24. Barium ene ma is a diagnostic medical procedure in which the inside of the l

Question

24. Barium ene ma is a diagnostic medical procedure in which the inside of the large intestine is coated with an aqueous slurry of insoluble BaSO, and imaged using X-ray. If you're a chemist, this probably rings all sorts of alarm bells because Ba is a heavy metal that's absorbed throughout the gastrointestinal tract and levels in drinking water as low as 10 mg/L (about 7 x 10-5 M) have been shown to result in an elevated risk of heart attack and stroke. If you ask the medical folks theyll say "Oh, that's not a problem because BaSO, is completely insoluble in water." Of course you know that's questionable because your Quantitative Chemistry textbook lists a solubility product for BaSO, so there's got to be a litle Ba* in that solution. a. So what is the molar concentration of Ba? in a saturated solution of BaSO, in deionized water? b. Of course they don't make this slurry in deionized water. They make it up in a saline solution that contains 0.137 M NaCI, 0.0027 M KCI, 0.0809 M Na,HPO, (which dissociates into Na* and HPO,2 ions) and 0.0176 M KH2PO4 (which dissociates into k and H2PO, ions). Assuming that no acid-base shenanigans take place, what's the ionic strength of this solution, ignoring the contributions of Ba2* and SO,2 that'll be present? c. What's the molar concentration of Ba2 in that slurry realy? d. In calculating the ionic strength in 024b we assumed that the Ba?* and the SO,2 didn't contribute significantly. Is that a reasonable assumption?

Explanation / Answer

a)

[Ba+2] = mol of Ba+2 / V

Ksp = [Ba+2][SO4-2]

Ksp fo BaSO4 =1.1*10^-10

then assume, in equilibrium

[Ba+2] = [SO4-2] = S

then Ksp = (S)(S)

1.1*10^-10 = S^2

S = sqrt(1.1*10^-10)

= 0.00001048808 M

b.

ionic strength = moles in solution

NaCL = 2 ions

KCl = 2 ions

Na2HPO4 = 3 ions

KH2PO4 = 2 ions

Ionic strenght = 1/2(Sum of Ci*Zi^2)

NaCL = 2 ions --> (0.137)(1)^2 + (0.137)(-1)^2 = 0.274

KCl = 2 ions --> (0.0027)(1)^2 + (0.0027)(-1)^2 = 0.0054

Na2HPO4 = 3 ions --> (2*0.0809)(1)^2 + (0.0809)(-2)^2 = 0.4854

KH2PO4 = 2 ions --> (0.0176)(1)^2 + (0.0176)(-1)^2 = 0.0352

Total ionic strenrght = 1/2*(0.274+0.0054+0.4854+0.0352)

= 0.4

c.

Molar concentration of Ba+2

assume it is saturate, therefore [Ba+2] = [Ba+2]saturaiton = S = 0.00001048808

d.

It is reasonably, since their concnetrationsa re too low, the effect is mathematically neglegible

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