Calcium Phosphate Production Stoichiometry Calculation
#h1 Calcium phosphate, a crucial mineral for bones and teeth, can be synthesized through a chemical reaction involving sodium phosphate and calcium chloride. In this comprehensive article, we will delve into the stoichiometry of this reaction, focusing on calculating the amount of calcium phosphate produced from a given quantity of calcium chloride. Our scenario involves 379.4 grams of calcium chloride reacting with an excess of sodium phosphate. We will leverage the principles of stoichiometry, molar masses, and the balanced chemical equation to determine the theoretical yield of calcium phosphate.
Understanding the Reaction
The reaction between sodium phosphate (Na₃PO₄) and calcium chloride (CaCl₂) results in the formation of sodium chloride (NaCl) and calcium phosphate (Ca₃(PO₄)₂). The balanced chemical equation for this reaction is:
3 CaCl₂ (aq) + 2 Na₃PO₄ (aq) → 6 NaCl (aq) + Ca₃(PO₄)₂ (s)
This equation tells us that 3 moles of calcium chloride react with 2 moles of sodium phosphate to produce 6 moles of sodium chloride and 1 mole of calcium phosphate. This mole ratio is the key to our stoichiometric calculations.
Molar Masses: The Bridge Between Grams and Moles
To convert between grams and moles, we need the molar masses of the compounds involved. Using the periodic table, we can calculate these:
- Calcium chloride (CaClâ‚‚): 40.08 (Ca) + 2 * 35.45 (Cl) = 110.98 g/mol
- Calcium phosphate (Ca₃(PO₄)₂): 3 * 40.08 (Ca) + 2 * (30.97 (P) + 4 * 16.00 (O)) = 310.18 g/mol
These molar masses will serve as conversion factors in our calculations.
Step-by-Step Calculation
Now, let's break down the calculation into manageable steps:
1. Convert Grams of Calcium Chloride to Moles
We are given 379.4 grams of calcium chloride. To convert this to moles, we divide by the molar mass of CaClâ‚‚:
Moles of CaClâ‚‚ = 379.4 g / 110.98 g/mol = 3.42 mol
2. Use the Mole Ratio to Find Moles of Calcium Phosphate
From the balanced equation, we know that 3 moles of CaCl₂ produce 1 mole of Ca₃(PO₄)₂. We use this ratio to find the moles of calcium phosphate produced:
Moles of Ca₃(PO₄)₂ = 3.42 mol CaCl₂ * (1 mol Ca₃(PO₄)₂ / 3 mol CaCl₂) = 1.14 mol
3. Convert Moles of Calcium Phosphate to Grams
Finally, we convert moles of Ca₃(PO₄)₂ to grams by multiplying by its molar mass:
Grams of Ca₃(PO₄)₂ = 1.14 mol * 310.18 g/mol = 353.6 g
Therefore, 379.4 grams of calcium chloride can theoretically produce 353.6 grams of calcium phosphate when reacted with an excess of sodium phosphate. This calculation exemplifies the power of stoichiometry in predicting the outcome of chemical reactions.
Excess Reactant: Ensuring Complete Reaction
The Role of Excess Reactant
In this scenario, sodium phosphate is present in excess. This means that there is more than enough sodium phosphate to react completely with all of the calcium chloride. By ensuring an excess of one reactant, we guarantee that the limiting reactant, in this case, calcium chloride, will be fully consumed. This maximizes the yield of the desired product, calcium phosphate.
Why Use Excess?
Using an excess reactant is a common technique in chemistry for several reasons:
- Complete Reaction: It drives the reaction to completion, ensuring that the limiting reactant is fully used up.
- Maximizing Product Yield: By fully consuming the limiting reactant, we obtain the maximum possible amount of product.
- Simplifying Calculations: It allows us to base our calculations solely on the limiting reactant, as its quantity dictates the amount of product formed.
In our calculation, the excess sodium phosphate ensures that all 379.4 grams of calcium chloride react, leading to the formation of the calculated 353.6 grams of calcium phosphate. Without an excess of sodium phosphate, the reaction might not proceed to completion, and the yield of calcium phosphate would be lower.
Theoretical Yield vs. Actual Yield
Theoretical Yield
The 353.6 grams of calcium phosphate we calculated represents the theoretical yield. This is the maximum amount of product that can be formed based on the stoichiometry of the reaction and the amount of limiting reactant used. It assumes ideal conditions and a perfect reaction with no losses.
Actual Yield
In reality, the amount of product obtained in a chemical reaction, the actual yield, is often less than the theoretical yield. This difference can arise from several factors:
- Incomplete Reactions: Some reactions may not proceed to completion, even with an excess of one reactant.
- Side Reactions: Other reactions may occur simultaneously, consuming reactants and forming unwanted byproducts.
- Losses During Transfer and Purification: Some product may be lost during the transfer of materials between containers or during purification steps.
Percent Yield
The percent yield is a measure of the efficiency of a reaction. It is calculated as:
Percent Yield = (Actual Yield / Theoretical Yield) * 100%
For example, if the actual yield of calcium phosphate in our reaction was 300 grams, the percent yield would be:
Percent Yield = (300 g / 353.6 g) * 100% = 84.8%
A high percent yield indicates an efficient reaction with minimal losses, while a low percent yield suggests that the reaction was less efficient, and significant product losses occurred.
Applications of Calcium Phosphate
Biological Significance
Calcium phosphate is a vital mineral in biological systems, primarily as the main component of bones and teeth. It provides rigidity and strength to the skeletal structure. The specific form of calcium phosphate in bones is a complex mineral called hydroxyapatite (Ca₅(PO₄)₃(OH)).
Medical Applications
Due to its biocompatibility and osteoconductive properties, calcium phosphate is widely used in various medical applications, including:
- Bone Grafts: Calcium phosphate ceramics are used as bone graft substitutes to repair bone defects and promote bone regeneration.
- Dental Implants: Coatings of calcium phosphate on dental implants enhance osseointegration, the process by which the implant integrates with the surrounding bone.
- Drug Delivery: Calcium phosphate nanoparticles can be used as carriers for drug delivery, targeting specific tissues or cells.
Industrial Applications
Calcium phosphate also has several industrial applications, including:
- Fertilizers: It is a source of phosphorus, an essential nutrient for plant growth, and is used in the production of fertilizers.
- Animal Feed: It is added to animal feed as a source of calcium and phosphorus, promoting healthy bone development.
- Food Additives: It is used as a food additive in some processed foods as a source of calcium and to improve texture.
Conclusion
In conclusion, we have successfully calculated the theoretical yield of calcium phosphate produced from the reaction of 379.4 grams of calcium chloride with excess sodium phosphate. By applying the principles of stoichiometry, molar masses, and the balanced chemical equation, we determined that 353.6 grams of calcium phosphate can be formed. We also discussed the importance of excess reactants, the difference between theoretical and actual yields, and the diverse applications of calcium phosphate in biology, medicine, and industry. This detailed analysis highlights the significance of stoichiometry in understanding and predicting chemical reactions and their outcomes. Understanding these concepts is crucial for success in chemistry and related fields. Remember to always double-check your calculations and consider the practical implications of your results. Accurate stoichiometric calculations are essential for optimizing chemical processes and ensuring efficient use of resources.
