Chem - chapter 9 study guide

9.2 The Nature of Energy: Key Definitions

Definitions and Types of Energy

Energy is a fundamental concept in chemistry, essential for understanding chemical reactions and physical changes. The main types of energy relevant to chemistry include:

• Kinetic Energy: The energy of motion, given by $E_k = \frac{1}{2}mv^2$, where m is mass and v is velocity.

• Potential Energy: The energy stored due to position or composition, such as chemical bonds.

• Thermal Energy: The energy associated with the random motion of atoms and molecules; a form of kinetic energy.

• Chemical Energy: A type of potential energy stored within chemical bonds.

Key Point: The difference between kinetic and potential energy is that kinetic energy is due to motion, while potential energy is due to position or arrangement.

Example: A rolling ball has kinetic energy; a ball held at a height has potential energy.

Law of Conservation of Energy

• First Law of Thermodynamics: Energy cannot be created or destroyed, only transformed from one form to another.

• The total energy of the universe is constant.

System vs. Surroundings: The system is the part of the universe under study (e.g., a chemical reaction), while the surroundings are everything else.

9.3 The First Law of Thermodynamics: There Is No Free Lunch

Internal Energy and State Functions

The internal energy (E) of a system is the sum of all kinetic and potential energies of its components. It is a state function, meaning its value depends only on the current state of the system, not on how it got there.

• State Functions: Properties that depend only on the state of the system (e.g., internal energy, pressure, volume, temperature).

• Path Functions: Properties that depend on the process or path taken (e.g., work, heat).

Energy Flow: Work and Heat

• Energy can be transferred between a system and its surroundings as work (w) or heat (q).

• The change in internal energy is given by:

$\Delta E = q + w$

• If energy is lost by the system, it is gained by the surroundings, and vice versa.

• Sign conventions: q is positive if heat is absorbed by the system; w is positive if work is done on the system.

Example: When a gas expands against a piston, it does work on the surroundings (w is negative for the system).

9.4 Quantifying Heat and Work

Heat Capacity and Calorimetry

• Heat Capacity (C): The amount of heat required to raise the temperature of an object by 1°C.

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Molar Heat Capacity: The amount of heat required to raise the temperature of 1 mole of a substance by 1°C.

The heat flow to a substance is calculated by:

$q = mc\Delta T$

or, for molar heat capacity:

$q = nC_m\Delta T$

• m: mass (g), c: specific heat (J/g·°C), n: moles, C_m: molar heat capacity (J/mol·°C), ΔT: temperature change (°C).

Work Done by Expanding Gases

• Work done by a gas at constant pressure is:

$w = -P\Delta V$

• P: pressure, ΔV: change in volume.

• Work is negative when the system expands (does work on surroundings).

9.5 Measuring ΔE for Chemical Reactions: Constant-Volume Calorimetry

Bomb Calorimetry

• Constant-volume calorimetry is used to measure the heat exchanged at constant volume, typically in a bomb calorimeter.

• The heat released or absorbed is equal to the change in internal energy ($\Delta E$) of the system.

Example: Combustion reactions are often studied using bomb calorimetry.

9.6 Enthalpy: Constant-Pressure Calorimetry

Definition and Calculation of Enthalpy

• Enthalpy (H): A state function defined as $H = E + PV$, where E is internal energy, P is pressure, and V is volume.

• The change in enthalpy ($\Delta H$) at constant pressure equals the heat exchanged:

$\Delta H = q_p$

• q_p: heat at constant pressure.

• Enthalpy changes are used to describe heat flow in chemical reactions at constant pressure.

Endothermic and Exothermic Reactions

• Endothermic Reaction: Absorbs heat from surroundings ($\Delta H > 0$).

• Exothermic Reaction: Releases heat to surroundings ($\Delta H < 0$).

• Predict reaction type based on the sign of $\Delta H$.

Stoichiometry of Enthalpy Changes

• Enthalpy changes can be calculated using the stoichiometry of chemical equations.

9.7 Measuring ΔH for Chemical Reactions: Constant-Pressure Calorimetry

Coffee-Cup Calorimetry

• Constant-pressure calorimetry (e.g., coffee-cup calorimeter) is used to measure enthalpy changes ($\Delta H$) for reactions in solution.

• Heat flow at constant pressure is measured, and $\Delta H$ is calculated.

• Difference between constant-volume and constant-pressure calorimetry: constant-volume measures $\Delta E$, while constant-pressure measures $\Delta H$.

Calorimetry Type	Constant Parameter	Measures	Typical Use
Bomb Calorimeter	Volume	$\Delta E$ (internal energy change)	Combustion reactions
Coffee-Cup Calorimeter	Pressure	$\Delta H$ (enthalpy change)	Reactions in solution

Example: Dissolving salts in water and measuring temperature change in a coffee-cup calorimeter to determine $\Delta H$.