Chem 150 Week 7 Handout 1 Thermochemistry (I) Define Energy: The capacity to do work or to transfer heat. Work Energy used to move an object over some distance. w = F x d, where w is work, F is the force, and d is the distance over which the force is exerted. Heat Energy used to cause the temperature of an object to rise. Heat flows from warmer objects to cooler objects. System and Surroundings exchange of energy and matter can occur in an open system in a closed system energy can exchange but matter cannot in an isolated system neither heat nor matter can be exchanged with the surroundings First Law of Thermodynamics Energy is neither created nor destroyed; it is conserved. In other words, the total energy of the universe is a constant; if the system loses energy, it must be gained by the surroundings, and vice versa. Internal Energy The internal energy of a system is the sum of all kinetic and potential energies of all components of the system; we call it U. By definition, the change in internal energy, U, is the final energy of the system minus the initial energy of the system: Changes in Internal Energy U = U final U initial When energy is exchanged between the system and the surroundings, it is exchanged as either heat (q) or work (w). That is: U = q + w.
If U > 0 i.e. U final > U initial Therefore, the system absorbed energy from the surroundings. This energy change is called endothermic. If U < 0 i.e. U final < U initial Therefore, the system released energy to the surroundings. This energy change is called exothermic. State functions Usually we have no way of knowing the internal energy of a system; finding that value is simply too complex a problem. However, we do know that the internal energy of a system is independent of the path by which the system achieved that state. In the system above, the water could have reached room temperature from either direction. Therefore, internal energy is a state function. It depends only on the present state of the system, not on the path by which the system arrived at that state. And so, U depends only on U initial and U final.
However, q and w are not state functions. Enthalpy Whether the battery is shorted out or is discharged by running the fan, its U is the same. But q and w are different in the two cases. If a process takes place at constant pressure (as do the majority of processes we study) and the only work done is this pressure-volume work, we can account for heat flow during the process by measuring the enthalpy of the system. Enthalpy is the internal energy plus the product of pressure and volume: H = U + PV Since U = q + w and w = P V, we can substitute these into the enthalpy expression: H = U + P V H = (q+w) w H = q So, at constant pressure the change in enthalpy is the heat gained or lost. In other words the enthalpy of a reaction is the heat of a reaction at constant pressure. Enthalpies of Reaction The change in enthalpy, H, is the enthalpy of the products minus the enthalpy of the reactants and is called the enthalpy of reaction or the heat of reaction. H = H products H reactants
Brown, LeMay About Enthalpy: 1. Enthalpy is an extensive property (depends on amount of substance) 2. H for a reaction in the forward direction is equal in size, but opposite in sign, to H for the reverse reaction. 3. H for a reaction depends on the state of the products and the state of the reactants. How different are H and U? Consider the following reaction: 2CO + O 2 2CO 2
Calorimetry As with U we cannot know the exact enthalpy of the reactants and products, but we can measure H through calorimetry, the measurement of heat flow. Heat Capacity and Specific Heat The amount of energy required to raise the temperature of a substance by 1 K (1 C) is its heat capacity. We define specific heat capacity (or simply specific heat) as the amount of energy required to raise the temperature of 1 g of a substance by 1 K. Specific heat = (quantity of heat transferred)/{(grams of substance)x(temprature change)}, c = q/(m ΔT) By carrying out a reaction in aqueous solution in a simple calorimeter one can indirectly measure the heat change for the system by measuring the heat change for the water in the calorimeter. Because the specific heat for water is well known (4.184 J/mol K), we can measure H for the reaction with this equation: q rxn = (specific heat of solution) x (grams of solution) T Hess s Law Hess s law states that If a reaction is carried out in a series of steps, H for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps, or simply: H total = H 1 + H 2 +. + H n Enthalpies of Formation An enthalpy of formation, f H, is defined as the enthalpy change for the reaction in which a compound is made from its constituent elements in their elemental forms. Standard enthalpies of formation, f H, are measured under standard conditions (298 K and 1.00 bar pressure). Many are tabulated and we can simply look them up.
Example to apply Hess law Calculation of H of reactions that cannot be measured (or carried out) like the formation of propane directly from the elements: If the reaction of hydrogen with carbon is carried out in practice a mixture of products is obtained and more importantly the reaction does not proceed quantitatively meaning there are still unreacted carbon and hydrogen left after equilibrium has established. Calculating the enthalpy change associated with this reaction can help us partly understand why this might be the case. 3C (graphite) + 4H 2 (g) C 3 H 8 (g) H =? What can we measure? We can measure the heat of combustion of propane: C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O (l) H = -2220 kj/mol We can also measure the heat of formations of CO 2 and H 2 O from the elements C (graphite) + O 2 (g) CO 2 (g) H 2 (g) + 1/2 O 2 (g) H 2 O (l) H = -393.5 kj/mol H = -285.8 kj/mol Rearranging these equations can give us the heat of formation of propane 3 CO 2 (g) + 4 H 2 O (l) C 3 H 8 (g) + 5 O 2 (g) H = +2220 kj/mol 3 C (graphite) + 3 O 2 (g) 3 CO 2 (g) H = 3x(-393.5 kj/mol) 4 H 2 (g) + 2 O 2 (g) 4 H 2 O (l) H = 4x(-285.8 kj/mol) 3C (graphite) + 4H 2 (g) C 3 H 8 (g) H = -103.7 kj/mol Definition: An enthalpy of formation, f H, is defined as the enthalpy change for the reaction in which a compound is made from its constituent elements in their elemental forms. (Arbitrary if the reaction can actually be carried out in this way or not- we get important information on the energy that is stored (ore used) in compounds relative to the elements it is made up from) We can use Hess s law in another way: H = n H f(products) - m H f(reactants) where n and m are the stoichiometric coefficients. Calculate the heat of combustion of sucrose (use data in the table from handout thermochemistry II) C 12 H 22 O 11 (s) + 12O 2 (g) 12CO 2 (g) + 11H 2 O (l)
H = n fh(products) - m fh(reactants) H = Energy in Foods and Fuels Tables from: Brown LeMay Chemistry the Central Science Most of the fuel in the food we eat comes from carbohydrates and fats. While most of the fuel consumed by society today comes from fossil fuels, natural gas, etc.