Thermochemistry

Nature of Energy

Thermodynamics

• Definition: Study and measurement of heat evolved or absorbed during chemical reactions.

Energy

• Definition: Capacity to do work or produce heat.

Internal Energy (E)

• Definition: Sum of kinetic and potential energies of all particles in a system.
• Change in Internal Energy:

$$\Delta E=q+w$$

• From the System’s Perspective:
• Energy Inflows (+):
• Heat absorbed (( q > 0 ))
• Work done on the system (( w > 0 ))
• Energy Outflows (-):
• Heat removed (( q < 0 ))
• Work done by the system (( w < 0 ))

System and Surroundings

• System: The part of the universe chosen for study (e.g., reactants and products in chemistry).
• Surroundings: Everything else interacting with the system.

Work

• Types of Work:
• Work by Gas:

$$W=P\Delta V$$

• Where:

$$P=\frac{F}{A}\text{or}F=P\cdot A$$ $$\Delta V=V_{\text{final}}-V_{\text{initial}}=A\cdot \Delta h$$

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Thermic Reactions

Exothermic Reactions

• Definition: Reactions that release heat.

Endothermic Reactions

• Definition: Reactions that absorb heat.

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Enthalpy (H)

Definition

$$H=E+PV$$

• At Constant Pressure:

$$\Delta H=q_p$$

• Derived from:

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

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Molar Heat Capacity

Definition

• Energy required to raise the temperature of 1 mole by 1 K.

For an Ideal Gas

• Constant Volume:

$$C_v=\frac{3}{2}R$$

• Constant Pressure:

$$C_p=C_v+R=\frac{5}{2}R$$

• Reason: Includes energy for both heating and ( PV ) work.

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Thermodynamics of Ideal Gases

Kinetic Energy

$$(\text{KE}{)}_{\text{avg}}=\frac{3}{2}RT\text{per mole}$$

• Change KE by changing temperature only.

Molar Heat Capacity Relationship

$$C_p=C_v+R$$

Heat Flow Expressions

• Constant Volume:

$$q_v=n{C}_v\Delta T$$

• Constant Pressure:

$$q_p=n{C}_p\Delta T$$

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Heating an Ideal Gas

Change in Enthalpy

$$\Delta H=\Delta E+\Delta (PV)=n{C}_p\Delta T$$

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The State Function

Definition

• Depends only on the current state, not on the path taken.
• Characteristics:
• Change in property depends only on initial and final states.
• Examples:
• State Functions: Internal energy (E), Enthalpy (H)
• Not State Functions: Heat (q), Work (w)

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Key Formulas

• Internal Energy Change:

$$\Delta E=q+w$$

• Enthalpy:

$$H=E+PV\text{and}\Delta H=q_p$$

• Work by Gas:

$$W=P\Delta V$$

• Heat Capacity Relationships:

$$C_p=C_v+R$$

• Heat Flow:

$$q_v=n{C}_v\Delta T\text{and}{q}_p=n{C}_p\Delta T$$