Enthalpy, Calorimetry, and Hess's Law (General Chemistry Study Notes)

Enthalpy and Thermochemistry

Introduction to Enthalpy

Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system at constant pressure. In chemical reactions, the change in enthalpy (ΔH) indicates whether heat is absorbed or released.

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

• Equation: $\Delta H = \Delta E + P\Delta V$

• Endothermic Reaction: Absorbs heat; ΔH is positive. Feels cold to the touch.

• Exothermic Reaction: Releases heat; ΔH is negative. Feels warm to the touch.

Example: Combustion reactions are typically exothermic, releasing energy as heat.

Enthalpy of Reaction

Extensive Property of Enthalpy

The enthalpy change for a chemical reaction depends on the amount of reactants used. It is an extensive property, meaning it scales with the size of the system.

• Calculate ΔH for the number of moles specified in the balanced equation.

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

Example:

• For the reaction: $5\,O_2(g) \rightarrow 3\,CO_2(g) + 4\,H_2O(g)$, $\Delta H = -2044\,\text{kJ}$

• For 1 mol $C_3H_8(g)$, $\Delta H = -2044\,\text{kJ}$

Practice Problem: Enthalpy of Reaction

Given the reaction:

• $CH_4(g) + 2\,O_2(g) \rightarrow CO_2(g) + 2\,H_2O(g)$, $\Delta H_{rxn} = -802\,\text{kJ}$

• Calculate the heat released when 250 g of $CH_4$ reacts. ($M_{CH_4} = 16.04\,\text{g/mol}$)

Solution Steps:

• Convert grams to moles: $250\,\text{g} / 16.04\,\text{g/mol} = 15.59\,\text{mol}$

• Calculate heat released: $q_{rxn} = 15.59\,\text{mol} \times (-802\,\text{kJ/mol}) = -12,503\,\text{kJ}$

Calorimetry at Constant Pressure

Coffee-Cup Calorimeter

Calorimetry is the measurement of heat flow in chemical reactions. A coffee-cup calorimeter is commonly used for reactions in aqueous solution at constant pressure.

• Setup: Nested foam cups, thermometer, and stirrer.

• Purpose: Measures enthalpy changes for reactions in solution.

• Equation: $q_{soln} = \text{mass}_{soln} \times C_s \times \Delta T$

• Relationship: Heat gained by reaction = heat lost by solution.

Example: Dissolving salts or acid-base reactions in water.

Practice Problem: Calorimetry

Calculate the enthalpy change for the reaction:

• $Zn(s) + 2\,HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g)$

• Given: $V = 120.0\,\text{mL}$, $\Delta T = +6.2^\circ\text{C}$, $d = 1.00\,\text{g/mL}$, $C_s = 4.18\,\text{J/g}^\circ\text{C}$

Solution Steps:

• Calculate mass: $120.0\,\text{mL} \times 1.00\,\text{g/mL} = 120.0\,\text{g}$

• Calculate heat: $q_{soln} = 120.0\,\text{g} \times 4.18\,\text{J/g}^\circ\text{C} \times 6.2^\circ\text{C} = 3,109.92\,\text{J}$

• Heat of reaction: $q_{rxn} = -q_{soln} = -3,109.92\,\text{J}$

• Divide by moles of Zn to get per mole value.

Relationships Involving ΔH and Hess's Law

Manipulating Chemical Equations

The enthalpy change of a reaction is affected by how the chemical equation is manipulated:

• If the equation is multiplied by a factor, ΔH is multiplied by the same factor.

• If the equation is reversed, the sign of ΔH is changed.

Example:

• $CO_2(g) \rightarrow C(s) + O_2(g)$, $\Delta H = +393.5\,\text{kJ}$ (reverse of combustion)

Hess's Law

Hess's Law states that if a reaction can be expressed as a series of steps, the overall enthalpy change is the sum of the enthalpy changes for each step.

• Equation: $\Delta H_{overall} = \Delta H_1 + \Delta H_2 + \ldots$

• Allows calculation of enthalpy changes for reactions not easily measured directly.

Example: Formation of $AlCl_3$ from $Al$ and $Cl_2$ using known enthalpy changes for intermediate steps.

Practice Problem: Hess's Law

Given:

• $2Al(s) + 3Cl_2(g) \rightarrow 2AlCl_3(s)$

• Step 1: $Al(g) + 1.5Cl_2(g) \rightarrow AlCl_3(s)$, $\Delta H_1 = -704\,\text{kJ}$

• Step 2: $Al(s) \rightarrow Al(g)$, $\Delta H_2 = +330\,\text{kJ}$

Multiply each step by 2 and sum:

• $2Al(g) + 3Cl_2(g) \rightarrow 2AlCl_3(s)$, $2 \times (-704) = -1408\,\text{kJ}$

• $2Al(s) \rightarrow 2Al(g)$, $2 \times 330 = +660\,\text{kJ}$

• Overall: $2Al(s) + 3Cl_2(g) \rightarrow 2AlCl_3(s)$, $\Delta H = -1408 + 660 = -748\,\text{kJ}$

Summary Table: Key Concepts in Enthalpy and Calorimetry

Concept	Description	Equation
Enthalpy Change (ΔH)	Heat transferred at constant pressure	$\Delta H = \Delta E + P\Delta V$
Calorimetry	Measurement of heat flow	$q = \text{mass} \times C_s \times \Delta T$
Hess's Law	Sum of enthalpy changes for reaction steps	$\Delta H_{overall} = \sum \Delta H_{steps}$
Endothermic Reaction	Absorbs heat, ΔH > 0	—
Exothermic Reaction	Releases heat, ΔH < 0	—

Additional info: These notes cover core concepts in thermochemistry, including enthalpy, calorimetry, and Hess's Law, which are essential for understanding energy changes in chemical reactions in General Chemistry.