Pseudogout, a condition with symptoms similar to those of gout (see Problem 126), is caused by the formation of calcium diphosphate (Ca₂P₂O₇) crystals within tendons, cartilage, and ligaments. Calcium diphosphate will precipitate out of blood plasma when diphosphate levels become abnormally high. If the calcium concentration in blood plasma is 9.2 mg/dL, and K_sp for calcium diphosphate is 8.64 * 10^-13, what minimum concentration of diphosphate results in precipitation?

Problem 126

Gout—a condition that results in joint swelling and pain—is caused by the formation of sodium urate (NaC₅H₃N₄O₃) crystals within tendons, cartilage, and ligaments. Sodium urate precipitates out of blood plasma when uric acid levels become abnormally high. This sometimes happens as a result of eating too many rich foods and consuming too much alcohol, which is why gout is sometimes referred to as the “disease of kings.” If the sodium concentration in blood plasma is 0.140 M, and K_sp for sodium urate is 5.76 * 10^-8, what minimum concentration of urate would result in precipitation?