Thermochemistry: Enthalpy, Calorimetry, and Heat Capacity

Ch.5 Thermochemistry

Interpreting the Signs of q & W

In thermochemistry, it is important to understand the direction of heat (q) and work (W) transfer in chemical systems. The sign conventions help determine whether energy is entering or leaving the system.

• q: Heat transferred into (+) or out of (−) the system.

• W: Work done on (+) or by (−) the system.

• Internal energy change: $\Delta U = q + w$

Process	q	w	$\Delta U$
Endothermic	+	Varies	Increases
Exothermic	−	Varies	Decreases

Endothermic processes absorb heat; exothermic processes release heat.

Enthalpy and Heat

Enthalpy (H) is a thermodynamic quantity defined as $H = U + PV$, where U is internal energy, P is pressure, and V is volume. It is especially useful for processes occurring at constant pressure.

• Enthalpy change ($\Delta H$): $\Delta H = \Delta U + P\Delta V$

• At constant pressure: $\Delta H = q_p$ (heat transferred at constant pressure)

• Enthalpy cannot be measured directly, but changes in enthalpy ($\Delta H$) can be determined experimentally.

Example: A cylinder with a piston simulates a closed system that can involve PV work.

Enthalpy Change ($\Delta H$)

Enthalpy change is the heat transferred at constant pressure. It is positive for endothermic processes and negative for exothermic processes.

• $\Delta H > 0$: Endothermic process (heat absorbed)

• $\Delta H < 0$: Exothermic process (heat released)

Equation: $\Delta H = \Delta U + P\Delta V$

Enthalpy of Reaction

The enthalpy change for a chemical reaction is the difference between the enthalpy of products and reactants.

• $\Delta H = H_{final} - H_{initial}$

• $\Delta H = H_{products} - H_{reactants}$

• Enthalpy depends on the physical state of reactants and products.

• Reversing a reaction changes the sign of $\Delta H$.

Example: $CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O$, $\Delta H = -890$ kJ (exothermic)

Spontaneity in Thermochemistry

Spontaneity refers to whether a process occurs naturally without outside intervention. Thermodynamically favored processes are spontaneous, but may occur fast or slow.

• Spontaneous process: Occurs without outside energy input.

• Thermodynamically favored: A process that is spontaneous under given conditions.

• Spontaneity does not indicate rate; a process can be spontaneous but slow.

Example: Graphite is thermodynamically more stable than diamond, but conversion is extremely slow.

Calorimetry

Calorimetry is the measurement of heat flow in chemical reactions. It uses devices called calorimeters to determine heat changes.

• Heat capacity (C): Amount of heat needed to raise the temperature of a substance by 1 K (or 1 °C).

• Specific heat (c): Heat needed to raise 1 g of a substance by 1 K (or 1 °C).

• Molar heat capacity: Heat needed to raise 1 mol of a substance by 1 K (or 1 °C).

Substance	Specific Heat (J/g·K)
H2O (l)	4.18
Al (s)	0.90
Fe (s)	0.45
Cu (s)	0.39
CH3OH (l)	2.50
CO2 (g)	0.84

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

Where $C_s$ is specific heat, $m$ is mass, and $\Delta T$ is temperature change.

Heat Capacity—Example

To calculate the energy required to heat a substance:

• Given: $C_s$ for iron = 0.451 J/g·°C

• Calculate $q$ for heating 500.0 g of iron from 22°C to 55°C:

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

Molar Heat Capacity

When using molar heat capacity, the heat required is:

$q = c_{m} \times n \times \Delta T$

• $c_{m}$: molar heat capacity

• $n$: number of moles

• $\Delta T$: temperature change

Calorimetry at Constant Pressure

Constant pressure calorimeters (e.g., coffee-cup calorimeter) are used to measure enthalpy changes for reactions in solution.

• Heat absorbed or released: $q = C_s \times m \times \Delta T$

• For neutralization reactions, the temperature change of the solution is measured.

Example: Mixing 50 mL of 1.0 M HCl and 50 mL of 1.0 M NaOH, measuring temperature change to calculate enthalpy of reaction.

Bomb Calorimetry

Bomb calorimeters are used for reactions at constant volume, such as combustion reactions. The heat measured is related to the change in internal energy ($\Delta U$).

• Heat released: $q = C_{cal} \times \Delta T$

• Combustion reactions are performed in a sealed container (bomb) under constant volume.

Example: Combustion of rocket fuel, methylhydrazine, in a bomb calorimeter to determine heat of reaction.

Practice Problems

• Calculating final temperature after heat transfer between substances.

• Determining heat released or absorbed using specific heat and temperature change.

Example: 24.3 kJ of energy lost by a 250 g aluminum block; calculate final temperature.

Additional info: These notes cover key concepts from Ch.5 Thermochemistry, including enthalpy, calorimetry, heat capacity, and spontaneity, with relevant equations and examples for General Chemistry students.