Passage
Kidney stones are a common ailment affecting approximately 10% of adults in the United States. They form when solutes precipitate out of solution as crystals in the urinary tract, and they can cause severe pain in the side, back, abdomen, and groin. Individuals who have been previously diagnosed with kidney stones have an increased probability of developing new stones relative to unaffected individuals. Different measures may help prevent the formation of different kinds of stones, so analysis of the composition of stones that have been passed or removed can aid in preventing recurrence. Stones can be ground into fine powders, dissolved in a small amount of solvent, and analyzed by infrared (IR) spectroscopy, as shown in Figure 1.
Figure 1 Schematic of kidney stone analysis by IR spectroscopyIR analysis of kidney stones from 50 individuals revealed the percentage of stones that contain each component, shown in Table 1 along with solubility data.Table 1 Kidney Stone Composition Parameters
Some studies indicate that potassium citrate, taken orally, may prevent the formation of calcium oxalate crystals, the most abundant component of kidney stones. Oxalic acid, shown in Figure 2, is significantly more soluble than calcium oxalate.
Figure 2 Structure of oxalic acid and its associated anions with increasing pHPotassium citrate alkalinizes the urine, potentially causing a decrease in oxalate solubility and the formation of more crystals. However, potassium citrate can also react with calcium oxalate according to the unbalanced equation shown in Reaction 1:CaC₂O₄ + K₃(C₆H₅O₇) → Ca₃(C₆H₅O₇) ₂ + K₂C₂O₄Reaction 1Calcium citrate and potassium oxalate are both hundreds of times more soluble than calcium oxalate, so the presence of citrate and potassium ions can help maintain calcium and oxalate ions in solution. This effect may be sufficient to overcome the decreased solubility that occurs at higher pH levels.
Adapted from Primiano A, Persichilli S, Gambaro G, et al. FT-IR analysis of urinary stones: a helpful tool for clinician comparison with the chemical spot test. Dis Markers. 2014;2014:176165.
-Given the unbalanced equation (Reaction 1) and the molecular weight of calcium citrate (498.5 g/mol) , if 15 nmol of calcium oxalate is mixed with 15 nmol of potassium citrate, what is the approximate theoretical yield of calcium citrate?

Question

Passage
Kidney stones are a common ailment affecting approximately 10% of adults in the United States. They form when solutes precipitate out of solution as crystals in the urinary tract, and they can cause severe pain in the side, back, abdomen, and groin. Individuals who have been previously diagnosed with kidney stones have an increased probability of developing new stones relative to unaffected individuals. Different measures may help prevent the formation of different kinds of stones, so analysis of the composition of stones that have been passed or removed can aid in preventing recurrence. Stones can be ground into fine powders, dissolved in a small amount of solvent, and analyzed by infrared (IR) spectroscopy, as shown in Figure 1.

Figure 1 Schematic of kidney stone analysis by IR spectroscopyIR analysis of kidney stones from 50 individuals revealed the percentage of stones that contain each component, shown in Table 1 along with solubility data.Table 1 Kidney Stone Composition Parameters

Some studies indicate that potassium citrate, taken orally, may prevent the formation of calcium oxalate crystals, the most abundant component of kidney stones. Oxalic acid, shown in Figure 2, is significantly more soluble than calcium oxalate.

Figure 2 Structure of oxalic acid and its associated anions with increasing pHPotassium citrate alkalinizes the urine, potentially causing a decrease in oxalate solubility and the formation of more crystals. However, potassium citrate can also react with calcium oxalate according to the unbalanced equation shown in Reaction 1:CaC₂O₄ + K₃(C₆H₅O₇) → Ca₃(C₆H₅O₇) ₂ + K₂C₂O₄Reaction 1Calcium citrate and potassium oxalate are both hundreds of times more soluble than calcium oxalate, so the presence of citrate and potassium ions can help maintain calcium and oxalate ions in solution. This effect may be sufficient to overcome the decreased solubility that occurs at higher pH levels.
Adapted from Primiano A, Persichilli S, Gambaro G, et al. FT-IR analysis of urinary stones: a helpful tool for clinician comparison with the chemical spot test. Dis Markers. 2014;2014:176165.
-Given the unbalanced equation (Reaction 1) and the molecular weight of calcium citrate (498.5 g/mol) , if 15 nmol of calcium oxalate is mixed with 15 nmol of potassium citrate, what is the approximate theoretical yield of calcium citrate?

Quizplus · Accepted Answer

11ecba2d_11bb_12d5_a3bf_91a70f6e6a7c_MD0008_00 Theoretical yield is the maximum amount of product that can form during a reaction based on the limiting reactant, which is the reactant that will be entirely consumed if the reaction goes to completion. The limiting reactant can be determined from the balanced chemical equation and the number of moles of each reactant. The passage gives the unbalanced equation for the reaction between calcium oxalate and potassium citrate. The equation must be balanced to determine the limiting reactant. The balanced equation is: 3 CaC₂O₄ + 2 K₃C₆H₅O₇ → Ca₃(C₆H₅O₇)₂ + 3 K₂C₂O₄ The equation shows that the formation of 1 mole of calcium citrate requires 3 moles of calcium oxalate but only 2 moles of potassium citrate. The question states that 15 nmol of each reactant were mixed together. As such, a quantity of 15 nmol of calcium oxalate can form 5 nmol of calcium citrate: 11ecba2d_11bb_12d6_a3bf_7b25dec6267b_MD0008_00 However, 15 nmol of potassium citrate can produce 7.5 nmol of calcium citrate: 11ecba2d_11bb_12d7_a3bf_93060db45925_MD0008_00 The limiting reactant is the one that yields the least product. In this case, calcium oxalate is the limiting reactant. The amount of calcium citrate possible from the reaction can be calculated by converting nmol to ng using the molecular weight of calcium citrate (≈ 500 g/mol) evaluated on the nanoscale: 11ecba2d_11bb_39e8_a3bf_a529fdb51e83_MD0008_00 Therefore, the theoretical yield is 2,500 ng of calcium citrate. (Choice A) This value is half of the correct answer. Concentration, not total number of moles, must be divided by 2 when equal volumes of different solutions are mixed. (Choice C) If calcium oxalate was in excess, potassium citrate would be the limiting reactant, and 7.5 nmol or 3,750 ng of calcium citrate would be the theoretical yield. (Choice D) Using a 1:1 molar ratiofor the reactants and products (from the unbalanced reaction) incorrectly determines that 15 nmol of each reactant would produce 15 nmol of calcium citrate with a mass of 7,500 ng. However, the reaction must be balanced to achieve the correct molar ratios. Educational objective: Theoretical yield is the maximum amount of product that can be formed in a reaction. It is governed by the limiting reactant, which is determined by the balanced equation and the molar amounts of each reactant available.

Passage Kidney Stones Are a Common Ailment Affecting Approximately 10% of of Adults