Calorimetry 1: The Enthalpy of Formation of MgO Overview Getting Started Techniques Procedure FAQ Full Lab Manual Introduction & Goals Chemistry & Background Key Questions Prelab Problems Safety Procedure In Your Write-up Experiments Index ChemLab Home		The Adiabatic Calorimeter In most systems, without special precautions, the system not only exchanges enthalpy with its surroundings but also suffers a change in its temperature. In order to avoid such a complicated situation, thermochemists use the adiabatic calorimeter, a device so well insulated thermally that the transfer of energy (and enthalpy) as heat across the boundary between the calorimeter and its surroundings is effectively zero during the experiment. In practice, perfect insulation or matching of temperatures between system and surroundings is never achieved, but, if the energy flow is small and steady, the necessary corrections can be made. The use of an adiabatic calorimeter can be understood with the help of the following diagram of the thermodynamic states. The reaction path observed in the laboratory is adiabatic, along the path labeled 3: A (at T1) + B (at T1) C(at T2) + D(at T2) All that is known (or need be known) about path 3 is that it is adiabatic; that is, the entire system has not gained or lost heat to the surroundings, so that, by definition, q3 = Hpath 3 = 0 (1) But changes in state functions, such as enthalpy, are independent of path; thus Hpath 3 = Hpath 1 + Hpath 2 = 0 (2) where path 1 is the isothermal reaction at T1, and path 2 is the simple heating of products from T1 to T2. Since Hpath 3 = 0 , we have Hpath 1 = - Hpath 2 (3) Hpath 1 is the desired isothermal isothermal enthalpy change for the reaction, which is tabulated in the literature. Equation 3 tells us that Hpath 1 is the negative of the enthalpy required to raise C + D (and the apparatus) from T1 to T2. This enthalpy, to raise the temperature of the products and apparatus, depends upon the heat capacity of both. The constant pressure heat capacity, Cp, is defined as the enthalpy required to increase the temperature of a substance by one Kelvin. If the heat capacities are assumed constant over this temperature range, and are designated by Cprod and Ccal (for products and calorimeter, in units of J KÐ1), then the isothermal enthalpy change Hpath 1, in joules, is: Hpath 1 = - Hpath 2 = -(Cprod + Ccal)(T2 - T1) = -Ctotal T (4) The heat capacity Ctotal is the heat required to raise the temperature of the products and calorimeter by one Kelvin. It will have contributions from the product ions, the thermometer, the cups, the lid, and, most importantly, the water in the calorimeter. To summarize, in an adiabatic experiment, the change in the temperature of the system is observed. If the heat capacities at constant pressure are known for the products of the reaction and for the apparatus (container, stirrer, and thermometer), the value of H that would correspond to the isothermal reaction at the initial temperature can be obtained. Recall that enthalpy is an extensive property and depends on the amount of reactants that react. It is customary to report a molar value of H, in units of kJ molÐ1. A molar enthalpy change is obtained by dividing the observed enthalpy change by the number of moles of reaction that occurred, n. Since we have eliminated all H values but the desired isothermal enthalpy change, Hpath 1 , we can drop the subscripts and call the molar value simply H. The moles of reaction, n, can be found by determining the limiting reagent of the reaction. This molar enthalpy change is the extensive property recorded in the literature in units of kJ/mol. You will compare your experimental results for the molar H to the molar literature values, like those in Table 1. The adiabatic calorimeter in our experiment consists of a double styrofoam cup fitted with a thermometer calibrated in tenths of a degree, permitting temperatures to be estimated to about ±0.02°C. The two reactants, both at the same initial temperature, are placed in the calorimeter and the change in temperature during the course of reaction is observed. If one assumes that the reaction is rapid, then equation (4) can be expected to hold. General Approach To determine an enthalpy of reaction using Equation 4, it is necessary to determine Cprod + Ccal = Ctotal and T = T2-T1. The heat capacity, Ctotal, can be determined by measuring the temperature change for any reaction, for which H is known. We will use the easily observed solution reaction between a strong acid and a strong base: HCl(0.5 M) + NaOH(0.5 M) H2O(l) + NaCl(0.25 M) H = -57.36 kJ mol-1 = -13.71 kcal mol-1. By measuring T for this reaction, using the known molar H, and knowing the number of moles of reaction that occurred, Ctotal can be calculated from equation (4). If we then study other reactions in which we keep the volume of water fixed, then Ctotal will remain approximately constant. We are able to make this approximation because the major contribution to Ctotal is made by the water. Variation in Cprod due to the different ions in the product solution are quite small. Thus, the value of (Cprod + Ccal) obtained above for the acid-base reaction with a known H can be used to determine unknown H's for other reactions, by solving equation (4) for the enthalpy of reaction. Note that this approximation works when the volume of solution is identical, for the different reactions observed. Also note that for each reaction, there must be a conversion between the molar enthalpy change and the enthalpy change of the observed reaction, for the actual moles of reaction that occurs, based on the limiting reagent.
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