Comprehensive Notes on Thermodynamics and Hess's Law

Energy of Systems

• The starting and ending points of a process remain the same, but the path taken can change.
• The overall difference between the starting and ending points remains constant.

Signs of Units and Energy

• The signs of energy units indicate what's happening in the system.
• They tell whether energy needs to be added to the system for a reaction to proceed, or if energy needs to be removed for the reactions to stay stable.
• Stable chemistry is generally desired.

Delta U

• The sign of $\,Delta U$ indicates whether the system has lost or gained energy.
• Runaway reactions occur when a system gains energy uncontrollably, leading to undesirable outcomes.

Initial and Final States

• A system transitions from an initial state to a final state.
• If the final state has lower energy, energy is released to the environment.
• If the final state has higher energy, the surroundings must supply energy for the transformation.
• It's important to consider the system's viewpoint when assessing energy changes.
  • Is the system's energy increasing or decreasing?

First Law of Thermodynamics

• The first law of thermodynamics states that overall energy is conserved; it is neither created nor destroyed.
• If one system loses energy, another system must gain energy.
• Energy can be converted, but the total energy in the system remains constant, similar to mass and charge conservation.
• If a reaction produces energy, the surroundings absorb it. This is why cooling systems are used in cars. Radiators remove heat generated by the engine.
• If energy is consumed by the system, it must be supplied from elsewhere, such as the exterior.
• The first law is also known as the law of conservation of energy.
• $\,Delta U$ relates to the change in the system's internal energy and is influenced by heat transfer ($q$) and work done on the system.

Measuring Delta U

• Measuring $\,Delta U$ can be challenging due to the complexity of systems with many atoms and molecules.
• Chemical reactions can either lose heat (exothermic, surroundings get hotter) or gain heat (endothermic, surroundings get cooler).
• Temperature can be measured accurately, which helps in understanding energy transfer within the system.
• We need to know how effective the components of the system influence heating.

Heat Capacity

• Heat capacity is the amount of energy required to raise a substance's temperature by one degree per gram.
• Units are typically in joules per Kelvin ($\frac{J}{K}$) or joules per gram per Kelvin ($\frac{J}{g \cdot K}$).
• A larger heat capacity means more energy is required to warm up the substance.
• Different materials have different abilities to cool, warm, and dissipate heat.
• Water is one of the most effective cooling materials due to its high heat capacity.

Extensive Property

• Heat capacity is an extensive property, meaning the energy required depends on the amount of substance.
• The more material, the more energy is needed to raise the temperature.
• It's easy to warm a teaspoon of water but difficult to warm an Olympic ice swimming pool due to thermal mass.

Specific Heat Capacity

• Specific heat capacity is defined as C, which is energy per gram of substance.
• $C = \frac{Q}{m \cdot \Delta T}$, where:
  • $Q$ is the quantity of energy transferred (heat).
  • $m$ is the mass in grams.
  • $\,Delta T$ is the change in temperature (Kelvin or Celsius).
• Specific heat capacity is determined experimentally.

Table of Specific Heat Capacities

• Specific heat capacity is usually provided in a table providing element, specific and molar heat capacities.

• Molar heat capacity is the specific heat capacity multiplied by the molecular weight.

• Materials like lead heat up easily (low specific heat capacity), while water requires much more energy to heat up.

• Metals like gold, silver, and copper warm up easily and dissipate heat, making them good thermal conductors.

• The ability to warm things up is used in cooling applications.

• If you know the heat capacity of a substance, you can use the equation $Q = mc \Delta T$ to calculate the final temperature or the heat capacity.

  • You can rearrange the formula to isolate any of the four variables if you know the other three.

• $\,Delta T$ is always the final temperature minus the initial temperature, and it can be negative.

Example

• To calculate the energy required to heat 250 grams of iron from 22°C to 325°C, given the specific heat capacity of iron is 0.45 J/g·K:
  1. $m = 250$ grams
  2. $\,Delta T = 325 - 22 = 303$ °C
  3. $C = 0.45 \frac{J}{g \cdot K}$
  4. $Q = mc \Delta T = 250 \cdot 0.45 \cdot 303 \approx 3.4 \times 10^4$ Joules or 34 kJ
• Supplying the same energy to water would only increase its temperature by about 10% compared to iron.
• On a mole basis, the molar heat capacity is the specific heat capacity times the molar mass.

Importance of Heat Capacity

• Water's high heat capacity allows it to absorb large amounts of energy without significant temperature increases.
• Oceans absorb vast amounts of energy, helping to regulate global temperatures.
• Nuclear power plants and other facilities use water for cooling.
• Evaporative cooling systems and sweating utilize water's properties to cool down environments and bodies.
• Water can be used to calculate the specific heat capacities of other materials.
• Known quantities of materials are heated and then dropped into a known quantity of water, and the temperature change is measured.

