Mass Balance (chemical engineering)
A mass balance (also called a material balance) is the systematic application of the law of conservation of mass to a defined control volume or process unit, accounting for all mass entering, leaving, generated by reaction, and accumulating within the system. It is the foundational tool of chemical process design, enabling engineers to size equipment, determine conversion, specify recycle streams, and detect leaks or unaccounted losses. At steady state with no reaction, the balance simplifies to: mass in = mass out.
Key Formula
m_dot_in - m_dot_out + m_dot_gen = d(m_sys)/dt
LaTeX: \dot{m}_{in} - \dot{m}_{out} + \dot{m}_{gen} = \frac{dm_{sys}}{dt}
| Symbol | Meaning | Unit |
|---|---|---|
| \dot{m}_{in} | Mass flow rate entering system | kg/s |
| \dot{m}_{out} | Mass flow rate leaving system | kg/s |
| \dot{m}_{gen} | Mass generation rate by reaction | kg/s |
| m_{sys} | Total mass within system boundary | kg |
| t | Time | s |
Worked Example
Problem
A mixing tank receives two inlet streams: Stream 1 at 5 kg/s of pure water and Stream 2 at 3 kg/s of 40 wt% NaCl solution. The tank operates at steady state. Find the total outlet mass flow rate and the outlet NaCl concentration.
Solution
Step 1: Overall mass balance (steady state, no reaction). ṁ_out = ṁ_in,1 + ṁ_in,2 = 5 + 3 = 8 kg/s Step 2: Component balance on NaCl. ṁ_NaCl,in = 0 + (0.40 × 3) = 1.2 kg/s At steady state: ṁ_NaCl,out = 1.2 kg/s Step 3: Outlet concentration = ṁ_NaCl,out / ṁ_out = 1.2 / 8 = 0.15
Answer
Total outlet flow = 8 kg/s; Outlet NaCl concentration = 15 wt%
Types of Mass Balance and Their Conditions
| Balance Type | Reaction | Steady State | Typical Use | Key Simplification |
|---|---|---|---|---|
| Total mass balance | No | Yes | Mixing, splitting | ṁ_in = ṁ_out |
| Component balance | No | Yes | Mixing with species | ṁ_i,in = ṁ_i,out |
| Reactive balance | Yes | Yes | Reactors | Stoichiometry needed |
| Transient balance | No | No | Batch tanks | dm/dt ≠ 0 |
| Reactive transient | Yes | No | Batch reactors | Full ODE required |
Interactive Tools
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Related Terms
Energy Balance (chemical engineering)
An energy balance is the application of the first law of thermodynamics to a process system, tracking all energy entering, leaving, generated, and stored within a defined control volume in the forms of enthalpy, heat, work, and kinetic/potential energy. For steady-state, open flow systems (the most common case in chemical plants), the balance relates the enthalpy change of process streams to the net heat added and shaft work. Energy balances are essential for designing heat exchangers, reactors, distillation columns, and assessing process efficiency.
Distillation
Distillation is a thermal separation process that exploits differences in the volatility (relative volatility) of mixture components: a liquid feed is partially vaporised, the vapour enriched in the more volatile component rises and is condensed, while the less volatile component concentrates in the liquid bottoms. In a continuous distillation column, repeated vapour-liquid equilibrium stages—either trays or structured packing—progressively sharpen the separation, with the reflux ratio governing the trade-off between product purity and energy consumption. It is the most widely used separation process in the petrochemical, pharmaceutical, and food industries.
Absorption Column
An absorption column (absorber) is a mass-transfer device in which a gas mixture flows upward counter-currently against a descending liquid solvent, causing one or more gaseous components to dissolve into the liquid phase driven by a concentration gradient and governed by vapour-liquid equilibrium. The height of the packed or trayed column is determined by the Number of Transfer Units (NTU) and the Height of a Transfer Unit (HTU), or by the number of theoretical stages. Absorption is widely used to remove acid gases (CO₂, H₂S) from natural gas, SO₂ from flue gas, and ammonia from industrial off-gas streams.
From Latin "massa" (lump, dough) and "bilanx" (having two scale pans), referring to weighing. The concept formalises Antoine Lavoisier's 1789 law of conservation of mass; the term "material balance" became standard in chemical engineering textbooks of the early 20th century.