Chemical Thermodynamics Mit Apr 2026
From (dG = -SdT + VdP): [ -\left(\frac\partial S\partial P\right)_T = \left(\frac\partial V\partial T\right)_P ]
For non-ideal systems: [ \mu_i = \mu_i^\circ + RT \ln a_i ] where (a_i) = activity, and activity coefficient (\gamma_i = a_i / x_i) (for Raoult’s law basis). chemical thermodynamics mit
(temperature dependence of (K)): [ \fracd\ln KdT = \frac\Delta H^\circRT^2 ] MIT 5.60 trick: Integrate this assuming (\Delta H^\circ) constant for small (T) range, or use (\Delta H^\circ(T) = \Delta H^\circ_298 + \int_298^T \Delta C_p , dT). 8. Connection to Statistical Mechanics (MIT 5.62 Bridge) The partition function (Q(N,V,T)) relates to Helmholtz free energy: [ A = -kT \ln Q ] Then: [ P = -\left(\frac\partial A\partial V\right) T,N = kT \left(\frac\partial \ln Q\partial V\right) T,N ] [ U = kT^2 \left(\frac\partial \ln Q\partial T\right)_V,N ] [ S = k \ln Q + \fracUT ] From (dG = -SdT + VdP): [ -\left(\frac\partial
