Premed · Premed · General Chemistry 1
Lecture 6: Calorimetry and Hess's Law
General Chemistry I
Learning Objectives
By the end of this lecture, students will be able to:
- Define heat capacity and specific heat and use them in calorimetry calculations
- Perform calculations for coffee-cup (constant-pressure) calorimetry
- Perform calculations for bomb (constant-volume) calorimetry
- State Hess's law and use it to calculate enthalpy changes for reactions
- Apply Hess's law by manipulating and combining thermochemical equations
- Use standard enthalpies of formation to calculate delta_H_rxn via Hess's law
Lecture Content
I. Heat Capacity and Specific Heat
Heat capacity (C) is the amount of heat required to raise the temperature of an object by 1 degree C (or 1 K), measured in J/C or J/K. Because it depends on how much material is present, heat capacity is an extensive property. Specific heat capacity (c or s), by contrast, is the heat required to raise the temperature of exactly 1 gram of a substance by 1 degree C, measured in J/(gC) or J/(gK). Being independent of the amount of material, specific heat is an intensive property. Water has an unusually high specific heat of 4.184 J/(gC), a fact of enormous importance for biology and climate regulation. Metals tend to have much lower specific heats -- iron is 0.449 J/(gC) and aluminum is 0.897 J/(gC). The molar heat capacity (C_m) expresses heat per mole per degree, in units of J/(molC).
The fundamental equation connecting heat to temperature change is q = m c delta_T, where q is the heat absorbed or released (in J), m is the mass of the substance (in g), c is the specific heat, and delta_T = T_final - T_initial. When q is positive, the substance absorbs heat and its temperature rises; when q is negative, the substance releases heat and its temperature drops.
II. Calorimetry: Measuring Heat Changes
Calorimetry is the science of measuring heat changes during chemical or physical processes. The foundational principle is that heat lost by one component of an isolated system equals the heat gained by another: q_system = -q_surroundings.
A. Coffee-Cup Calorimetry (Constant Pressure)
A coffee-cup calorimeter is a simple device consisting of two nested Styrofoam cups fitted with a lid and thermometer. It is used for reactions that occur in solution, such as neutralizations and salt dissolutions. At constant pressure, the heat of the reaction is calculated as q_rxn = -q_solution = -m_solution c_solution delta_T. Several practical assumptions simplify the calculation: the calorimeter itself absorbs negligible heat (Styrofoam is an excellent insulator), the solution has a density of approximately 1.00 g/mL, and dilute aqueous solutions have a specific heat close to 4.184 J/(g*C). Because the pressure is constant, q_rxn equals delta_H. To express the result per mole, divide q_rxn by the moles of limiting reagent.
<image>A labeled cross-section diagram of a coffee-cup calorimeter. Two nested Styrofoam cups are shown with a cardboard lid on top. A thermometer extends through the lid into the solution. A stirrer also passes through the lid. The inner cup contains the reacting solution (labeled). Labels point to: outer cup (insulation), inner cup (reaction vessel), thermometer, stirrer, and lid. An inset graph shows a typical temperature-vs-time plot: temperature rising sharply at the moment of mixing and then leveling off, with T_initial and T_final marked and delta_T indicated by an arrow.</image>
B. Bomb Calorimetry (Constant Volume)
Bomb calorimetry is designed for combustion reactions. The sample is placed inside a heavy-walled, sealed steel container (the bomb), which is then immersed in a known mass of water. The sample is ignited electrically in the presence of excess O2, and the resulting temperature change is measured. At constant volume, q_rxn = -q_calorimeter = -(C_cal * delta_T), where C_cal is the heat capacity of the entire calorimeter assembly, determined by calibration with a substance of known heat of combustion such as benzoic acid. Because volume rather than pressure is held constant, the measured quantity is delta_E rather than delta_H. For most reactions, however, the difference between delta_H and delta_E is small unless large volumes of gas are produced or consumed.
