Question

Asked Sep 3, 2019

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34.4 gallon of toluene, 85.4 lbm of ethyl acetate, and 3.26 ft cubic of ethanol is poured into a tank. Find the mass fraction of each component.

Step 1

Given information:

Volume of Toluene (*v _{t}*)= 34.4 gallon

Mass of Ethyl acetate (*m _{e}*) = 85.4 lbm

Volume of Ethanol (*v _{EtOH}*) = 3.26 ft

The mass fraction for all above components, poured into a tank, is to be calculated. Since, the volume is given for Toluene and Ethanol, the first step is to calculate the mass (in kg) using the density of these components.

Density of Toluene *ρ _{t} *= 867 kg/m

Density of Ethanol *ρ _{EtOH}* = 789 kg/m

As the density is in SI units, the following unit conversions are to be considered while calculating mass of all the components.

Unit conversion:

1 gallon = 0.0038 m^{3}

1 ft^{3} = 0.028 m^{3}

1 lbm = 0.4536 kg

The unit conversion of mass of Ethyl acetate to kg is given in equation (1). The unit conversion of volume of Toluene and Ethanol to m^{3} is shown in equation (2) and (3) respectively.

Step 2

It is known that density of a component is the ratio of its mass to volume. So, the mass for Toluene and Ethanol is calculated in equation (4) and (5) respectively.

Step 3

Mass fraction for an *ith* component in a given mixture of n components is given by equation (6). The total mass of the...

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