Enthalpy, Calorimetry, and Stoichiometry in Chemical Reactions

Enthalpy: The Heat Evolved in a Chemical Reaction at Constant Pressure

Definition and Context

Enthalpy (H) is a thermodynamic quantity that represents the total energy change (heat and work) during a chemical reaction under constant pressure. In most chemical reactions open to the atmosphere, the pressure remains constant, and the heat exchanged is referred to as the enthalpy change (ΔH).

• Enthalpy Change (ΔH): The amount of heat absorbed or released during a reaction at constant pressure.

• Equation: $\Delta H = q_p$ where $q_p$ is the heat exchanged at constant pressure.

• For reactions where only heat is exchanged (no work), $\Delta H$ and $\Delta E$ (internal energy change) are identical.

Example: Burning fuel in a stove to cook food involves heat transfer to the atmosphere, which is measured as enthalpy change.

The Difference Between ΔH and ΔE

Key Distinctions

ΔE is the total energy change (heat and work), while ΔH is the heat exchanged at constant pressure. For reactions with no pressure-volume work (such as combustion in open air), ΔH and ΔE are nearly the same.

Reaction	ΔH (kJ)	ΔE (kJ)
CH4 + 2O2 → CO2 + 2H2O	-890	-818
H2 + 1/2O2 → H2O	-286	-242
N2 + 3H2 → 2NH3	-92	-46

Additional info: The table compares enthalpy and internal energy changes for common reactions.

Endothermic vs. Exothermic Reactions

Classification by Heat Flow

Chemical reactions are classified based on whether they absorb or release heat:

• Endothermic Reaction: Absorbs heat from surroundings; ΔH is positive. Example: Water evaporating from skin (sweating).

• Exothermic Reaction: Releases heat to surroundings; ΔH is negative. Example: Wood burning in a fire.

Practice: Identify the sign of ΔH for the following: (a) Nail polish remover evaporating: Endothermic (b) Gasoline burning in a cylinder: Exothermic

Stoichiometry Involving ΔH: Thermochemical Equations

Relating Heat to Amount of Reaction

The enthalpy change for a chemical reaction is proportional to the amount of substance undergoing reaction. Thermochemical equations show the relationship between reactants, products, and heat exchanged.

• Example Equation: $\mathrm{C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g)} \qquad \Delta H = -2044\ \mathrm{kJ}$

• This means that 1 mol of propane reacts with 5 mol of oxygen to produce 3 mol of CO2, 4 mol of H2O, and releases 2044 kJ of heat.

Example: Stoichiometry Involving ΔH

Calculating Heat from Amounts of Reactants

Given a mass of propane, calculate the heat released:

• Strategy: Convert mass to moles, use stoichiometry to relate moles to ΔH.

• Equation: $\mathrm{C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g)} \qquad \Delta H = -2044\ \mathrm{kJ}$

• Calculation: For 13.2 g C3H8: $\text{Moles of C}_3\text{H}_8 = \frac{13.2\ \text{g}}{44.1\ \text{g/mol}} = 0.299\ \text{mol}$ $\text{Heat released} = 0.299\ \text{mol} \times \frac{-2044\ \text{kJ}}{1\ \text{mol}} = -611\ \text{kJ}$

Constant-Pressure Calorimetry: Measuring ΔH

Coffee-Cup Calorimeter

Calorimetry is used to measure the heat evolved or absorbed in a reaction. A coffee-cup calorimeter is a simple device for reactions at constant pressure.

• Setup: Solution in a cup, insulated to prevent heat loss, with a thermometer to measure temperature change.

• Equation: $q_{\text{solution}} = m_{\text{solution}} \times C_{\text{solution}} \times \Delta T$ where $m$ is mass, $C$ is specific heat, and $\Delta T$ is temperature change.

• For reactions at constant pressure: $q_{\text{reaction}} = -q_{\text{solution}}$ $\Delta H_{\text{rxn}} = q_{\text{reaction}}$

Example: Magnesium metal reacts with hydrochloric acid. The temperature change in the solution is used to calculate $\Delta H_{\text{rxn}}$.

Constant-Pressure vs. Constant-Volume Calorimetry

Comparison

Calorimeter Type	Measures	Equation
Coffee-cup (constant pressure)	ΔH	$q_p = \Delta H$
Bomb (constant volume)	ΔE	$q_v = \Delta E$

Additional info: Constant-volume calorimetry is used for reactions where pressure-volume work is significant.

Relationships Involving ΔHrxn

Quantitative Relationships and Hess's Law

Three key relationships allow calculation of enthalpy changes for reactions:

1. If a reaction is multiplied by a factor, ΔH is multiplied by the same factor.

2. If a reaction is reversed, the sign of ΔH is reversed.

3. If a reaction is the sum of multiple steps, ΔH for the overall reaction is the sum of ΔH for each step (Hess's Law).

Equation (Hess's Law): $\Delta H_{\text{overall}} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \ldots$

Example: If reaction A + 2B → C has $\Delta H_1$, and C → 2D has $\Delta H_2$, then A + 2B → 2D has $\Delta H_1 + \Delta H_2$.

Additional info: These relationships allow determination of enthalpy changes without direct measurement, which is useful for reactions that are difficult to study experimentally.