Comprehensive Study Guide for Thermochemistry Part 1

Introduction to Thermochemistry and Thermodynamics

  • Thermochemistry: Defined as the study of heat change specifically within the context of chemical reactions.
  • Thermodynamics: Defined as the broader study of energy and its various transformations from one form to another.

Fundamental Concepts of Thermal Energy

  • Thermal Energy: This is the energy associated with the random motion of atoms and molecules.
  • Temperature: This serves as the quantitative measure of thermal energy.
  • Heat: This is defined as the transfer of thermal energy between two distinct bodies that are at different temperatures.
  • Molecular Motion: The temperature of an object is defined by the average kinetic energy of its constituent atoms and molecules. All materials consist of atoms and molecules in constant movement, including vibration and rotation. Simplistically, as the movement of these particles increases, the temperature of the material increases accordingly.
  • The Kelvin Scale:
    • Derived from William Thomson (Lord Kelvin) in 1848.
    • It is the base unit of temperature in the SI system (International System of Units).
    • The abbreviation for the unit is K\text{K}. It is important to note that no degree sign (∘^{\circ}) is used with Kelvin.

Review of Temperature Units and Scales

Specific temperature values across common benchmarks include:

  • Boiling water (Finnish sauna):

    • 100∘C100^{\circ}\text{C}
    • 212∘F212^{\circ}\text{F}
    • 373.15 K373.15\,\text{K}
    • 671.67∘Ra671.67^{\circ}\text{Ra}
    • 80∘Re80^{\circ}\text{Re}

  • Human body temperature:

    • 37∘C37^{\circ}\text{C}
    • 98.6∘F98.6^{\circ}\text{F}
    • 310.15 K310.15\,\text{K}
    • 558.27∘Ra558.27^{\circ}\text{Ra}
    • 29.6∘Re29.6^{\circ}\text{Re}

  • Room temperature:

    • 21∘C21^{\circ}\text{C}
    • 69.8∘F69.8^{\circ}\text{F}
    • 294.15 K294.15\,\text{K}
    • 529.47∘Ra529.47^{\circ}\text{Ra}
    • 16.8∘Re16.8^{\circ}\text{Re}

  • Freezing point of water:

    • 0∘C0^{\circ}\text{C}
    • 32∘F32^{\circ}\text{F}
    • 273.15 K273.15\,\text{K}
    • 491.67∘Ra491.67^{\circ}\text{Ra}
    • 0∘Re0^{\circ}\text{Re}

  • Absolute zero:

    • −273.15∘C-273.15^{\circ}\text{C}
    • −459.67∘F-459.67^{\circ}\text{F}
    • 0 K0\,\text{K}
    • 0∘Ra0^{\circ}\text{Ra}
    • −218.52∘Re-218.52^{\circ}\text{Re}

Definitions and Units of Heat and Energy

  • Calorie (cal): By definition, 11 calorie is the amount of heat required to raise the temperature of 1.00 g1.00\,\text{g} of H2OH_2O by 1.0∘C1.0^{\circ}\text{C}.
  • Conversion Factors and Relationships:
    • 1000 cal=1 kilocalorie=1 kcal1000\,\text{cal} = 1\text{ kilocalorie} = 1\,\text{kcal}
    • 1 cal=4.184 joules1\,\text{cal} = 4.184\text{ joules}
    • 1 J=1 kg-m2/s21\,\text{J} = 1\,\text{kg-m}^2/\text{s}^2
    • 1 BTU=1055 joules=252 calories1\text{ BTU} = 1055\text{ joules} = 252\text{ calories}

Thermodynamic Systems, Surroundings, and Boundaries

  • System: The specific part of the universe that is the focus of interest in a study.
  • Surroundings: Every part of the universe that is not included in the system (the area outside the interest).
  • Boundary: The closed three-dimensional surface that encloses the system and physically separates it from the surroundings.
Types of Thermodynamic Systems
  • Open System: A system where both matter and energy can interact and be exchanged between the system and its surroundings.
    • Example: An open kettle, which allows water vapor to escape into the air while the liquid inside can be heated.
  • Closed System: This is a system where matter is conserved (it is not transferred across the boundary), while energy (heat) is still able to interact with the surroundings.
    • Example: A closed kettle, which prevents water vapor from exiting but still allows the water inside to be heated.
  • Isolated System: A system in which both matter and energy are conserved, meaning neither is transferred in or out of the system.
    • Example: A water thermos, which contains water and maintains its temperature for a very long period of time.

Exothermic and Endothermic Processes

  • Exothermic Process: Any process that gives off heat to the surroundings. It involves the transfer of thermal energy from the system outward to the surroundings.
  • Endothermic Process: Any process in which heat must be supplied to the system from the surroundings in order for the process to occur.

State Functions vs. Path Functions

  • State Functions:
    • These are properties determined solely by the current state of the system.
    • The change in the property is not dependent on the process or the path taken to reach that condition.
    • Examples: Energy (UU), Pressure (PP), Volume (VV), and Temperature (TT).
  • Path Functions:
    • These are properties or quantities whose values depend entirely on the transition or path the system takes from its initial state to its final state.
    • The change in property is dependent on the process.
    • Examples: Heat (QQ) and Work (ww).

