Chapter 16, Leaching and Washing Video Solutions, Separation Process Principles

Problem 1

Using experimental data from pilot-plant tests of soybean extraction by Othmer and Agarwal, summarized at the beginning of this chapter, check the mass balances for oil and hexane around the extractor, assuming the moisture is retained in the flakes, and compute the mass ratio of liquid oil to flakes in the leached solids leaving the extractor.
Section 16.2

Lottie Adams

Numerade Educator

02:28

Problem 2

Barium carbonate, which is essentially water insoluble, is to be made by precipitation from an aqueous solution containing $120,000 \mathrm{~kg} / \mathrm{day}$ of water and $40,000 \mathrm{~kg} / \mathrm{day}$ of barium sulfide, with the stoichiometric amount of solid sodium carbonate. The reaction also produces a by-product of water-soluble sodium sulfide. The process will be carried out in a continuous, countercurrent system of five thickeners. The reaction will take place completely in the first thickener to which will be fed the solid sodium carbonate, the aqueous solution of barium sulfide, and the overflow from the second thickener. Sufficient fresh water will enter the last thickener so that the overflow from the first thickener will be 10 wt $\%$ sodium sulfide, assuming that the underflow from each thickener contains two parts of water per one part of barium carbonate by weight.
(a) Draw a schematic diagram of the process and label it with all the given information.
(b) Determine the $\mathrm{kg} / \mathrm{day}$ of sodium carbonate required and the $\mathrm{kg} / \mathrm{day}$ of barium carbonate and sodium sulfide produced by the reaction.
(c) Determine the $\mathrm{kg} /$ day of fresh water needed, the wt $\%$ of sodium sulfide in the liquid portion of the underflow that leaves each thickener, and the $\mathrm{kg} /$ day of sodium sulfide that will remain with the barium carbonate product after it is dried.

Bhumika Jayee

Numerade Educator

06:04

Problem 3

Calcium-carbonate precipitate can be produced by the reaction of an aqueous solution of sodium carbonate and calcium oxide. The by-product is aqueous sodium hydroxide. Following decantation, the slurry leaving the precipitation tank is $$5 \mathrm{wt} \%$$ calcium carbonate, $$0.1$ wt $\$$ sodium hydroxide, and the balance water. One hundred thousand $\mathrm{lb} / \mathrm{h}$ of this slurry is fed to a two-stage, continuous, countercurrent washing system to be washed with $20,000 \mathrm{lb} / \mathrm{h}$ of fresh water. The underflow from each thickener will contain $20 \mathrm{wt} \%$ solids. Determine the percent recovery of sodium hydroxide in the extract and wt $\%$ sodium hydroxide in the dried, calciumcarbonate product. Based on calculations, is it worthwhile to add a third stage?

James Irizarry

Numerade Educator

05:39

Problem 4

Zinc is to be recovered from an ore containing zinc sulfide. The ore is first roasted with oxygen to produce zinc oxide, which is then leached with aqueous sulfuric acid to produce water-soluble zinc sulfate and an insoluble, worthless residue called gangue. The decanted sludge of $20,000 \mathrm{~kg} / \mathrm{h}$ contains 5 wt $\%$ water, 10 wt 8 zinc sulfate, and the balance as gangue. This sludge is to be washed with water in a continuous, countercurrent washing system to produce an extract, called a strong solution, of $10 \mathrm{wt} \%$ zinc sulfate in water, with a $98 \%$ recovery of the zinc sulfate. Assume that the underflow from each washing stage contains, by weight, two parts of water (sulfate-free basis) per part of gangue. Determine the number of stages required.

Dylan Gunawardene

Numerade Educator

04:19

Problem 5

Fifty-thousand $\mathrm{kg} / \mathrm{h}$ of flaked soybeans, containing $20 \mathrm{wt} \%$ oil, is to be leached of the oil with the same flow rate of $n$-hexane in a countercurrent-flow system consisting of an ideal leaching stage and three ideal washing stages. Experiments show that the underflow from each stage will contain $0.8 \mathrm{~kg}$ liquid/ $/ \mathrm{kg}$ soybeans (oil-free basis).
(a) Determine the $\%$ recovery of oil in the final extract.
(b) If leaching requires three of the four stages, such that one-third of the leaching occurs in each of these three stages, followed by just one true washing stage, determine the $\%$ recovery of oil in the final extract.

Lottie Adams

Numerade Educator

03:13

Problem 6

One hundred tons per hour of a feed containing $20 \mathrm{wt} \%$ $\mathrm{Na}_{2} \mathrm{CO}_{3}$ and the balance insoluble solids is to be leached and washed with water in a continuous, countercurrent system. Assume that leaching will be completed in one ideal stage. It is desired to obtain a final extract containing 15 wt\% solute, with a $98 \%$ recovery of solute. The underflow from each stage will contain $0.5 \mathrm{lb}$ solution/lb insoluble solids. Determine the number of ideal washing stages required.

