Overall differential mass balance: \[\frac{dW}{dt}\,=\,-\dot{D}\;\;\;\;I.C.\;\;at\;\;t=0,\;W=W_0\]

Balance on more-volatile component (MVC) \[\frac{d(Wx_W)}{dt}\,=\,-\dot{D}y_D\;\;\;\;I.C.\;at\;t=0,\,x_w=x_{w0}\]

where \(W\) = total moles in still at any time.
\(W_0\) = total moles in still at time = 0.
\(\dot{D}\) = rate of distillate being collected
\(x_w\) = mole fraction of MVC in still
\(y_D\) = mole fraction of MVC in vapor phase above still
\(x_{W0}\) = mole fraction of MVC in still at time = 0.

Rayleigh equation \[\int_{x_{w0}}^{x_w}\frac{dx_w}{y_d-x_w}=ln\left(\frac{W}{W_0}\right)\]

Overall mass balance \[W_0\,=\,W\,+\,D\] where \(D\) = total distillate collected

Overall mass balance on MVC \[x_{D,avg}\,=\,\left(W_0x_{w0}-Wx_w\right)/D\] where \(x_{D,avg}\) = average mole fraction of distillate collected.