Question

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 240 ml of a saturated barium sulfate solution, how much toxic ba2 ion has the patient consumed? the solubility product ksp of baso4 is 1.10×10−10.

Answer 1

To calculate the toxic Ba2+ ion ingested with a barium sulfate solution for medical imaging, use the Ksp of BaSO4 (1.10×10−10) to find the saturated concentration of Ba2+. Multiply by the volume ingested and convert moles to grams using the molar mass.

Step-by-step explanation:

The question presents a scenario in which a patient ingests 240 ml of a saturated barium sulfate solution, known as a "barium milkshake", for medical imaging of the gastrointestinal tract. To calculate how much toxic Ba2+ ion the patient has consumed, we need to use the provided Ksp of BaSO4 (1.10×10−10).

Firstly, we know the solubility product constant (Ksp) gives us the product of the concentrations of the ions at saturation, i.e., Ksp = [Ba2+][SO42−]. Since BaSO4 dissociates into one Ba2+ and one SO42−, their concentrations at saturation will be equal.

Thus, we can set up the equilibrium expression for the solubility product and solve for the Ba2+ concentration:Ksp = [Ba2+][SO42−] = x² → x = √(1.10×10−10)

Now, to find the amount of Ba2+, we multiply its molar solubility by the volume of the solution ingested (noting that 240 mL is 0.24 L), and then convert the moles to grams using the molar mass of Ba2+ (approximately 137.33 g/mol).

Moles of Ba2+ ingested = x * volume in liters = √(1.10×10−10) * 0.24 L.

After calculating the moles of Ba2+, we can determine the mass ingested using molar mass:

Mass (g) = moles of Ba2+ * molar mass of Ba2+.