Mass Balance ( Paul ASHALL )

  • Mass Balance

  • The accounting of all mass in a chemical/pharmaceutical process is referred to as a mass (or material) balance.

  • Uses

  • ‘day to day’ operation of process for monitoring operating efficiency

  • Making calculations for design and development of a process i.e. quantities required, sizing equipment, number of items of equipment

  • Simple example – batch mixing process

200 kg of a 40% w/w methanol/water solution is mixed with 100 kg of a 70% w/w methanol/water solution in a batch mixer unit.

What is the final quantity and composition?

  • continued

Total initial mass = total final mass = 300 kg

Initial methanol mass = final methanol mass

80 + 70 = final methanol mass = 150 kg

Therefore final composition of batch is (150/300) x 100 = 50 % by wt.

  • Exercise

1000 kg of 8% by wt. sodium hydroxide  (NaOH) solution is required. 20% sodium hydroxide solution in water and pure water are available. How much of each is required?

  • Batch processes

Batch processes operate to a batch cycle and are non-steady state. Materials are added to a vessel in one operation and then process is carried out and batch cycle repeated. Integral balances are carried out on batch processes where balances are carried out on the initial and final states of the system.

  • Batch cycle

  • Sequence of operations/steps repeated according to a cycle

  • Batch cycle time

  • Batch size

  • Simple batch reaction cycle

3 steps

  • Continuous processes

These processes are continuous in nature and operate in steady state and balances are carried out over a fixed period of time. Materials enter and leave process continuously.

  • Law of conservation of mass

When there is no net accumulation or depletion of mass in a system (steady state) then:

Total mass entering system = total mass leaving system

or total mass at start = total final mass

  • General mass balance equation

Input + generation – output – consumption = accumulation

Notes: 1. generation and consumption terms refer only to generation of products and consumption of reactants as a result of chemical reaction. If there is no chemical reaction then these terms are zero.

  1. Apply to a system

  2. Apply to total mass and component mass

  • Definitions

  • System – arbritary part or whole of a system

  • Steady state/non-steady state

  • Accumulation/depletion of mass in system

  • Basis for calculation of mass balance (unit of time, batch etc)

  • Component or substance

  • Exercise

1000 kg of a 10 % by wt. sodium chloride solution is concentrated to 50 % in a batch evaporator. Calculate the product mass and the mass of water evaporated from the evaporator.

  • Mixing of streams

  • Example

Calculate E and x

  • Flowsheets

  • Streams

  • Operations/equipment sequence

  • Standard symbols

  • Flowsheets

  • Process flow diagram

  • PID

  • Typical simple flowsheet arrangement

  • Exercise

A 1000 kg batch of a pharmaceutical powder containing 5 % by wt water is dried in a double cone drier. After drying 90 % of the water has been removed. Calculate the final batch composition and the weight of water removed.

  • Exercise – batch distillation

1000 kg of a 20% by wt mixture of acetone in water is separated by multistage batch distillation. The top product (distillate) contains 95% by wt. acetone and the still contains 2% acetone. Calculate the amount of distillate.

  • Use of molar quantities

It is often useful to calculate a mass balance using molar quantities of materials and to express composition as mole fractions or mole %.

Distillation is an example, where equilibrium data is often expressed in mole fractions.

  • Molar units

  • A mole is the molecular weight of a substance expressed in grams

  • To get the molecular weight of a substance you need its molecular formula and you can then add up the atomic weights of all the atoms in the molecule

  • To convert from moles of a substance to grams multiply by the molecular weight

  • To convert from grams to moles divide by the molecular weight.

  • Mole fraction is moles divided by total moles

  • Mole % is mole fraction multiplied by 100

  • Molar units

Benzene is C6H6. The molecular weight is (6×12) + (6×1) = 78

So 1 mole of benzene is 78 grams

1 kmol is 78 kg

  • Exercise – batch distillation

1000 kmol of an equimolar mixture of benzene and toluene is distilled in a multistage batch distillation unit. 90 % of the benzene is in the top product (distillate). The top product has a benzene mole fraction of 0.95. Calculate the quantities of top and bottom products and the composition of the bottom product.

