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