Lottie Adams

Numerade Educator

03:11

Problem 7

Titanium dioxide, which is the most common white pigment in paint, can be produced from the titanium mineral, rutile, by chlorination to $\mathrm{TiCl}_4$, followed by oxidation to $\mathrm{TiO}_2$. To purify the insoluble titanium dioxide, it is washed free of soluble impurities in a continuous, countercurrent system of thickeners with water. Two hundred thousand $\mathrm{kg} / \mathrm{h}$ of $99.9 \mathrm{wt} \%$ titanium dioxide pigment is to be produced by washing, followed by filtering and drying. The feed contains $50 \mathrm{wt} \% \mathrm{TiO}_2, 20 \mathrm{wt} \%$ soluble salts, and $30 \mathrm{wt} \%$ water. The wash liquid is pure water at a flow rate equal to that of the feed on a mass-flow basis.
(a) Determine the number of washing stages required if the underflow from each stage is 0.4 kg solution $/ \mathrm{kg} \mathrm{TiO}_2$.
(b) Determine the number of washing stages required if the underflow is variable as follows:
$$
\begin{array}{cc}
\begin{array}{c}
\text { Concentration of solute, } \\
\mathrm{kg} / \text { solute } / \mathrm{kg} \text { solution }
\end{array} & \begin{array}{c}
\text { Retention of solution, } \\
\mathrm{kg} \text { solution } / \mathrm{kg} \mathrm{TiO}_2
\end{array} \\
0.0 & 0.30 \\
0.2 & 0.34 \\
0.4 & 0.38 \\
0.6 & 0.42
\end{array}
$$

Madi Sousa

Numerade Educator

06:29

Problem 8

Derive (16-20), assuming that $\left(Y_{i}\right)_{b}, k_{c}, m$, and $a$ are constants and that $\left(X_{i}\right)_{o}$ is uniform through the solid.

Chris Trentman

Numerade Educator

06:29

Problem 8

Derive (16-20), assuming that $\left(Y_{i}\right)_{b}, k_{c}, m$, and $a$ are constants and that $\left(X_{i}\right)_{o}$ is uniform through the solid.

Chris Trentman

Numerade Educator

00:27

Problem 9

Derive (16-24).

Sneha Ravi

Numerade Educator

01:07

Problem 10

Data of Othmer and Agarwal [1] for the batch extraction of oil from soybeans by oil-free $n$-hexane at $80^{\circ} \mathrm{F}$ are as follows:
$\begin{array}{cc}\text { Time, min } & \begin{array}{c}\text { Oil content of Soybeans, } \\ \text { g/g Dry, Oil-free Soybeans }\end{array} \\ 0 & 0.203 \\ 0.5 & 0.1559 \\ 1 & 0.1359 \\ 2 & 0.1190 \\ 4 & 0.0981 \\ 7 & 0.0775 \\ 12 & 0.0591 \\ 20 & 0.04197 \\ 35 & 0.03055 \\ 60 & 0.02388 \\ 120 & 0.02107\end{array}$
Determine whether these data are consistent with a constant effective diffusivity of oil in soybeans.

Shu Naito

Numerade Educator

03:35

Problem 11

Estimate the molecular diffusivity of sucrose in water at infinite dilution at $80^{\circ} \mathrm{C}$, noting that the value is $0.54 \times 10^{-5} \mathrm{~cm}^{2} / \mathrm{s}$ at $25^{\circ} \mathrm{C}$. Give reasons for the difference between the value you obtain and the value for effective diffusivity in Example 16.6.

Eugene Schneider

University of Minnesota - Twin Cities

06:46

Problem 12

The sucrose in ground coffee particles of an average diameter of $2 \mathrm{~mm}$ is to be extracted with water in a continuous, countercurrent extractor at $25^{\circ} \mathrm{C}$. The diffusivity of the sucrose in the particles has been determined to be about $1.0 \times 10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$. Estimate the time in minutes to leach $95 \%$ of the sucrose. For a sphere, with $N_{\mathrm{FO}_{\mathrm{M}}}>0.10$,
$$
E_{\mathrm{ave}}=\frac{6}{\pi^{2}} \exp \left(\frac{-\pi^{2} D_{e} t}{a^{2}}\right)
$$

Bobby Barnes

University of North Texas

07:03

Problem 13

For the conditions of Example 16.8, determine the effect on leaching time of particle size over the range of $0.5 \mathrm{~mm}$ to $50 \mathrm{~mm}$.

Chareen Guzman

Numerade Educator

01:10

Problem 14

For the conditions of Example 16.8, determine the effect of $\%$ recovery of copper over the range of $50-100 \%$.

John Nicolle

Numerade Educator

01:50

Problem 15

Repeat Example 16.8, except that the ore contains 3 wt\% $\mathrm{Cu}_{2} \mathrm{O}$.

Morgan Cheatham

Numerade Educator

02:02

Problem 16

For the shrinking-core model, if the rate of leaching is controlled by an interface chemical reaction that is first order in the concentration of reactant $A$, derive the expression,
$$
t=\frac{\mathrm{p}_{\mathrm{B}} r_{s}}{b M_{\mathrm{B}} k C_{\mathrm{A}_{s}}}\left(1-\frac{r_{c}}{r_{s}}\right)
$$
where $\mathrm{k}=$ first-order rate constant.

Veer Yadav

Numerade Educator