Thermochemistry and Gas Laws: Exam Learning Objectives

Thermochemistry

First Law of Thermodynamics

The First Law of Thermodynamics is a fundamental principle stating that energy cannot be created or destroyed, only transferred or transformed. It is often expressed as:

• Definition: The total energy of an isolated system is constant.

• Equation: $\Delta E = q + w$ where $\Delta E$ is the change in internal energy, $q$ is heat, and $w$ is work.

• System and Surroundings: Energy changes are considered from the perspective of the system and its surroundings.

Work and Heat

• Work ($w$): Energy transferred when an object is moved by a force.

• Heat ($q$): Energy transferred due to temperature difference.

• Sign Conventions: Work done by the system is negative; work done on the system is positive. Heat absorbed by the system is positive; heat released is negative.

State Functions and Path Functions

• State Function: A property dependent only on the current state, not the path taken (e.g., internal energy, enthalpy).

• Path Function: Depends on the process (e.g., work, heat).

Heat Capacity and Calorimetry

• Heat Capacity ($C$): Amount of heat required to raise the temperature of a substance by 1 K.

• Specific Heat Capacity ($c$): Heat required to raise 1 g of a substance by 1 K.

• Calorimetry: Experimental technique to measure heat flow using a calorimeter.

• Equation: $q = mc\Delta T$ where $m$ is mass, $c$ is specific heat, and $\Delta T$ is temperature change.

Enthalpy ($H$) and Enthalpy Changes

• Enthalpy ($H$): $H = E + PV$ (where $E$ is internal energy, $P$ is pressure, $V$ is volume).

• Enthalpy Change ($\Delta H$): Heat change at constant pressure.

• Endothermic: $\Delta H > 0$ (system absorbs heat).

• Exothermic: $\Delta H < 0$ (system releases heat).

Hess's Law

• Statement: The enthalpy change for a reaction is the same, regardless of the number of steps.

• Application: Used to calculate $\Delta H$ for reactions by summing enthalpy changes of individual steps.

Standard Enthalpy of Formation ($\Delta H_f^\circ$)

• Definition: Enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• Standard State: Most stable form of an element at 1 atm and 25°C.

• Calculation: $\Delta H_{rxn}^\circ = \sum n\Delta H_f^\circ (\text{products}) - \sum n\Delta H_f^\circ (\text{reactants})$

Bond Enthalpy

• Bond Enthalpy: Energy required to break one mole of a bond in a gaseous molecule.

• Calculation of $\Delta H$: $\Delta H = \sum \text{Bond Energies (bonds broken)} - \sum \text{Bond Energies (bonds formed)}$

Gases and Gas Laws

Gas Properties and Kinetic Molecular Theory

• Ideal Gas: Hypothetical gas that perfectly follows the gas laws.

• Kinetic Molecular Theory: Explains gas behavior based on particle motion, negligible volume, and elastic collisions.

• Root Mean Square Speed ($u_{rms}$): $u_{rms} = \sqrt{\frac{3RT}{M}}$ where $R$ is the gas constant, $T$ is temperature (K), $M$ is molar mass (kg/mol).

Gas Laws

• Boyle's Law: $P_1V_1 = P_2V_2$ (at constant $T$ and $n$)

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant $P$ and $n$)

• Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (at constant $P$ and $T$)

• Ideal Gas Law: $PV = nRT$

• Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Gas Mixtures and Partial Pressures

• Dalton's Law of Partial Pressures: $P_{total} = \sum P_i$ where $P_i$ is the partial pressure of each gas in the mixture.

• Mole Fraction ($X_i$): $X_i = \frac{n_i}{n_{total}}$

• Partial Pressure: $P_i = X_i P_{total}$

Deviations from Ideal Gas Behavior

• Real Gases: Deviate from ideal behavior at high pressure and low temperature.

• van der Waals Equation: $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$ where $a$ and $b$ are constants for intermolecular forces and molecular volume.

Gas Stoichiometry

• Gas Volume and Moles: At STP (0°C, 1 atm), 1 mole of an ideal gas occupies 22.4 L.

• Stoichiometric Calculations: Use the ideal gas law to relate gas volume, pressure, temperature, and moles in chemical reactions.

Summary Table: Key Gas Laws

Law	Equation	Constant
Boyle's Law	$P_1V_1 = P_2V_2$	$T$, $n$
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	$P$, $n$
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	$P$, $T$
Ideal Gas Law	$PV = nRT$	—

Example: Calculating Gas Volume at STP

• Problem: What volume does 2.00 mol of an ideal gas occupy at STP?

• Solution: $V = nRT/P = (2.00 \text{ mol})(0.0821 \text{ L·atm·mol}^{-1}\text{K}^{-1})(273 \text{ K})/1.00 \text{ atm} = 44.8 \text{ L}$

Additional info: These notes are based on a list of exam learning objectives covering thermochemistry and gas laws, including key equations, definitions, and applications relevant to a General Chemistry course.