Gout-a condition that results in joint swelling and pain-is caused by the
formation of sodium urate \(\left(\mathrm{NaC}_{5} \mathrm{H}_{3}
\mathrm{~N}_{4} \mathrm{O}_{3}\right)\) 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 \(0.140 \mathrm{M},\) and \(K_{\mathrm{sp}}\) for sodium urate is \(5.76
\times 10^{-8}\), what minimum concentration
of urate would result in precipitation?