3.1 Conservation of mass

Conservation of Mass in Chemical Engineering

The Law of Conservation of Mass

The law of conservation of mass states that matter cannot be created or destroyed in an isolated system. It can only change form. This principle is the foundation of every material balance you'll write in chemical engineering.

In any chemical reaction, the total mass of reactants equals the total mass of products because atoms are rearranged, not created or lost. Chemical engineers rely on this fact to track mass through processes, figure out flow rates and compositions, and design systems that hit production targets while minimizing waste.

Real-world applications include:

• Wastewater treatment: tracking pollutants from inlet to outlet to ensure discharge limits are met
• Biofuel production: balancing feedstock input against fuel, byproduct, and waste outputs
• Emissions monitoring: quantifying greenhouse gas output by accounting for all carbon entering and leaving a process

Applications in Chemical Engineering

• Material balances: Determine flow rates, compositions, and quantities of materials entering and leaving a system.
• Process design: Size equipment like reactors, distillation columns, and absorption towers based on how much material they need to handle.
• Optimization: Identify where recycling streams or heat integration can reduce waste and raw material consumption.
• Environmental impact assessment: Track where pollutants and byproducts end up so you can quantify things like wastewater discharge or carbon emissions.

System Boundaries for Material Balances

Defining System Boundaries

A system boundary is an imaginary surface you draw around whatever you're analyzing. Everything inside the boundary is your system; everything outside is the surroundings. The boundary determines which streams of matter (and energy) you need to account for.

You can draw a boundary around a single piece of equipment (one reactor), a group of units (a reactor plus a separator), or an entire plant. Choosing the right boundary is often the most important step in solving a material balance problem, because it determines which unknowns appear in your equations and whether you have enough information to solve them.

Types of Systems

• Open system: Matter and energy both cross the boundary. Most continuous processes fall here (e.g., a continuous stirred-tank reactor, a heat exchanger).
• Closed system: Energy can cross the boundary, but matter stays inside. A sealed batch reactor is a common example.
• Isolated system: Neither matter nor energy crosses the boundary. A perfectly insulated, sealed container would qualify (this is an idealization; real systems are never perfectly isolated).

These categories describe what crosses the boundary. You also need to consider when things change:

• Steady-state: Conditions inside the system don't change with time. What flows in equals what flows out, with no accumulation. A continuously operating distillation column at stable conditions is a good example.
• Unsteady-state (transient): Conditions change over time, so mass can accumulate or deplete inside the boundary. Filling a tank, draining a vessel, or starting up a process are all unsteady-state situations.

Solving Steady-State Material Balances

The Steady-State Material Balance Equation

At steady state, nothing accumulates inside the system. The general balance simplifies to:

$\text{Input} + \text{Generation} = \text{Output} + \text{Consumption}$

Generation and Consumption refer to material produced or used up by chemical reactions inside the boundary. If no reaction occurs, the equation reduces further to:

$\text{Input} = \text{Output}$

You can write this equation for the total mass or for each individual chemical species. When reactions are involved, you'll need stoichiometric relationships to connect generation and consumption terms to the extent of reaction.

Problem-Solving Strategy

Follow these steps for any steady-state material balance problem:

1. Read carefully. Identify what's given and what you need to find.
2. Draw a process flow diagram. Sketch the system, draw the boundary, and label every stream with known and unknown flow rates and compositions.
3. Perform a degrees-of-freedom analysis. Count your unknowns and your independent equations. If the number of unknowns equals the number of independent equations, the problem is solvable. If not, look for missing information or a different boundary choice.
4. Write balance equations. Write a mass balance for each component and/or the total mass. Add any extra relationships you need (reaction stoichiometry, phase equilibrium, etc.).
5. Solve. Work through the algebra to find the unknowns.
6. Check your answer. Verify that results are physically reasonable (no negative flow rates, compositions that add to 100%, values in expected ranges).

A few practical tips:

• Keep units consistent throughout. Convert everything to the same unit system (SI or otherwise) before you start solving.
• Order-of-magnitude estimates are a quick sanity check. If a small lab reactor somehow produces 10,000 kg/hr of product, something went wrong.

Extensive vs. Intensive Properties in Material Balances

Defining Extensive and Intensive Properties

Extensive properties depend on how much material you have. Mass, volume, total energy, and moles are all extensive. If you double the amount of material, these values double. Extensive properties are additive: the total mass of a mixture equals the sum of the component masses.

Intensive properties do not depend on the amount of material. Temperature, pressure, density, concentration, and boiling point are intensive. A cup of water at 80°C has the same temperature as a swimming pool at 80°C.

Using These Properties in Material Balances

In balance equations, you work directly with extensive properties because those are what's conserved. Mass flow rates of individual components and total mass flow rates go straight into your conservation equations.

Intensive properties aren't conserved, but they're essential for connecting information between streams. For example:

• Density ($\rho = m/V$) lets you convert between mass flow and volumetric flow.
• Mass fraction or mole fraction lets you break a total stream flow into component flows.
• Temperature and pressure let you look up or calculate other properties (using the ideal gas law, steam tables, etc.).

When you mix streams, extensive properties simply add up. Intensive properties generally don't. If you mix a hot stream with a cold stream, the final temperature isn't the sum of the two temperatures. Instead, you'd calculate a weighted average based on the mass (or energy) each stream contributes.