# Useful Chemistry Equations

This article is part of the ChemHelp Tutoring Wiki |

## Contents

## 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