Calculate Mass Of 4.50 Moles Of Calcium Phosphate $Ca_3(PO_4)_2$

Introduction

In chemistry, stoichiometry plays a vital role in understanding the quantitative relationships between reactants and products in chemical reactions. One of the fundamental concepts in stoichiometry is the mole, which is the SI unit for the amount of substance. The mole allows us to relate the number of particles (atoms, molecules, ions, etc.) to the mass of a substance. This article focuses on how to calculate the mass of a given number of moles of a compound, specifically 4.50 moles of calcium phosphate ($Ca_3(PO_4)_2$). This calculation is crucial in various chemical applications, including preparing solutions, conducting experiments, and understanding chemical reactions. Understanding these calculations is fundamental to grasp more advanced concepts in chemistry.

Understanding Moles and Molar Mass

The mole is defined as the amount of a substance that contains as many entities (atoms, molecules, ions, or other particles) as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number, approximately $6.022 imes 10^{23}$ entities per mole. The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). The molar mass is numerically equivalent to the atomic or molecular weight of the substance, which can be found on the periodic table or calculated from the chemical formula. For instance, the molar mass of an element is the atomic weight listed on the periodic table, while the molar mass of a compound is the sum of the atomic weights of all the atoms in the compound's formula.

Calculating Molar Mass of Calcium Phosphate ($Ca_3(PO_4)_2$)

To determine the mass of 4.50 moles of calcium phosphate, the first step is to calculate the molar mass of $Ca_3(PO_4)_2$. Calcium phosphate is an ionic compound composed of calcium cations ($Ca^{2+}$) and phosphate anions ($PO_4^{3-}$). The chemical formula indicates that each molecule of calcium phosphate contains three calcium atoms, two phosphorus atoms, and eight oxygen atoms. To calculate the molar mass, we need the atomic masses of each element from the periodic table:

• Calcium (Ca): 40.08 g/mol
• Phosphorus (P): 30.97 g/mol
• Oxygen (O): 16.00 g/mol

The molar mass of $Ca_3(PO_4)_2$ is calculated as follows:

$(3 imes ext{Molar mass of Ca}) + (2 imes ext{Molar mass of P}) + (8 imes ext{Molar mass of O})$

$(3 imes 40.08 ext{ g/mol}) + (2 imes 30.97 ext{ g/mol}) + (8 imes 16.00 ext{ g/mol})$

$120.24 ext{ g/mol} + 61.94 ext{ g/mol} + 128.00 ext{ g/mol} = 310.18 ext{ g/mol}$

Therefore, the molar mass of calcium phosphate ($Ca_3(PO_4)_2$) is 310.18 g/mol. This value is essential for converting moles to grams.

Step-by-Step Calculation

Now that we have the molar mass of calcium phosphate, we can calculate the mass of 4.50 moles of the compound. The formula to convert moles to mass is:

$$ext{Mass} = ext{Number of moles} imes ext{Molar mass}$$

Given:

• Number of moles of $Ca_3(PO_4)_2$ = 4.50 moles
• Molar mass of $Ca_3(PO_4)_2$ = 310.18 g/mol

Plugging in the values:

$$ext{Mass} = 4.50 ext{ moles} imes 310.18 ext{ g/mol}$$

$$ext{Mass} = 1395.81 ext{ grams}$$

Therefore, the mass of 4.50 moles of calcium phosphate ($Ca_3(PO_4)_2$) is approximately 1395.81 grams. This result shows how the concept of molar mass and moles is applied to convert between the amount of a substance and its mass, a crucial skill in quantitative chemistry.

Practical Implications and Uses of Calcium Phosphate

Understanding how to calculate the mass of calcium phosphate from moles has practical implications in various fields. Calcium phosphate is a significant compound with numerous applications in different industries, including medicine, agriculture, and materials science. In the medical field, calcium phosphate is a primary component of bone and teeth, making it essential in bone grafts and dental implants. The ability to accurately calculate the mass of calcium phosphate is crucial for preparing these materials in the correct proportions, ensuring their effectiveness and biocompatibility. In agriculture, calcium phosphate is used as a fertilizer to provide plants with essential nutrients, particularly phosphorus, which is vital for plant growth and development. Determining the appropriate amount of calcium phosphate to use as fertilizer requires precise calculations to optimize plant health and yield.

In materials science, calcium phosphate is used in the production of bioceramics, which are materials designed for use in biological environments. These bioceramics are used in a variety of applications, including bone tissue engineering and drug delivery systems. The synthesis of these materials often requires precise control over the stoichiometry of the reactants, making the calculation of mass from moles indispensable. Furthermore, the accurate calculation of the mass of calcium phosphate is crucial in research settings where experiments require specific amounts of chemicals to ensure reproducible and reliable results. This ability to convert between moles and mass allows scientists and researchers to prepare solutions and conduct reactions with precision.