  • Mass balance – crystalliser

A crystalliser contains 1000 kg of a saturated solution of potassium chloride at 80 deg cent. It is required to crystallise 100 kg KCl  from this solution. To what temperature must the solution be cooled?

At 80 deg cent satd soln contains (51.1/151.1)x100 % KCl i.e. 33.8% by wt

So in 1000 kg there is 338 kg KCl & 662 kg water.

Crystallising 100 kg out of soln leaves a satd soln containing 238 kg KCl and 662kg water i.e. 238/6.62 g KCl/100g water which is 36 g KCl/100g. So temperature required is approx 27 deg cent from table.

  • Mass balance filtration/centrifuge

  • Filtration

  • Mass balance – drier

  • Mass balance – extraction/phase split

  • Example (single stage extraction; immiscible solvents)

F = 195 kg; xf = 0.11 kg API/kgwater

S = 596 kg chloroform

y = 1.72x, where y is kgAPI/kg chloroform in extract and x is kg API/kg water in raffinate.

Total balance 195 + 596 = E + R

API balance 19.5 = 175.5×1 + 596y1

19.5 = 175.5×1 + 596.1.72×1

x1 = 0.0162 and y1 = 0.029

R is 175.5 kg water + 2.84 kg API

and E is 596 kg chloroform + 17.28 kg API

Note: chloroform and water are essentially immiscible

  • Mass balance – absorption unit

  • Mass balances – multiple units

  • Overall balance

  • Unit balances

  • Component balances

  • Multiple units

E – evaporator; C – crystalliser; F – filter unit

F1 – fresh feed; W2 – evaporated water; P3 – solid product; R4 – recycle of saturated solution from filter unit

  • Mass balance procedures

  • Process description

  • Flowsheet

  • Label

  • Assign algebraic symbols to unknowns (compositions, concentrations, quantities)

  • Select basis

  • Write mass balance equations (overall, total, component, unit)

  • Solve equations for unknowns

  • Exercise

A mass balance and tracking of usage of a solvent used in an API production process is required for a Pollution Emission Register (PER).

Discuss and outline in general terms how you would do this.


  • Definitions

  • Stoichiometric quantities

  • Limiting reactant

  • Excess reactant

  • Conversion

  • Yield

  • Selectivity

  • Extent of reaction

  • Stoichiometry

  • Refers to quantities of reactants and products in a balanced chemical reaction.

aA + bB    cC + dD

i.e. a moles of A react with b moles of B to give c moles of C and d moles of D.

a,b,c,d are stoichiometric quantities

  • Reactor mass balances

  • Example – aspirin synthesis reaction

  • Limiting reactant/excess reactant

  • In practice a reactant may be used in excess of the stoichiometric quantity for various reasons. In this case the other reactant is limiting i.e. it will limit the yield of product(s)

  • continued

A reactant is in excess if it is present in a quantity greater than its stoichiometric proportion.

% excess = [(moles supplied – stoichiometric moles)/stoichiometric moles] x 100

  • Example – aspirin synthesis

  • Conversion

  • Fractional conversion = amount reactant consumed/amount reactant supplied

  • % conversion = fractional conversion x 100

  • Note: conversion may apply to single pass reactor conversion or overall process conversion

  • Yield

Yield = (moles product/moles limiting reactant supplied) x s.f. x 100

Where s.f. is the stoichiometric factor = stoichiometric moles reactant required per mole  product

  • Example – aspirin synthesis

  • Selectivity

Selectivity = (moles product/moles reactant converted) x s.f. x100


Selectivity = moles desired product/moles byproduct

  • Extent

Extent of reaction = (moles of component leaving reactor – moles of component entering reactor)/stoichiometric coefficient of component

Note: the stoichiometric coefficient of a component in a chemical reaction is the no. of moles in the balanced chemical equation ( -ve for reactants and +ve for products)

  • Examples

A   B

i.e. stoichiometric coefficients a = 1; b = 1

100 kmol fresh feed A; 90 % single pass conversion in reactor; unreacted A is separated and recycled and therefore overall process conversion is 100%

  • Discussion – Synthesis of 3,3 dimethylindoline

  • Discussion – Aspirin synthesis

  • References

  • Elementary Principles of Chemical Processes, R. M. Felder and R. W. Rousseau, 3rd edition, John Wiley, 2000

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