Barium sulfate,BaSO4 , is used in medical imaging of the gastrointestinal tract because it is opaque to X rays. A bariu...

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Barium sulfate,BaSO4 , is used in medical imaging of the gastrointestinal tract because it is opaque to X rays. A bariu...

Barium sulfate,BaSO4 , is used in medical imaging of the gastrointestinal tract because it is opaque to X rays. A barium sulfate solution, sometimes called a cocktail, is ingested by the patient, whose stomach and intestines can then be visualized via X-ray imaging. If a patient ingests 400 mL of a saturated barium sulfate solution, how much toxic Ba2+ ion has the patient consumed?
The solubility product Ksp of BaSO4 is 1.1*10^-10 .

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Answer 1

Answer #1

Concepts and reason

The concept used in this question is based on the solubility product, the molarity of a substance, and moles of a substance.

Initially, the molar concentration of barium ion is determined by using the expression of the solubility product. Then, the moles of barium ions consumed by the patient is calculated by using the formula of molarity of a solution. Lastly, the mass of barium ion consumed by the patient is determined by using the expression of moles of a substance.

Fundamentals

The solubility product of any salt can be expressed as the product of the concentration of the ions of product that are formed in the solution raised to the power of their stoichiometric coefficients.

For example, consider a salt AX. Its dissociation can be expressed by the following equation.

AX(s) =
A(aq) + X (aq)

The solubility product at the equilibrium of the above reaction can be given as shown below.

[-x][_v]= y …… (1)

Here, the solubility product is K_sp, the concentration of the products so formed are and .

The molarity of a substance can be expressed as follows.

Moles of a substance
Molarity =
Volume (L) …… (2)

The SI unit of molarity is molar (M) or mole per liter.

The moles of a substance can be expressed by using the following expression.

Mass
Moles of substance =
Molar mass …… (3)

The dissociation of barium sulfate in aqueous solution is shown as follows.

BaSO,(s) = Ba²+ (aq) + soz (aq)

So, the solubility product of the above reaction can be expressed as follows.

[os][ -zea] = y

Substitute the given value of K., =1.1x10-10 in the above expression.

1.1x10-1° = [Ba?* ][80]
1.1x10-5° = [Ba?)
[Ba’* ] = V1.1x10-10
[Ba²+] =1.05x10-S M

Therefore, the molar concentration of the barium ion is 1.05x10 M .

Substitute the volume of solution as 400 ml and the molarity of barium ion as in equation (2) to obtain the moles of barium ion.

$1.05x10-5 M - Moles of Ba2+ 1000 ml 400 mL * {IL=1000 mL} 2+ _1.05x10 mol/Lx 400 mLx1L 1000 ml Moles of Ba2+ = 4.2x10 mol$

The mass of barium ion consumed by the patient is therefore calculated by substituting the above-calculated moles of barium ions in equation (3). The molar mass of barium ion is 137.33 g/mol .

4.2x10mol = Mass of Ba2+
137.33 g/mol
Mass of Ba2+ = 4.2x10 molx137.33 g/mol
Mass of Ba2+ = 5.8x104 g

Therefore, the mass of barium ion consumed by the patient is 5.8x10 g .

Ans:

The mass of toxic barium ion consumed by the patient is .

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Barium sulfate,BaSO4 , is used in medical imaging of the gastrointestinal tract because it is opaque to X rays. A bariu...

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