III. Hess's Law of Constant Heat Summation
Hess's Law states that if a reaction can be expressed as the sum of two or more simpler reactions, then the enthalpy change for the overall reaction is simply the sum of the enthalpy changes of the individual steps. This principle rests on the fact that enthalpy is a state function -- delta_H depends only on the initial and final states, not on the pathway connecting them. Hess's Law is extraordinarily powerful because it allows the calculation of delta_H for reactions that are difficult or impossible to measure directly.
IV. Applying Hess's Law: Combining Equations
The strategy for applying Hess's Law begins with identifying the target reaction. Next, manipulate the given reactions so that, when added together, they yield the target. Two rules govern the manipulation: reversing a reaction changes the sign of delta_H, and multiplying all coefficients by a factor n requires multiplying delta_H by the same factor. After manipulation, add the equations together, canceling species that appear on both sides, and sum the corresponding delta_H values.
As an example, suppose you need to find delta_H for C(s) + 1/2 O2(g) -> CO(g). Given that (1) C(s) + O2(g) -> CO2(g) with delta_H_1 = -393.5 kJ, and (2) CO(g) + 1/2 O2(g) -> CO2(g) with delta_H_2 = -283.0 kJ, the strategy is to keep reaction (1) as written and reverse reaction (2). The reversed reaction (2) becomes CO2(g) -> CO(g) + 1/2 O2(g) with delta_H = +283.0 kJ. Adding the two gives C(s) + 1/2 O2(g) -> CO(g), with delta_H = -393.5 + 283.0 = -110.5 kJ.
<image>A Hess's law energy cycle diagram for the formation of CO from C and O2. The diagram shows three enthalpy levels connected by arrows. At the top: C(s, graphite) + O2(g). A direct diagonal arrow going down-right to CO(g) + 1/2 O2(g) represents the target reaction (delta_H = ?). A vertical arrow going straight down from the top level to the bottom level represents reaction 1: C + O2 -> CO2 (delta_H_1 = -393.5 kJ). A diagonal arrow going up-right from CO2(g) at the bottom to CO(g) + 1/2 O2(g) at the middle level represents the reverse of reaction 2 (delta_H = +283.0 kJ). The cycle demonstrates that delta_H_target = delta_H_1 + (-delta_H_2) = -110.5 kJ.</image>
V. Standard Enthalpies of Formation -- Hess's Law Application
The standard enthalpy of formation (delta_H_f^0) is the enthalpy change when one mole of a compound forms from its elements in their standard states (1 atm, 25 C or 298 K, 1 M for solutions). Any reaction can be conceptually broken down into two sets of steps: decomposing all reactants into their elements (the reverse of formation reactions) and then forming all products from those elements (forward formation reactions). This reasoning leads directly to the most commonly used form of Hess's Law: delta_H_rxn^0 = sum[n delta_H_f^0(products)] - sum[n delta_H_f^0(reactants)]. This is the most efficient way to calculate reaction enthalpies when standard formation data are available. As always, delta_H_f^0 = 0 for any element in its standard state.
VI. Worked Example Using Standard Enthalpies of Formation
Consider the combustion of methane: CH4(g) + 2 O2(g) -> CO2(g) + 2 H2O(l). Using standard enthalpies of formation in kJ/mol -- CH4(g) = -74.8, O2(g) = 0, CO2(g) = -393.5, H2O(l) = -285.8 -- the calculation proceeds as follows: delta_H_rxn^0 = [1(-393.5) + 2(-285.8)] - [1(-74.8) + 2(0)] = [-393.5 + (-571.6)] - [-74.8] = -965.1 + 74.8 = -890.3 kJ. The large negative value confirms that the combustion of methane is a highly exothermic process.
VII. Common Mistakes and Tips
Several pitfalls frequently trip up students in this area. Always verify that the target equation is correctly balanced before beginning a Hess's Law problem. When reversing an equation, remember to reverse all species and change the sign of delta_H. When multiplying an equation by a factor, multiply all coefficients and delta_H by the same factor. Pay careful attention to phases, because delta_H depends on states of matter -- H2O(l) and H2O(g) differ by the heat of vaporization (44.0 kJ/mol at 25 C). In calorimetry problems, the sign of q_rxn is always opposite to the sign of q_solution or q_calorimeter. Finally, remember that delta_T = T_final - T_initial, not the reverse.
