\(\Delta U = U_{\rm f} - U_{\rm i}\)
\(\Delta U = q + w\)
\(q = m\cdot C_{\rm s}\cdot \Delta T\)
\(q = n\cdot C_{\rm m}\cdot \Delta T\)
\(q = m\cdot\Delta H_{\rm trans}\)
\(q = n\cdot\Delta H_{\rm trans}\)
\(w = - P_{\rm ext}\Delta V\)
\(w = -\Delta n_{\rm gas}RT\)
Δngas = (#mol gas prod) - (#mol gas react)
\(H = U + PV\)
\(\Delta H = \Delta U + P\Delta V\)
\(\Delta U = \Delta H - P\Delta V\)
\(\Delta U = \Delta H -\Delta nRT\)
\(\Delta H = q_{\rm P}\)
\(\Delta U = q_{\rm V}\)
\(q_{\rm cal} = -q_{\rm sys}\)
\(q_{\rm cal} = C_{\rm cal}\Delta T\)
\(q_{\rm cal} = m_{\rm water}\cdot C_{\rm s,water}\cdot \Delta T\) \(+ C_{\rm hardware}\Delta T\)
\(w = -nRT \ln\left({V_{\rm f}\over V_{\rm i}}\right)\)
\(q = nRT \ln\left({V_{\rm f}\over V_{\rm i}}\right)\)
\(\Delta H_{\rm rxn} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \cdots\)
\(\Delta H^\circ_{\rm rxn} = \sum n\Delta H^\circ_{\rm f}{\rm (products)}\) \(- \sum n\Delta H^\circ_{\rm f}{\rm (reactants)} \)
\(\Delta H^\circ_{\rm rxn} = \sum n\Delta H_{\rm bond}{\rm (breaking)}\) \(- \sum n\Delta H_{\rm bond}{\rm (making)} \)
\(\Delta S_{\rm univ} = \Delta S_{\rm sys} + \Delta S_{\rm surr}\)
\(S = k \ln \Omega\)
\(\displaystyle\Delta S = {q_{\rm rev}\over T}\)
\(\displaystyle\Delta S = n\;C_{\rm m} \ln\left(T_{\rm f}\over T_{\rm i}\right)\)
\(\displaystyle\Delta S = n\;R \ln\left(V_{\rm f}\over V_{\rm i}\right)\)
\(\displaystyle\Delta S = {\Delta H_{\rm trans}\over T_{\rm trans}}\)
\(\Delta S^\circ_{\rm rxn} = \sum n S^\circ{\rm (products)}\)\(- \sum n S^\circ{\rm (reactants)} \)
\(G = H - TS\)
\(\Delta G = \Delta H - T\Delta S\)
\(\Delta G^\circ_{\rm rxn} = \sum n\Delta G^\circ_{\rm f}{\rm (products)}\) \(- \sum n\Delta G^\circ_{\rm f}{\rm (reactants)} \)
\(\Delta H = T_{\rm eq}\Delta S\)