Useful Chemistry Equations
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ΔE = q + W
ΔE = change in energy of the system
q = heat absorbed by the system
W = work done on the system
W = -PΔV , ΔE = q_{p} - PΔV at constant P
Derivation:
Substituting P = F/A into W = FΔd, we get W = PAΔd or W = PΔV
The increase in volume will decrease the system's ability to do work, therefore work has been done by the system, so the equation becomes W = -PΔV.
Substituting into the first equation, we get ΔE = q_{p} - PΔV
ΔE = q_{v} at constant V
A special case of the previous equation where ΔV is zero
H = E + PV
H = enthalpy
it is a state function. It is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings
ΔH = q_{p} at constant P
Derivation:
ΔH = ΔE + Δ(PV) = q + W + PΔV = q + (-PΔV) + PΔV at constant P
The PΔV's cancel out, leaving ΔH = q_{p}
Summary of ΔE equations in different conditions
ΔE = q + W , general conditions
ΔE = q_{v} , at constant V
ΔE = q_{p} + W_{p} = ΔH - PΔV , at constant P
Entropy (S) and Gibbs Free energy (G)
ΔG = ΔH - TΔSb, at constant T
ΔG_{rxn} = ΔG°_{rxn} + RTlnQ where ΔG°_{rxn} = -RTlnK
ΔG_{rxn} = RTln(Q/K)
ΔS = q_{rev}/T , for all reversible processes at constant T
ΔS_{Total} ≥ 0
Notes: both entropy and gibb's Free energy are state functions