Balance of Material and Energy

Basic concepts and Material Balance in Steady State

Unit conversion, mole unit, mass and molar fractions

Perform the following conversions: 1.5 10-6a kg s-1 cm-1345 Btu lb-1a kcal cm-1; y 160°F a °C, °R y K.
2. Air is pumped through a hole immersed in a liquid. The size of the bubbles that come out
The flow through the orifice depends on the diameter of the orifice and the properties of the liquid. The equation that
( ) 3
−
this situation is represented as follows: =6
0
Where g=32.174 ft s-2(gravitational
acceleration); =1 g cm-3(liquid density); 0.081 lb ft-3
(gas density) it is the diameter of the bubble; 70.8 dyn cm-1(surface tension gas-liquid); and
0 =1 mm (diameter of the hole). Calculate the diameter of the bubble. in cm.
3. Natural gas is burned and 200 kcal is produced gmol-1If 40 kilos of that gas are burned in one hour,
How many kW are generated? Natural gas is essentially methane.
A gaseous mixture contains 20 g of N283 g of O2and 45 g of CO2Calculate the composition in
mole fractions and the average molecular weight of the mixture.
A liquid solution contains 1.15% by weight of a protein, 0.27% by weight of KCl, and the rest is water.
The average molecular weight of the protein by gel permeation is 525,000 g∙g.mol-1Calculate the
mole fractions of the components in the solution.
6. Calculate the volumetric flow rate of hexane in a pipe, if the mass flow rate is 6.59 g/s.

Balances in Simple and Multiple Units

1. If 1 L of ethyl alcohol is mixed with 1 L of water, how many kilograms of solution are obtained?
A solution composed of 50% ethanol, 10% methanol, and 40% water is fed at a rate of 100.
kg h-1to a separator that produces two output streams: the first at a rate of 60 kg h-1whose
composition is 80% ethanol, 15% methanol, and 5% water, and a second stream of composition
unknown. Calculate the composition (in %) of the three components and the output flow of the current
unknown in kg h-1.
3. In the production of fish meal, a dehydration process is used. In a batch of cake of
fish (oil-free) that contains 80% moisture, 100 kg of water is removed, so that it
It obtains a cake with 40% humidity. Calculate the weight of the fish cake that was introduced.
initially in the dryer.
In a mixing tank, 125 kg of fermented corn liquor is mixed, which contains 2.5% of
inverted sugars, 50% water and the rest can be considered solid, with 45 kg of molasses
beet that contains 50% sucrose, 1% inverted sugars, 18% water, and the rest are solids.
Pure water is also added to the tank to produce a diluted sugar mixture that contains 2%
(p/p) of inverted sugars. Calculate: a) the amount of water required and b) the concentration of
sucrose in the final mixture.
5. In a process to make jelly, the mashed fruit containing 14% by weight of soluble solids is
mix with sugar (1.22 kg of sugar/1.00 kg of fruit) and pectin (0.0025 kg pectin/1.00 kg of fruit).
The resulting mixture is evaporated in a pot to produce a jelly containing 67% by weight of
soluble solids. Calculate, for a feed of 1000 kg of macerated fruit, the kg of mixture.
obtained, the kg of evaporated water and the kg of jelly produced.
6. A material balance is to be established for each of the components in the processing.
of a lot of soybeans with the following characteristics:
100 kg
ii) composición: aceite 18 %, proteína 35 %, carbohidratos 27.1 %, fibras y cenizas 9.4 % y humedad
10.5 %.

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 Material and Energy Balance

The material undergoes the following processes:

a) Crushing and mechanical extraction: At this stage, the oil content is reduced to 6 %
b) Solvent extraction: The oil is extracted until a paste with 0.5% oil is obtained.
c) Drying: The paste is dehydrated until it contains 8% moisture.
Note: Assume that there is no loss of components with the oil.

100 L/h is desired.-1evaporated milk with 18.61% non-fat solids made from whole milk
whose total solids content is 11.87% and fat content is 3.4%. To perform the calculations, consider a
average density of milk of 1030 kg∙m-3.
a) Calculate the amount of whole milk required and the amount of water that needs to be removed to
carry out the operation.
b) Calculate the fat and water content in evaporated milk.

The diagram shows the process of concentrating a saline solution (NaCl) in an evaporator.
triple effect. The molar fraction of salt at the exit (D) of the third effect is 0.01593. Consider that in
each effect removes the same amount of water.

Calculate the following:

The total amount of water eliminated
b) The concentration of salt in the solution that comes out of the second effect (C).

Balances in Multiple Units with Derivation and Recirculation

To concentrate orange juice, it starts from an extract that contains 12% solids. The juice is passed
to an evaporator that works in a vacuum, but before entering, a part is diverted, and then the juice is diluted
concentrate that comes out of the evaporator with 58% solids up to the final concentration of 42%
solids. The purpose is to improve the flavor of the juice, as it loses certain qualities during evaporation.
volatile flavorings.
a) Calculate the amount of water evaporated and the amount of juice produced per 100 kg/s of juice.
diluted that enters the process.
b) Calculate the amount of juice that is derived

A potato frying production process is developed as described in the following diagram.

of blocks. Calculate the production of french fries and the consumption of oil, knowing that the line is
feeds with 1000 kg of potato per hour.

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 Material and Energy Balance

Potato (80% water)

French fries
(60% water and 0.5% oil)
3. In a process that produces KNO3the evaporator is fed with 1000 kg h-1of a solution that
contains 20% KNO3in weight and is concentrated at 422 K to obtain a KNO solution3at 50%
weight. This solution feeds into a crystallizer at 311 K, where KNO crystals are obtained.3of 96%
in weight. The saturated solution that contains 37.5% of KNO3In weight, it circulates back to the evaporator.
Calculate the recirculation current Ren kg/h and the outlet stream of crystals Pen
kg/h.

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