# Mass Balance of Binary Mixtures

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This Demonstration lets you calculate the amount of lean and rich component needed to produce a given mass of a mixture having a desired concentration of salt, sugar, fat, alcohol, etc. It also lets you calculate the mass of a mixture produced from chosen combinations of rich and lean fractions of known concentrations.

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA

## Details

Degrees Brix (symbol °Bx) is a measure of the dissolved sugar-to-water mass ratio of a liquid.

Snapshot 1: preparing orange juice concentrate with 45% total soluble solids (45 °Bx) from 65% concentrate (65 °Bx) and fresh juice 12% total soluble solids (12 °Bx)

Snapshot 2: wine fortification with brandy

Snapshot 3: mixing lean and fat meat

Snapshot 4: diluting a tomato concentrate with water to produce single-strength juice

This Demonstration lets you calculate the quantity of ingredients having specified concentrations needed to make a given amount of mixture with a desired concentration. It also allows calculation of the amount of mixture produced from given amounts of the ingredients whose units can be mass (e.g., kilograms, pounds, tons) or mass flow rate (e.g., kg/min, lb/s, tons/hr). The adjustable parameters, all entered with sliders, are the quantities involved (mixture, rich, and lean masses) and the corresponding concentrations in percent on a wet basis. The known quantity is identified using a setter bar to determine which two quantities will be calculated. The program solves simultaneously the equations:

, ,

where , , and are the mixture, rich fraction, and lean fraction's masses and , , and are their respective concentrations. (For dilution, the lean concentration is set to zero.) The calculated masses are displayed above the plot that depicts the relationship between the masses for the chosen concentrations. (The selected specific conditions are identified by a colored point on the line.)

## Permanent Citation

Mark D. Normand and Micha Peleg

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