Chapter 7: Thermochemistry and Thermodynamics – Study Notes

Thermodynamics: Key Concepts

Introduction to Thermodynamics

Thermodynamics is the study of energy changes, particularly heat and work, that accompany chemical and physical processes. It provides a framework for understanding how energy is transferred within a system and between a system and its surroundings.

• System: The part of the universe under study (e.g., a chemical reaction in a beaker).

• Surroundings: Everything outside the system that can exchange energy with it.

• 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.

• Energy Conservation: $\Delta E_{sys} = -\Delta E_{surr}$

Energy changes are tracked using sign conventions:

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

Internal Energy and Calculations

Internal Energy (ΔE)

Internal energy is the total energy contained within a system. It can be changed by heat (q) and work (w):

• Formula: $\Delta E = q + w$

Example Problems:

• Calculate the change in internal energy for a gas in a piston if the gas absorbs 5.973 kJ of heat and does 0.589 kJ of work by pushing the piston.

• Determine the work done by a system if a balloon loses 206 J of heat and the overall change in internal energy is +458 J. Did the balloon expand or contract?

Heat Capacity and Calorimetry

Heat Capacity

Heat capacity is a measure of the amount of heat required to change a system's temperature by a given amount.

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

• Formula: $q = m \times C_s \times \Delta T$

Example Calculations:

• How much heat is required to warm 420.0 grams of ethylene glycol from 22.2°C to 100.0°C? ($C_{s, ethylene\ glycol} = 2.78 \ J/g^\circ C$)

• What is the final temperature of a lump of gold (5.009 g, $C_{s, Au} = 0.129 \ J/g^\circ C$) after absorbing 11.04 J of heat energy?

• Calculate the heat absorbed by 1.0 tablespoon of chicken broth (assume $C_{s, broth} = 4.184 \ J/g^\circ C$) when heated from 22.2°C to 100.0°C.

• Determine the change in temperature for a 63.1 g silver spoon ($C_{s, Ag} = 0.240 \ J/g^\circ C$) if it absorbs the same heat as the broth above.

• Find the mass of a hot piece of iron ($C_{s, Fe} = 0.449 \ J/g^\circ C$) placed in 200 g of water ($C_{s, H_2O} = 4.184 \ J/g^\circ C$) when equilibrium is reached at 28.1°C (initially 275.8°C for iron, 22.2°C for water).

Pressure-Volume Work

Work Done by Expanding Gases

Pressure-volume (PV) work occurs when a system changes volume against an external pressure.

• Formula: $w = -P_{ext} \Delta V$

• Conversion: $1.00 \ atm \cdot L = 101.31 \ J$

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

Calorimetry: Measuring Energy Changes

Constant Volume Calorimetry (Bomb Calorimeter)

Bomb calorimetry measures the change in internal energy (ΔE) at constant volume. All energy from the reaction is converted to heat because $\Delta V = 0$.

• Calorimeter is isolated: matter cannot leave, and no heat is exchanged with the outside.

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

Example Calculations:

• Determine $\Delta E_{rxn}$ for the combustion of ethanol if a 1.015 g sample causes the calorimeter temperature to rise from 22.8°C to 35.2°C. The calorimeter has a heat capacity of 5.936 kJ/°C.

• Find $\Delta E_{rxn}$ for the combustion of methanol (1.015 g, temperature change 21.4°C to 34.0°C, calorimeter heat capacity 4.90 kJ/°C).

• Calculate the calorimeter constant ($C_{cal}$) if 1.009 g of butane causes a 10.6°C temperature change. ($\Delta E_{rxn}$ for butane combustion = -2878 kJ/mol).

Constant Pressure Calorimetry (Coffee Cup Calorimeter)

Used for reactions open to the atmosphere (constant pressure). Measures enthalpy change ($\Delta H$) rather than internal energy ($\Delta E$).

• Cannot assume all work is zero; $\Delta E$ is related to $q_p$ (heat at constant pressure).

Enthalpy (H) and Enthalpy Change (ΔH)

Definition and Equations

Enthalpy is a thermodynamic property that represents the heat absorbed or released at constant pressure.

• Formula: $H = E + PV$

• Enthalpy Change: $\Delta H = \Delta E + P \Delta V$

• If $\Delta V$ is negligible, $\Delta H \approx \Delta E$

Example: The reaction of sodium and water produces 367.5 kJ of heat and does 2.5 kJ of work. Calculate $\Delta H$ and $\Delta E$ for the reaction.

Coffee Cup Calorimetry and Enthalpy

For aqueous reactions, $\Delta H_{rxn}$ can be determined using constant pressure calorimetry. The sign conventions for system and surroundings are important for interpreting results.

System	Surroundings
q = -	q = +
q = +	q = -

Summary Table: Exothermic vs. Endothermic Processes

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

Key Equations

• $\Delta E = q + w$

• $q = m \times C_s \times \Delta T$

• $w = -P_{ext} \Delta V$

• $H = E + PV$

• $\Delta H = \Delta E + P \Delta V$

Additional info:

• Thermochemistry is a branch of thermodynamics that specifically studies the heat involved in chemical and physical changes.

• Calorimetry is a practical technique for measuring heat changes in the laboratory.