Example

• A 15.5g block of chromium heated to 100°C is dropped into 55.5g of water initially at 16.5°C. The final temperature of the water is 18.9°C. What is the specific heat capacity of chromium?
  1. The energy lost by the chromium is gained by the water.
  2. $Q<em>{water} = m</em>{water} \cdot C<em>{water} \cdot \Delta T</em>{water} = 55.5 \cdot 4.184 \cdot (18.9 - 16.5) \approx 557.3$ Joules
  3. $Q_{chromium} = -557.3$ Joules (negative because it's losing energy)
  4. $C<em>{chromium} = \frac{Q</em>{chromium}}{m<em>{chromium} \cdot \Delta T</em>{chromium}} = \frac{-557.3}{15.5 \cdot (18.9 - 100)} \approx 0.43 \frac{J}{g \cdot K}$

Enthalpy

• Enthalpy is a better way of describing the energy of a system, especially when pressure and volume change.
• It's defined as $H = U + PV$, where $U$ is internal energy, $P$ is pressure, and $V$ is volume.
• Enthalpy tells us how much it will cost to do a chemical reaction or how much we are going to get back from it.

Changes in Enthalpy

• Enthalpy is a state function, so we measure changes in it by measuring heat flux in and out of a system.
• $\,Delta H = H<em>{final} - H</em>{initial}$, where:
  • $\,Delta H$ is the change in enthalpy.
  • $H_{final}$ is the enthalpy of the products.
    • $H_{initial}$ is the enthalpy of the reactants.
• At constant pressure, $\,Delta H$ is equivalent to the heat generated or consumed.
• Similar to $\,Delta U$, the sign of $\,Delta H$ is critical.
  • When \,Delta H < 0, heat flows from the system to the surroundings (exothermic).
  • When \,Delta H > 0, heat flows from the surroundings to the system (endothermic).
• Exothermic reactions release energy and get hot (e.g., hand warmers).
• Endothermic reactions require energy input and cool their surroundings (e.g., mixing barium hydroxide and ammonium nitrate).

Examples of Chemical Reactions

• Exothermic: Gives off sound, light and heat.
  • Barking Dog Reaction
    • $N<em>2O</em>2 + CS_2$ = Byproducts containing sound and energy.
    • Carbon disulfide is quite toxic.
• Endothermic: Absorbs heat from the surroundings cooling it.
  • Barium hydroxide and ammonium nitrate
    • Combining two solids reduces the temperature down to -30 degrees.

Hess's Law

• The energy released in one direction is equal to the amount of energy it takes to go back in the opposite direction.
• The energy needed to split water into hydrogen and oxygen is equal to the energy released when hydrogen and oxygen are burned to form water.
• For any chemical reaction, the $\,Delta H$ of the reverse reaction is exactly the same number but the opposite sign.
• If it costs you $5.71 to go this direction I'll get$5.71 by going back in that direction.
• Example:
  • Electrolysis of water: Requires energy (571 kJ).
  • Burning hydrogen and oxygen: Releases energy (571 kJ).
• The amount of energy released is proportional to the amount of material consumed.

Examples

• The Hindenburg disaster involved approximately 7,000,000 cubic feet of hydrogen, equivalent to 9,000,000 moles.
  • The energy released was substantial due to the large amount of hydrogen.
• Electrolysis of 100 mL of water only requires 2.6 mJ of energy.
  Sometimes size matters.

Same Reactions, Different States

• Consider two reactions:
  1. $CH<em>4(g) + O</em>2(g) \rightarrow CO<em>2(g) + H</em>2O(l) \quad \Delta H = -890 \frac{kJ}{mol}$
  2. $CH<em>4(g) + O</em>2(g) \rightarrow CO<em>2(g) + H</em>2O(g) \quad \Delta H = -802 \frac{kJ}{mol}$
• The difference in energy (88 kJ/mol) is due to the state of water (liquid vs. gas).
• The heat of vaporization is the origin of the difference in heat.

Rules for manipulating thermochemical equations:

1. If the equation is reversed, the sign of $\,Delta H$ must change.
2. Substances can only be canceled out if they are in the same state.
3. If the coefficients of the atoms in your equation are multiplied you must also multiply the $\,Delta H$.

• By reversing and combining the equations, we can calculate the heat of vaporization of water.

Thermochemical Equations

• A chemical equation accompanied by the $\,Delta H$ value is a thermochemical equation.

To combine

1. Reverse equations and change any signs.
2. Only cancel if in the same state, i.e. gas for gas.
3. If the coefficients are multiplied, you must also multiply the $\,Delta H$.

Implications of Delta H

• A negative $\,Delta H$ means it's exothermic giving up energy.
• A positive $\,Delta H$ means it's endothermic getting energy back.
• The value only tells you what and how much but doesn't tell you how it goes, this depends greatly on kinetics.

Combustion of Carbon - Hess's Law Example

• $C(s) + O<em>2(g) \rightarrow CO</em>2(g) \quad \Delta H = -393.5 \frac{kJ}{mol}$
• Alternative two-step route:
  1. $C(s) + \frac{1}{2} O<em>2(g) \rightarrow CO(g) \quad \Delta H</em>1 = -110 \frac{kJ}{mol}$
  2. $CO(g) + \frac{1}{2} O<em>2(g) \rightarrow CO</em>2(g) \quad \Delta H_2 = -283.5 \frac{kJ}{mol}$
• $\,Delta H<em>1 + \Delta H</em>2 = -393.5 \frac{kJ}{mol}$, which is the same as the direct route.
• Hess's Law: The overall energy change in a chemical reaction is independent of the pathway between the initial and final states.
• It doesn't matter the route you go from the starting materials to the product, energy of the system is constant.