Internal Energy: The change in internal energy (ΔE) of a system is given by the equation ΔE = Q + W, where:
Q: Heat energy (positive when absorbed, negative when released)
W: Work done by or on the system (positive when work is done on the system, negative when done by the system)
Heat Transfer
Heat flows from hot to cold, making Q negative if heat exits the system (exothermic) and positive if absorbed (endothermic).
Common conversions:
1 kJ = 1000 J
1 cal (lowercase) = 4.184 J
1 Cal (uppercase) = 1000 cal
Work Done by/On the System
W = -PΔV:
When gas expands, ΔV is positive, making work negative.
When gas compresses, ΔV is negative, making work positive.
1 L·atm = 101.3 J
Example Problem
Calculate change in internal energy:
Given: 300 J absorbed, gas expands from 2 L to 3 L at 5 atm.
Work (W) = -PΔV = -5 * (3-2) = -506.5 J
ΔE = Q + W = 300 - 506.5 = -206.5 J
Heat Calculations
Q = mcΔT:
m: mass
c: specific heat capacity (4.184 J/g°C for water)
ΔT: change in temperature (°C or K)
Example: Calculate energy to heat 50 g water from 25°C to 75°C:
Q = 50 * 4.184 * 50 = 10,460 J
Phase Change Calculations
Q = mΔH or Q = nΔH:
ΔH for phase changes (fusion, vaporization)
Example: Calculating heat to melt ice:
Heat of fusion = 6 kJ/mol
Convert grams to moles and multiply by ΔH
Thermochemical Equations
Example: Combustion reaction of propane releasing 1200 kJ
Balance: 3 CO2, 4 H2O, 5 O2
Convert grams of reactants to moles and calculate energy released using stoichiometry.
Enthalpy of Formation
ΔH_reaction = ΣΔH_products - ΣΔH_reactants
Example calculation using given enthalpies of formation.
Hess’s Law
Used to calculate enthalpy changes by modifying given reactions.
Reverse or multiply reactions to sum up to desired reaction.
Example: Modify reactions to find ΔH for a desired equation.
Conclusion
Understanding thermochemistry requires mastering equations for heat and work, conversions, and applying principles like Hess’s Law to solve energy-related problems in reactions.