BackThermochemistry, Spontaneity, Free Energy, and Gas Laws: Structured Study Notes
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Thermochemistry and Spontaneity
Standard Heats of Formation and Enthalpy Changes
Thermochemistry studies the energy changes that occur during chemical reactions, focusing on enthalpy and its role in determining reaction spontaneity.
Standard heat of formation (ΔHof): The enthalpy change for the formation of 1 mol of a substance in its standard state from its constituent elements in their standard states.
Standard state: The most stable form of an element at 1 atm and 25 °C.
To calculate ΔHo for a reaction using standard heats of formation:
If standard formation data is unavailable, estimate ΔH using average bond dissociation energies:
Energy released by chemical reactions comes from differences in relative bond strengths.
Energy and Chemical Reactions
Energy changes in chemical reactions are quantified by enthalpy (ΔH) and, to a lesser extent, internal energy (ΔE).
ΔH can be determined by:
Calorimetry
Hess's Law
Standard heats of formation
Average bond dissociation energies
Energy changes influence chemical reactivity and spontaneity.
Spontaneity of Chemical Processes
Spontaneity describes whether a process occurs without continuous external influence.
Spontaneous process: Proceeds on its own once started (e.g., a ball rolling downhill, a spring uncoiling, oxidation of sugar, rusting of iron).
Spontaneity is not related to reaction speed; spontaneous reactions can be fast or slow.
Enthalpy and Spontaneity
Exothermic reactions (ΔH < 0) often, but not always, occur spontaneously.
Most exothermic reactions are spontaneous; most endothermic reactions are nonspontaneous, but exceptions exist.
Example:
Decreases in enthalpy favor spontaneity, but do not guarantee it.
Entropy and Spontaneity
Entropy (S) measures the randomness or disorder of a system and is a key factor in spontaneity.
Spontaneous processes often involve an increase in entropy.
Entropy increases with greater disorder:
Entropy usually increases if a reaction leads to a net increase in the number of particles.
Example: 3 mol of solid reactants become 15 mol of dissolved ions and liquids.
Increases in entropy favor spontaneity, but do not guarantee it.
Factors Affecting Spontaneity
Both enthalpy and entropy changes influence whether a process is spontaneous.
ΔH | ΔS | Spontaneous? |
|---|---|---|
− | + | Yes |
− | − | Maybe |
+ | − | No |
+ | + | Maybe |
Temperature and Spontaneity
Temperature is a non-reaction-specific factor that can determine spontaneity, especially when only one of enthalpy or entropy favors the process.
At low temperatures, some reactions may become nonspontaneous even if ΔH and ΔS favor spontaneity.
Example: The reaction above is no longer spontaneous at sufficiently low temperatures.
Gibbs Free Energy
The combined effect of enthalpy, entropy, and temperature on spontaneity is described by the Gibbs free energy change (ΔG).
Formula: (Temperature in Kelvin)
Interpretation:
: Spontaneous process
: Equilibrium
: Nonspontaneous process
Free Energy Example Calculations
Example: Verify spontaneity at room temperature (25 °C):
Given: , ,
Calculation: (Spontaneous since ΔG < 0)
At equilibrium, ΔG = 0:
Set and solve for T: For the example:
Nonspontaneous temperatures: For T < 188 K, ΔG > 0.
Summary Table: Spontaneity and Temperature
ΔH | ΔS | Spontaneous? |
|---|---|---|
− | + | Always |
− | − | If T is small enough |
+ | − | Never |
+ | + | If T is large enough |
Temperature determines spontaneity when only one of enthalpy or entropy favors the process.
The Gas Laws
Physical Behavior of Gases
Gases exhibit similar physical behavior despite differences in chemical properties. Their behavior is described by four variables:
Pressure (P)
Temperature (T)
Volume (V)
Amount (n, in moles)
Atmospheric Pressure
Atmospheric pressure is the force per unit area exerted by the mass of air on Earth's surface, typically measured with a mercury barometer.
Pressure units:
1 mm Hg = 1 torr
1 atm = 760 torr
SI unit: 1 atm = 101325 Pa = 101.325 kPa
Gas Laws
Several laws describe the relationships between the variables for gases:
Boyle’s Law: Volume varies inversely with pressure (at constant n and T).
Charles’s Law: Volume varies directly with absolute temperature (at constant n and P).
Avogadro’s Law: Volume varies directly with the amount in moles (at constant P and T).
Amonton’s Law: Pressure varies directly with absolute temperature (at constant V and n).
The Ideal Gas Law
The four gas laws are combined into the ideal gas law, which relates all four variables:
Formula: where R = 0.08206 L·atm/mol·K
Each individual law is a special case of the ideal gas law with two variables held constant.
Standard Temperature and Pressure (STP)
STP is a reference set of conditions for gases:
Temperature: 0°C (273.15 K)
Pressure: 1 atm
Note: STP for gas laws differs from standard conditions in thermochemistry.
Using the Ideal Gas Law: Examples
To find temperature:
To find moles:
To find pressure or volume: Rearrange as needed.
Example: What is the temperature of 6.9 mol of N2 in a 1.5 L container at 42 atm?
Example: How many moles of Kr in 750 mL at 298 K and 1.10 atm?
Stoichiometry and the Gas Laws
Stoichiometry uses balanced chemical equations to relate amounts of reactants and products. The ideal gas law allows conversion between moles, pressure, volume, and temperature for gases.
Steps:
Convert grams to moles using molar mass.
Use coefficients from the balanced equation to relate moles of different substances.
Use the ideal gas law to convert moles of gas to volume, pressure, or temperature as needed.
Example: What volume of H2 at 1.15 atm and 225°C is needed to form 35.5 g of Cu from CuO?
Convert grams Cu to moles H2:
Convert moles H2 to volume using ideal gas law:
Example: How many grams of P4 react with 35.5 L O2 at STP to form P4O10?
Use to find moles O2, then use stoichiometry and molar mass to find grams P4.
Summary
A spontaneous process proceeds on its own once started, without continuous external influence.
Decreases in enthalpy (exothermic) and increases in entropy favor spontaneity, but do not guarantee it.
Temperature also affects spontaneity.
Spontaneity is determined by Gibbs free energy:
The ideal gas law () encompasses all individual gas laws and is used to calculate gas pressure, volume, temperature, and moles.
Stoichiometry combined with the gas laws allows conversion between moles, pressure, volume, and temperature of gases in chemical reactions.
Additional info: These notes expand on the original slides by providing definitions, formulas, and stepwise examples for key concepts in thermochemistry, spontaneity, free energy, and gas laws, suitable for General Chemistry students.