The First Law of Thermodynamics

  • Definition: Energy can be converted from one form to another but cannot be created nor destroyed.
  • Conservation of Energy: The amount of energy lost by a system must be exactly the same as the amount of energy absorbed by its surroundings, and vice versa.
  • Mathematical Expression:
    • −ΔUsystem=ΔUsurroundings-\Delta U_{\text{system}} = \Delta U_{\text{surroundings}}
    • (The negative sign indicates that energy is being released by the system).
  • Internal Energy Formula:
    • ΔU=Q+w\Delta U = Q + w
    • The total internal energy of a system is accounted for by the net heat transfer into the system (QQ) and the net work done on or by the system (ww).
Definitions of Variables:
  • Internal Energy (ΔU\Delta U): The total energy contained within a system, measured in Joules (J\text{J}).
  • Work (ww): The energy required to move an object against an opposing force, measured in Joules (J\text{J}).
  • Heat (QQ): The amount of energy flowing spontaneously from one body to another due to a temperature difference, measured in Joules (J\text{J}).

Sign Conventions for Heat and Work

  • Heat (QQ):
    • +Q+Q: Heat is absorbed by the system.
    • −Q-Q: Heat is released by the system.
  • Work (ww):
    • +w+w: Work is done to the system (on the system).
    • −w-w: Work is done by the system (on the surroundings).

Numerical Problem Solving and Examples

Problem 1: Calculating Work

A gas in a closed container is heated with 50 J50\,\text{J} of energy. If the change in energy of the system is 30 J30\,\text{J}, how much work was done by the system?

  • Formula: ΔU=Q+w\Delta U = Q + w
  • Given Data:
    • Q=+50 JQ = +50\,\text{J} (Positive because heat is supplied to the system/gas).
    • ΔU=30 J\Delta U = 30\,\text{J}.
  • Calculation:
    • 30 J=50 J+w30\,\text{J} = 50\,\text{J} + w
    • w=30 J−50 J=−20 Jw = 30\,\text{J} - 50\,\text{J} = -20\,\text{J}
  • Conclusion: −20 J-20\,\text{J} means the system has done 20 J20\,\text{J} of work to the surroundings.
Problem 2: Calculating Internal Energy Change

A gas does 135 J135\,\text{J} of work while expanding, and at the same time, it absorbs 156 J156\,\text{J} of heat. What is the change in internal energy?

  • Given:
    • w=−135 Jw = -135\,\text{J} (Work done by the system).
    • q=+156 Jq = +156\,\text{J} (Heat absorbed by the system).
  • Solution:
    • ΔU=q+w\Delta U = q + w
    • ΔU=+156 J+(−135 J)\Delta U = +156\,\text{J} + (-135\,\text{J})
    • ΔU=+21 J\Delta U = +21\,\text{J}
Problem 3: Expansion Work

A certain gas expands in volume from 2.0 L2.0\,\text{L} to 6.0 L6.0\,\text{L} at constant temperature. Calculate the work done by the gas if it expands (a) against a vacuum; and (b) against a constant pressure of 1.2 atm1.2\,\text{atm}.

  • Formula: W=−PΔVW = -P \Delta V
  • Part (a) Solution:
    • Because the external pressure is zero (vacuum), no work is done in the expansion.
    • W=−(0)(6.0−2.0) L=0W = -(0)(6.0 - 2.0)\,\text{L} = 0
  • Part (b) Solution:
    • The external, opposing pressure is 1.2 atm1.2\,\text{atm}.
    • W=−(1.2 atm)(6.0−2.0) LW = -(1.2\,\text{atm})(6.0 - 2.0)\,\text{L}
    • W=−4.8 L-atmW = -4.8\,\text{L-atm}
  • Conversion Note: To convert the answer to joules, specific conversion units must be applied. Because this is a gas expansion (work done by the system on the surroundings), the work done has a negative sign.
Additional Practice Scenarios
  1. Scenario: A gas in a closed container is heated with 15 J15\,\text{J} of energy. The gas performs 3 J3\,\text{J} of work to raise the lid. What is the change in internal energy of the system?
    • Answer: ΔU=12 J\Delta U = 12\,\text{J}.
  2. Scenario: The change in internal energy of a system is +100 J+100\,\text{J}. How much heat is evolved if the work done on the system is 200 J200\,\text{J}?
    • Answer Provided: ΔU=+300 J\Delta U = +300\,\text{J}.

References

  • Lawrence S. Brown and Thomas A. Holme (2018), Chemistry for Engineering Students: Cengage Learning.
  • Roxy Wilson (2018), Solutions to Red Exercises: Chemistry: The Central Science: United Kingdom: Pearson.
  • Theodore E. Brown, et. al. (2018), Chemistry: The Central Science (14th Edition): United Kingdom: Pearson.
  • Unknown Author (2018), Chemistry in Context: McGraw-Hill Education.
  • Chang, Raymond and Kenneth A. Goldsby (2016), Chemistry: New York: McGraw Hill International Edition.
  • Online References:
    • http://chemed.chem.purdue.edu/genchem/topicreview/index.php
    • http://www.sparknotes.com/chemistry/
    • http://m.learning.hccs.edu/faculty/laimutis.bytautas/chem1411