Che131_S2025_Lect-18s

Lecture Overview

• Topic: Calorimetry & Measuring Energy Changes

• Instructor: Prof. Roy A. Lacey, Stony Brook University

• Course: Chemistry 131, Spring 2025

Temperature and Molecular Motion

• Kinetic Energy of a molecule:

  • Average kinetic energy of one molecule is given by:\frac{1}{2} m = KE_{\text{ave}}

• Relationship between number of molecules and moles:

  • N = n N_a (where molecules = moles x molecules/mole)

• Ideal gas assumption:

  1. Divide by 3 (for 3 dimensions)

  2. Substituting into the ideal gas equation:

     • PV \propto N m u^2

• Equation simplification leads to:

  • PV = nRT

  • Average kinetic energy:

    • KE = \frac{3}{2} RT

Molecular Diffusion and Effusion

• Diffusion: Mixing of gases

• Effusion: Rate of gas passage through a tiny orifice. Example: ammonia (NH3) and hydrochloric acid (HCl) interaction.

• RMS Speed:

  • The higher the RMS speed, the higher probability of a gas molecule passing through a hole.

  • Example: Diffusion is notably slower compared to RMS speed; perfume example illustrates slow detectability despite high RMS speeds.

Real vs. Ideal Gases

• Ideal Gas Behavior:

  • Exhibited under low pressure and high temperature conditions.

• PV/RT Deviations:

  • For 1 mol gas, the ratio varies based on temperature and pressure.

  • Non-ideal behaviors increase at lower temperatures and higher pressures.

Kinetic Molecular Theory (KMT)

• KMT assumptions:

  • No interactions between gas particles and no volume occupied by particles.

  • Original equation:PV = nRT

• Van der Waals (1873) corrections:

  • $P_{corrected} V_{corrected} = nRT$ for attractive forces and molecular volume.

Energy in Thermodynamics

• Potential Energy: Energy due to an object's position; convertible to other energy forms.

• Electrostatic Energy:

  • E_{el} \propto \frac{Q_1 Q_2}{d}

Thermodynamic Definitions

• System: Part of the universe under analysis

• Surroundings: Everything outside the system

State Functions

• Describe equilibrium states: Internal energy, enthalpy, and entropy.

• Attributes of state functions:

  • Only depend on initial and final states of the system, not the path taken.

First Law of Thermodynamics

• Equation:

  • \Delta E = q + w

• Change in internal energy (E) is the sum of heat added/q and work done/w.

• Energy conservation principle: Energy cannot be created or destroyed.

Heat Flow

• In an exothermic process, heat flows from system to surroundings (q < 0).

• In an endothermic process, heat flows from surroundings to system (q > 0).

PV Work Example

• Scenario: Inflating helium balloons against atmospheric pressure.

• Total volume change for 100 balloons = 100 x 4.8 L.

• Work done by the system:

  • w = -P \Delta V = - 1.01 atm x 480 L

Enthalpy

• Definition:

  • Enthalpy (H) = E + PV

  • Change in enthalpy \Delta H = heat transfer at constant pressure:

    • \Delta H = q_P = \Delta E + P\Delta V

Calorimetry Basics

• Bomb Calorimeter:

  • Constant-volume device to measure heat of combustion.

  • Heat produced = heat gained:

  • \Delta H = -q_{cal} = -C_{cal} \Delta T

Heating Curves

• Heating curves relate temperature and phase changes.

• Phase change heat calculations are different from during temperature change.

• Molar heat of fusion/vaporization defined.

Specific Heat Capacities

• Molar heat capacity (c_p): Heat needed to raise 1 mole by 1°C.

• Specific heat (c_s): Heat needed to raise 1g by 1°C.

Energy Calculations Examplar

• Calculating energy required to heat water from 20.0°C to 25.0°C with specific heat.

Different scenarios of heat energy exchange

• Calculating heat loss/gain through thermal equilibrium between materials of varying temperatures.

Example Problems

• Identify energy requirements for phase changes and heat transfers in practical applications.