Pseudogout is a condition with symptoms similar to those of gout (joint swelling

Question

Pseudogout is a condition with symptoms similar to those of gout (joint swelling and pain) is caused by the formation of calcium diphosphate (Ca_2P_2O_7) crystals within tendons, cartilage, and ligaments. This can occur when diphosphate levels in the blood are too high, causing the calcium diphosphate to precipitate out. If the calcium concentration in blood plasma is typically 9.2 mg/dL, what minimum concentration of diphosphate will cause precipitation? The K_sp for calcium diphosphate is 8.64 Times 10^-13.

Explanation / Answer

Ca2+ concentration in blood plasma = 9.2 mg/dL = 0.092 g/L = 0.00092 M

Ca2P2O7(s) <-----------> 2Ca2+(aq) + P2O72-(aq)

Ksp = [Ca2+]2*[P2O72-]

or, 8.64*10-13 = (2x+0.00092)2*x

or, 8.64*10-13 = (4x2 + 8.464*10-7 + 3.68*10-3x)x

or, 4x3 + 3.68*10-3x2 + 8.464*10-7x - 8.64*10-13 = 0

or, x = 1.02*10-6 M = solubility of diphosphate

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