#### Material Balances on Transient Processes: Screencast

Describe the ordinary differential equation that is the material balance for a container with flow in and out.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

**Overall material balance**

\[ \frac{dm}{dt} = \dot{m}_{in}\, -\, \dot{m}_{out} \]

\[I.C. at\, t\, =\, 0, m = m_0\]

where \(m\) = the total mass in the tank at time \(t\)

\(m_0\) = the total mass in the tank at \(t\) = 0

\(\dot{m}_{in}\) = the total mass flow rate into the tank

\(\dot{m}_{out}\) = the total mass flow rate out of the tank

**Material balance on component \(i\)**

\[\frac{dm_i}{dt} = \dot{m}_{i,in}\, -\, \dot{m}_{i,out} + \dot{r}_{i,gen}\, -\, \dot{r}_{i,cons}\]

\[I.C. at\, t\, =\, 0, m_i = m_{i0}\]

where \(m_i\) = the mass of component \(i\) in the tank at time \(t\)

\(\dot{m}_{i,in}\) = the mass flow rate into the tank of component \(i\)

\(\dot{m}_{i,out}\) = the mass flow rate out of the tank of component \(i\)

\(\dot{r}_{i,gen}\) = the rate of generation in the tank of component \(i\)

\(\dot{r}_{i,cons}\) = the rate of consumption in the tank of component \(i\)

For a system with reaction, the material balances are usually written in terms of moles instead of mass.