Question

About 50% of urinary calculi (kidney stones) consist of calcium phosphate, Ca₃(PO₄)₂. The normal mid-range calcium content excreted in the urine is 0.10 g of Ca²⁺ per day. The normal mid-range amount of urine passed may be taken as 1.4 L per day. What is the maximum concentration of phosphate ion that urine can contain before a calculus begins to form?

a) 0.05 g/L

b) 0.10 g/L

c) 0.15 g/L

d) 0.20 g/L

Answer 1

The maximum concentration of phosphate ions in urine that can be tolerated before kidney stone formation can be determined by using the daily excretion of calcium, the volume of urine, and the Ksp of calcium phosphate. The calculations involve converting the daily excreted calcium into molarity and then using stoichiometry to find the phosphate concentration.

Step-by-step explanation:

To determine the maximum concentration of phosphate ion that urine can contain before kidney stones form, we need to consider the solubility product constant (Ksp) of calcium phosphate, Ca3(PO4)2. Given that the daily excretion of calcium is 0.10g of Ca2+, we can calculate the molarity of Ca2+ in the urine and then use the stoichiometry of the dissolution reaction of calcium phosphate to find the maximum concentration of phosphate ions.

The molarity of Ca2+ is found by converting grams to moles and dividing by the volume of urine excreted daily (1.4L). Since calcium phosphate dissolution involves 3 moles of Ca2+ for every 2 moles of PO43-, we can calculate the concentration of PO43- using mole ratios. After performing the calculations (which would require the Ksp value), we can determine which of the given options (a, b, c, or d) matches the calculated PO43- concentration before calcium phosphate precipitates form.