Thermochemistry - Energy, Work, and Calorimetry

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and changes of state. It is a fundamental topic in general chemistry, providing insight into how energy is transferred and conserved in chemical processes.

• Energy: Anything that has the capacity to do work.

• Kinetic energy: Energy associated with the motion of an object.

• Potential energy: Energy that is stored in an object.

• Work: Force acting over a distance.

• Heat: The flow of energy caused by a difference in temperature.

• Law of Conservation of Energy: States that energy cannot be created or destroyed.

• System: The material or process within which we are studying energy changes.

• Surroundings: Everything else with which the system can exchange energy.

Energy Exchange Between System and Surroundings

Energy transfers between the system and surroundings occur as heat or work. The direction and type of energy flow are crucial for understanding thermochemical processes.

• If the system loses energy, the surroundings gain the same amount of energy.

• If the system gains energy, the surroundings lose the same amount of energy.

• Energy is exchanged through heat (q) and work (w).

Process	System Gains	System Loses
Thermal Energy (q)	+ system gains thermal energy	- system loses thermal energy
Work (w)	+ work done on the system	- work done by the system
Internal Energy (ΔE)	+ energy flows into the system	- energy flows out of the system

Calculating Heat Transfer

The quantity of heat absorbed or released by an object can be calculated using its mass, specific heat, and temperature change.

• Specific heat capacity (Cs): The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

• Formula:

$q = m \times C_s \times \Delta T$

• q: Heat (Joules)

• m: Mass (grams)

• Cs: Specific heat capacity (J/g·°C)

• ΔT: Temperature change (°C)

Example Calculation

A silicon wafer (53.0 g) is heated from 23.5°C to 41.0°C. If the specific heat of silicon is 0.712 J/g·°C:

$q = 53.0 \times 0.712 \times (41.0 - 23.5) = 6.6 \times 10^2 \text{ J}$

Pressure-Volume Work

Pressure-volume work occurs when a force (caused by a change in pressure) moves through a distance against an external pressure. This is common in reactions involving gases.

• When gases expand, ΔV is positive and the system does work on the surroundings.

• If external pressure remains constant, work is defined by:

$w = -P \Delta V$

• P: External pressure

• ΔV: Change in volume

• To convert L·atm to Joules: $101.3 \text{ J} = 1 \text{ L} \cdot \text{atm}$

Example

If a balloon is inflated from 0.100 L to 1.75 L at 1.00 atm:

$w=-P_{ext}\Delta V=-(1.00atm)(1.75-0.100L)\times101.3\frac{J}{L\cdot atm}$

Calorimetry

Calorimetry is the measurement of heat flow in chemical reactions. There are two main types: constant volume (bomb calorimeter) and constant pressure (coffee-cup calorimeter).

Constant Volume Calorimetry

• Used to measure the change in internal energy (ΔE) for reactions.

• Bomb calorimeter: A sealed, insulated container filled with water.

• At constant volume, $w = 0$, so $ΔE = q_{v}$.

Constant Pressure Calorimetry

• Used to measure enthalpy change (ΔH) for reactions in solution.

• Coffee-cup calorimeter: Open to the atmosphere, measures heat at constant pressure.

• Heat gained by the solution equals heat lost by the reaction: $q_{rxn} = -q_{soln}$

• For aqueous solutions, use water's specific heat capacity: $q = m \times C_s \times \Delta T$

Enthalpy (ΔH) and Internal Energy (ΔE)

Enthalpy is the heat content of a system at constant pressure. It is closely related to internal energy but also accounts for pressure-volume work.

• $H = E + PV$

• ΔH is the heat exchanged at constant pressure.

• ΔE is the change in internal energy, including both heat and work.

• For reactions producing or consuming gases, the difference between ΔH and ΔE is significant.

Endothermic and Exothermic Reactions

Reactions are classified based on the direction of heat flow:

• Endothermic reaction: Heat flows into the system; ΔH is positive. Example: Cold pack for injuries.

• Exothermic reaction: Heat flows out of the system; ΔH is negative. Example: Chemical hand warmer.

Microscopic View

• Exothermic: Products have less chemical potential energy than reactants; energy is released as heat.

• Endothermic: Products have more chemical potential energy than reactants; energy is absorbed from surroundings.

Enthalpy of Reaction (ΔHrxn)

The enthalpy change for a chemical reaction is called the enthalpy of reaction or heat of reaction. It depends on the amounts of reactants and products.

• ΔHrxn is an extensive property; it scales with the amount of substance.

• Stoichiometric ratios can be used to relate moles of reactants/products to heat exchanged.

Example Thermochemical Equation

$\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \quad \Delta H = -2044 \text{ kJ}$

• When 1 mol of propane reacts, 2044 kJ of heat is emitted.

Stoichiometric Calculations Involving ΔH

Stoichiometric ratios can be used as conversion factors between amounts of reactants/products and heat exchanged.

• Example: Calculate heat emitted when a given mass of propane is combusted.

• Conceptual plan: $\text{g} \rightarrow \text{mol gas} \rightarrow \text{kJ}$

Calorimetry at Constant Pressure: Coffee-Cup Calorimeter

Used for reactions in aqueous solution to determine ΔH. The temperature change of the solution is measured and used to calculate the heat exchanged.

• Assume density of solution is 1.00 g/mL and specific heat is 4.18 J/g·°C (for water).

• Calculate $q_{soln}$ using $q = m \times C_s \times \Delta T$.

• Relate $q_{rxn}$ to $q_{soln}$: $q_{rxn} = -q_{soln}$

• To find ΔH per mole, divide by the number of moles reacted.

Example Calculation

Magnesium reacts with hydrochloric acid in a coffee-cup calorimeter. 0.158 g Mg is combined with enough HCl to make 100.0 mL solution. Temperature rises from 25.6°C to 32.8°C. Density = 1.00 g/mL, $C_s$ = 4.18 J/g·°C.

• Calculate mass: $100.0 \text{ mL} \times 1.00 \text{ g/mL} = 100.0 \text{ g}$

• Calculate $q_{soln}$: $100.0 \times 4.18 \times (32.8 - 25.6) = 3009.6 \text{ J}$

• ΔH per mole Mg: $\frac{3009.6 \text{ J}}{0.00651 \text{ mol Mg}} = 4.62 \times 10^5 \text{ J/mol}$

Summary Table: Types of Calorimetry

Type	Measured Quantity	Typical Use
Bomb Calorimeter	ΔE (internal energy)	Reactions at constant volume
Coffee-Cup Calorimeter	ΔH (enthalpy)	Reactions at constant pressure (solution)

Key Equations

• $q = m \times C_s \times \Delta T$

• $w = -P \Delta V$

• $\Delta E = q + w$

• $H = E + PV$

• $q_{rxn} = -q_{soln}$

Additional info:

• Some context and examples were expanded for clarity and completeness.

• Tables were recreated and summarized for academic utility.