Mass balance

A mass balance accounts for material entering, leaving and accumulating within a stated system. For total mass in ordinary nonrelativistic process calculations, $dM/dt=\sum {\dot{m}}_{\mathrm{in}}-\sum {\dot{m}}_{\mathrm{out}}$. A balance for one chemical species also includes its net production or consumption by chemical reactions.

For a well-mixed tank of constant volume $V$ flushed at flow $Q$ with solute-free liquid, the solute concentration satisfies $VdC/dt=-QC$. Thus $C(t)=C(0)e^{-Qt/V}$. With $V=100$ litres and $Q=10$ litres per minute, the concentration falls by a factor $e$ in ten minutes. The tank is at steady total inventory while its composition changes, showing why a total-mass balance and a species balance answer different questions.