Your company is interested in purchasing a small company that produces barium that they sell to superconductor and electroceramic manufacturers. They have asked you to do some lab scale batch-washing experiments with barium sulfide \((\mathrm{BaS})\).

a. First, you obtain some dry solids from the BaS plant that has all of the \(\mathrm{BaS}\) removed, put the solids in a graduated cylinder, and gently shake the cylinder until the solids have settled. You measure \(80.6 \mathrm{ml}\) of dry solids, which you then put in a large beaker, add \(200.0 \mathrm{ml}\) of distilled water, let the mixture settle completely, and siphon off the extra water, which is \(169 \mathrm{ml}\). You repeat the experiment twice more, starting with a new charge of \(91.5 \mathrm{ml}\) dry solids and \(85.2 \mathrm{ml}\) dry solids, adding \(200 \mathrm{ml}\) water each time, and collect 164.3 and \(166.4 \mathrm{ml}\) of siphoned water respectively. What is the average value of Uvol \(\mathrm{ml}\) water/ \(\mathrm{ml}\) dry solids? What is the average value of \(\varepsilon\) ?

Before continuing, check answer to part a in Answers (immediately before index).

b. You now make an aqueous solution of \(\mathrm{BaS}\) that is \(0.20 \mathrm{~g} / \mathrm{ml} \mathrm{BaS}\) with a total volume of \(125 \mathrm{ml}\). You add \(225 \mathrm{ml}\) of dry inert solids to this solution in a large beaker and stir. You add \(75 \mathrm{ml}\) of wash water, stir, settle the solids with gentle shaking, and siphon off the water. How much water is siphoned off, and what is its concentration?

c. You now do a second step: you add \(75 \mathrm{ml}\) of wash water, stir, settle the solids with gentle shaking, and siphon off the water. How much water is siphoned off, and what is its concentration?

d. You compare results with the company running the continuous plant (see Problem 14.D14) and find your \(\varepsilon\) is much smaller than they observe in the continuous plant. Why does this occur?+

Problem 14.D4

Wash alumina solids to remove \(\mathrm{NaOH}\) from the entrained liquid. Underflow from the settler tank is \(20.0 \mathrm{vol} \%\) solid and \(80.0 \mathrm{vol} \%\) liquid. Two feeds to the system are also \(20.0 \mathrm{vol} \%\) solids. In one of these feeds, the \(\mathrm{NaOH}\) concentration in the liquid is \(5.0 \mathrm{wt} \%\). This feed's solid flow rate (on a dry basis) is \(1000.0 \mathrm{~kg} / \mathrm{h}\). The second feed has a \(\mathrm{NaOH}\) concentration in the liquid of \(2.0 \mathrm{wt} \%\), and its solids flow rate (on a dry basis) is 2000.0 \(\mathrm{kg} / \mathrm{h}\). We desire the final \(\mathrm{NaOH}\) concentration in underflow liquid to be 0.6 \(\mathrm{wt} \% \mathrm{NaOH}\). A countercurrent operation is used. Inlet washing water is pure and flows at \(4000.0 \mathrm{~kg} / \mathrm{h}\). Find the optimum feed location for the intermediate feed and the number of equilibrium stages required.

D4. ata: \(ho_{\mathrm{w}}=1.0 \mathrm{~kg} /\) liter (constant), \(ho_{\text {alumina }}=2.5 \mathrm{~kg} /\) liter (dry crushed).