Chapter 7: Thermochemistry and Thermodynamics Study Notes

Thermodynamics: Key Concepts

System, Surroundings, and Universe

Thermodynamics is the study of energy changes, particularly in chemical reactions and physical processes. Understanding the distinction between the system and its surroundings is fundamental:

• System: The part of the universe under study, typically the chemical reaction or physical process of interest.

• Surroundings: Everything else in the universe outside the system.

• Universe: The sum of the system and its surroundings.

Key Principle: The total energy of the universe is constant. Energy lost by the system is gained by the surroundings and vice versa.

Mathematical Expression:

$\Delta E_{sys} = -\Delta E_{surr}$

Sign Conventions in Thermodynamics

Thermodynamic quantities such as heat (q), work (w), and change in internal energy (ΔE) are assigned positive or negative signs depending on the direction of energy flow:

Quantity	Sign (System)	Change for System	Sign (Surroundings)	Change for Surroundings
q	+	Absorbing heat (Endothermic)	-	Losing heat
q	-	Losing heat (Exothermic)	+	Absorbing heat
w	+	Work done on system (decreasing volume)	-	Doing work (increasing volume)
w	-	Work done by system (increasing volume)	+	Work done on surroundings (decreasing volume)
ΔE	+	Gaining energy	-	Losing energy
ΔE	-	Losing energy	+	Gaining energy

Internal Energy and Its Calculation

Definition and Formula

Internal energy (E) is the total energy contained within a system. The change in internal energy (ΔE) is given by:

$\Delta E = q + w$

• q: Heat exchanged with the surroundings

• w: Work done by or on the system

Sample Problems

• Example 1: A gas absorbs 5.973 kJ of heat and does 0.589 kJ of work by pushing a piston. What is ΔE?

• Example 2: A 10.0 L balloon loses 206 J of heat, and ΔE = -485 J. What is the value of work (w)? Did the balloon expand or contract?

Heat Capacity and Calorimetry

Specific Heat and Molar Heat Capacity

Specific heat (C_s): The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

Molar heat capacity (C_m): The amount of heat required to raise the temperature of one mole of a substance by one degree Celsius.

Formula:

$q = m \times C_s \times \Delta T$

• q: Heat absorbed or released

• m: Mass of the substance

• C_s: Specific heat capacity

• ΔT: Change in temperature

Sample Calorimetry Problems

• Calculate the heat required to warm 420.0 g of ethylene glycol from 22.2°C to 100.0°C. (C_s = 2.78 J/g°C, d = 1.1132 g/mL)

• Find the final temperature of 5.009 g of gold at 37.0°C after absorbing 11.04 J of heat. (C_s = 0.129 J/g°C)

• Determine the heat absorbed by 1.0 tablespoon of chicken broth heated from 22.2°C to 100.0°C. (Assume properties of water: d = 0.99875 g/mL, C_s = 4.184 J/g°C)

• Calculate the temperature change for a 63.1 g silver spoon absorbing the same heat as above. (C_s = 0.240 J/g°C)

• Find the final temperature of the silver spoon.

• A hot piece of iron at 275.5°C is placed in 200 g of water at 22.2°C. Final temperature is 28.1°C. What is the mass of the iron? (C_s,Fe = 0.449 J/g°C, C_s,water = 4.184 J/g°C)

Pressure-Volume Work

Definition and Formula

Pressure-volume (P-V) work occurs when the volume of a system changes against an external pressure. The work done by the system is:

$w = -P_{ext} \Delta V$

Where:

• Pext: External pressure

• ΔV: Change in volume

To convert between units:

$1.00\ \text{atm} \cdot \text{L} = 101.31\ \text{J}$

Sample Problem

• Calculate the work done (in Joules) by inflating a balloon from 2.0 L to 3.8 L on the moon, where atmospheric pressure is 0.00500 atm.

Calorimetry: Measuring Energy Changes

Constant Volume Calorimetry (Bomb Calorimeter)

Bomb calorimetry is used to measure the change in internal energy (ΔE) of a reaction at constant volume. In this setup:

• The system is sealed, so no matter can enter or leave.

• All energy from the reaction is transferred as heat, since ΔV = 0 and no P-V work is done.

• The heat absorbed by the calorimeter equals the energy released or absorbed by the reaction.

Relationship: $q_{rxn} = -q_{cal}$ (no heat is lost to the surroundings)

Temperature and Energy Relationships

Process	q (Reaction)	T (Reaction)	q (Calorimeter)	T (Calorimeter)
Exothermic	-	Decreases	+	Increases
Endothermic	+	Increases	-	Decreases

Sample Bomb Calorimeter Calculations

• Determine ΔErxn for the combustion of ethanol if 1.015 g of ethanol causes the calorimeter temperature to rise from 22.8°C to 35.2°C. (Calorimeter heat capacity = 5.936 kJ/°C)

• Determine ΔErxn for the combustion of CH3OH if 1.015 g of CH3OH causes the temperature to rise from 21.4°C to 34.0°C. (Calorimeter heat capacity = 4.90 kJ/°C)

• Find the calorimeter constant if 1.009 g of butane causes a 10.6°C temperature change. (ΔErxn for butane = -2878 kJ/mol)

Constant Pressure Calorimetry (Coffee Cup Calorimeter)

Used for reactions open to the atmosphere (constant pressure). The heat measured (qp) is related to the enthalpy change (ΔH) of the reaction.

• Cannot assume all work is zero; only pressure-volume work is considered.

• ΔH is the thermodynamic property measured at constant pressure.

Enthalpy (H)

Definition and Equations

Enthalpy (H): A thermodynamic property defined as the sum of the internal energy and the product of pressure and volume.

$H = E + PV$

The change in enthalpy (ΔH) is:

$\Delta H = \Delta E + P\Delta V$

• If ΔV is negligible, then ΔH ≈ ΔE.

Sample Enthalpy Calculation

• The reaction of one mole of sodium with water produces 367.5 kJ of heat and does 2.5 kJ of work. Calculate ΔH and ΔE for the reaction.

Coffee Cup Calorimeter Calculations

• For aqueous reactions, ΔHrxn can be determined using constant pressure calorimetry.

• System: chemical reaction; Surroundings: water and calorimeter.

Summary Table: Key Thermodynamic Quantities

Quantity	Symbol	Definition	Units
Internal Energy	E	Total energy of a system	J (Joules)
Change in Internal Energy	ΔE	q + w	J (Joules)
Enthalpy	H	E + PV	J (Joules)
Change in Enthalpy	ΔH	ΔE + PΔV	J (Joules)
Heat	q	Energy transferred due to temperature difference	J (Joules)
Work	w	Energy transferred when an object is moved by a force	J (Joules)

Additional info: These notes cover the core concepts of thermochemistry and thermodynamics as outlined in a general chemistry curriculum, including definitions, sign conventions, calorimetry, and sample calculations. The included images directly support the explanation of key concepts, formulas, and apparatus.