know the specific heat, the mass, or the temperature. We can also calculate the mass if we have the other three variables. So it's really important that you learn how to rearrange this equation in a way that you can determine mass or the change in temperature or the heat that has been transferred. By carrying out a reaction in excess solution in a simple calorimeter, the heat change for the system can be found by measuring the heat change for the water in the calorimeter. The specific heat for water is well-known, 4.184 joules per gram per Kelvin. We can calculate the change in enthalpy for the reaction with this equation. If we want to determine the heat, we can rearrange the specific heat equation that we saw before and have this equation. So now we can multiply the mass by the specific heat by the change in temperature, and that will give us the heat that has been transferred in the reaction. Now, how much heat is needed to warm 250 grams of water from 22 degrees Celsius to 298 degrees Celsius. So here, we must find the quantity of heat, Q. The question is how much heat, so we need to determine the Q given the mass of water and also the change in temperature that we can calculate from here. Remember, the formula for calculating the change in temperature is the final temperature minus the initial temperature. In this case, we are dealing with water, and we know the specific heat for water is 4.18 joules per gram per Kelvin. We are given the mass of water as 250 grams and a change in temperature of 349 Kelvin. By substituting these values into the equation, we can calculate that the heat transfer in this system is 3.6 x 10^5 joules. This is the amount of heat needed to raise the temperature of 250 grams of water from 22,000 degrees Celsius to 298 degrees Celsius. Now let's discuss Hess's Law. The change in enthalpy (Delta H) for a reaction can be estimated using published Delta H values and the properties of enthalpy. Hess's Law states that if a reaction is carried out in a series of steps, the Delta H for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps. Because Delta H is a state function, the total enthalpy changes depend only on the initial and final states of the reaction. In this example, we have a reaction involving propane (C3H8) and oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). This reaction occurs in three steps, each with its own Delta H value. By adding these equations together, we obtain the overall equation for the reaction. To simplify the equation, we can cancel out certain reactants with products from other steps. For example, the three carbon atoms in the first reaction can be cancelled out with the three carbon atoms in the second reaction. Similarly, the four hydrogen atoms can be cancelled out as well. This is why these atoms do not appear in the final equation. The Delta H values for the three steps are as follows: 103.85 kJ/mol for step one, -1181 kJ/mol for step two, and -1143 kJ/mol for step three. When these values are added together, we get a final Delta H of -2220 kJ/mol, which matches the Delta H of the overall reaction. In summary, Hess's Law allows us to calculate the Delta H for a reaction by summing up the Delta H values for individual steps. We can cancel out reactants and products to simplify the equation and obtain the final Delta H value. So here we have the first reaction, Delta H, and secondly, we get a reaction and Delta H. So we are given two thermochemical equations and our goal is to combine them in such a way as to obtain the third equation and its enthalpy. So we need to use something; we need to add these two reactions to create this one. But we have something here: in equation number two, carbon monoxide is the reactant, while in equation three, carbon monoxide is in the product. So we can manipulate any of those steps in a way that we can have the reactants and the products in the same positions. Okay, because we have this in the products, we need to have this in the products. So we flip this reaction: what is in the products, we move it to the reactants, and whatever is in the reactant, we move it to the product. And because we interchange, we flip this too. Now, also the sign of the Delta H must be changed. The number is going to be equal - the amount of energy that has been released is going to be the same as gain. We just interchange the process. So here we have this equation, and we're going to keep that way because we have carbon in the final reaction. That is this one. We have carbon as the reactant, and we're going to switch this equation so we can have carbon dioxide in the reactants and carbon monoxide and one-half of oxygen in the products. And because we flip this, we also need to change the sign of the Delta H. And now we can add all these equations. But we can see here that carbon dioxide is in the purple reactants here - in the first equation - and is in the products. So we can cancel this carbon dioxide with this one. Also, we have one mole of oxygen here, but we have one-half here in the products. So we can cancel this one-half of oxygen with one-half of this mole. So in the end, we're going to have one-half of this - the one that was left because we just cancel one-half with this one-half. We also move the carbon here to the reactants and the carbon monoxide that is in the product here. So now we just add this plus this, and the Delta H is going to be minus 110.5 kilojoules. So that's how you can determine or calculate the Delta H for a reaction using the Hess law. So we just look for those different steps that can produce the final equation. And if we need to flip some of them so we can have the same products and the same reactants as the final one. If we flip that, the only thing that we're going to do with the Delta H is we're going to change the sign - if it was positive, we can change it to negative; if it was negative, we can change it to positive. And that is only if we need to arrange this equation so we can have our final reaction expressed. Now we can also use the enthalpy of formation. The Delta H of formation is defined as the enthalpy change for the reaction in which a compound is made from its constituent elements in their elemental forms. So every compound has a Delta H of formation as an energy that was transferred or released to create that compound. The standard enthalpies of formation, the Delta H0, are measured under standard conditions - 25 degrees Celsius and 1 atmosphere of pressure. So if the enthalpy of formation was measured under these conditions, those enthalpies of formation are known as standard enthalpies of formation. And here we have an example of different standard enthalpies of formation. All of this type of Delta H were determined under these standard conditions. We can see here that we have positives and negatives because to create some of them, we're going to release or absorb energy to obtain those products. So we can also use the Hess law to calculate the Delta H by using the Delta H of formation. The Delta H of the reaction is going to be equal to the sum of n times the Delta H of formation of the products minus the sum of m times the Delta H of formation of the reactants, where N and M are the stoichiometric coefficients. And what are those stoichiometric coefficients? Those are the numbers in front of the molecules in a chemical reaction. Here, we just have the chemical formula for this compound, so it's 1. Can we assume it's 1? Here we have five of oxygen to get carbon dioxide and four of water. So if we want to determine the Delta H for this reaction by using the standard enthalpy, we need to look. For the standard enthalpy of water, carbon dioxide, oxygen, and C3H8 in the table, okay, so we have here. Remember that the ΔH is the sum of their products minus the reactants. So, for carbon dioxide, the ΔH of formation is -393.5 kilojoules. We're going to multiply that by the coefficient of carbon dioxide, which is 3. Next, we have water, both in gas and liquid form, with a ΔH of formation of -285.8 kilojoules. By the reaction, we have 4 moles of water, so we're going to use 4 times the ΔH of formation of water. These are the only two reactants, so we need to solve this. Whatever value we obtain here, we're going to subtract by 1 times -103.85 kilojoules, which is the standard enthalpy for C3H8. For oxygen, the standard enthalpy of formation is 0, so we multiply this by 3. It's going to be -1180.5 kilojoules. Next, we have -1143.2 kilojoules. Now, we just add these two values, and also, the negative sign in the negative is going to be positive. So, it's going to be this minus this plus this. The result is -2219.9 kilojoules. Okay, so here is basically the same Hess's Law, using the standard enthalpy of formation for each of them. We can obtain this from a table for basically all the natural compounds. For example, oxygen, hydrogen, chlorine, Cl2, have a heat of formation of 0. The other ones, we can find them in the table, and we just substitute them here. Remember, we start with the products and then subtract the reactants. We multiply by each coefficient to the specific enthalpy of formation. For CO2, we have 3. The enthalpy of formation for water is -285.8 kilojoules. For C3H8, it's -103.85 kilojoules times 1, because we just have 1. The enthalpy of formation for oxygen is 0. Then we solve using our mathematical knowledge to determine the ΔH of formation for this reaction.