Example Problems and Practice

To reinforce your understanding of calculating mass from moles, let's work through a few example problems. These problems will help illustrate the application of the concept in different scenarios and provide practice for mastering these calculations. By solving various problems, you can build confidence in your ability to handle stoichiometric calculations and develop a deeper understanding of the relationships between moles, molar mass, and mass.

Example Problem 1

What is the mass of 2.75 moles of sodium chloride (NaCl)?

• Step 1: Find the molar mass of NaCl.

  • Molar mass of Na = 22.99 g/mol
  • Molar mass of Cl = 35.45 g/mol
  • Molar mass of NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol

• Step 2: Use the formula: Mass = Number of moles × Molar mass

  • Mass = 2.75 moles × 58.44 g/mol
  • Mass = 160.71 grams

Therefore, the mass of 2.75 moles of sodium chloride is 160.71 grams. This example demonstrates a straightforward application of the formula, using the molar mass of sodium chloride to convert moles to mass. Sodium chloride, commonly known as table salt, is a fundamental compound in chemistry and everyday life, making this calculation relevant and practical.

Example Problem 2

Calculate the mass of 1.50 moles of sulfuric acid ($H_2SO_4$).

• Step 1: Find the molar mass of $H_2SO_4$.

  • Molar mass of H = 1.01 g/mol
  • Molar mass of S = 32.07 g/mol
  • Molar mass of O = 16.00 g/mol
  • Molar mass of $H_2SO_4$ = $(2 imes 1.01 ext{ g/mol}) + (1 imes 32.07 ext{ g/mol}) + (4 imes 16.00 ext{ g/mol})$
  • Molar mass of $H_2SO_4$ = 2.02 g/mol + 32.07 g/mol + 64.00 g/mol = 98.09 g/mol

• Step 2: Use the formula: Mass = Number of moles × Molar mass

  • Mass = 1.50 moles × 98.09 g/mol
  • Mass = 147.14 grams

Thus, the mass of 1.50 moles of sulfuric acid is 147.14 grams. This example involves a slightly more complex compound, sulfuric acid, which requires careful calculation of the molar mass by considering the number of atoms of each element. Sulfuric acid is a widely used chemical in various industrial processes, making this calculation highly relevant in industrial chemistry.

Practice Problems

To further enhance your skills, try solving these practice problems:

1. What is the mass of 3.25 moles of water ($H_2O$)?
2. Calculate the mass of 0.75 moles of glucose ($C_6H_{12}O_6$).
3. Determine the mass of 2.00 moles of potassium permanganate ($KMnO_4$).

Working through these problems will solidify your understanding of converting moles to mass and improve your problem-solving abilities in stoichiometry. Practice is essential for mastering these concepts and being able to apply them effectively in various chemical calculations. By regularly practicing such calculations, one can develop a strong foundation in stoichiometry, a crucial area of chemistry.

Common Mistakes and How to Avoid Them

When calculating mass from moles, several common mistakes can occur, leading to incorrect results. Being aware of these pitfalls and learning how to avoid them is crucial for accurate stoichiometric calculations. One frequent error is miscalculating the molar mass of a compound. This often happens when students forget to account for the correct number of atoms of each element in the compound's formula or use incorrect atomic masses from the periodic table. To avoid this, always double-check the chemical formula and ensure you are using the accurate atomic masses for each element. It's also helpful to break down the calculation into smaller steps, calculating the contribution of each element separately and then summing them up.

Another common mistake is using the wrong units or not including units in the calculation. Mass should be expressed in grams, molar mass in grams per mole (g/mol), and the amount of substance in moles. Always include units in your calculations and make sure they cancel out correctly. This practice helps to identify errors and ensures the final answer is in the correct unit. For example, when multiplying moles by molar mass, the moles unit should cancel out, leaving grams as the unit for the mass. A third error is incorrectly applying the formula. The formula to convert moles to mass is: Mass = Number of moles × Molar mass. Some students may inadvertently divide by molar mass instead of multiplying. To prevent this, always write down the formula and ensure you are plugging in the values correctly. It can also be helpful to think about the units: mass is a larger quantity than moles for most substances, so multiplying by molar mass (which is typically a value greater than one) makes logical sense.

Finally, rounding errors can also lead to inaccuracies in the final result. To minimize these errors, try to keep as many significant figures as possible throughout the calculation and only round off the final answer to the appropriate number of significant figures. It’s often best to use the full precision of your calculator until the very end of the calculation. By being mindful of these common mistakes and following these strategies, you can significantly improve your accuracy in stoichiometric calculations.

Conclusion

In summary, calculating the mass of a substance from a given number of moles is a fundamental skill in chemistry. This process involves determining the molar mass of the substance and then using the formula: Mass = Number of moles × Molar mass. We have demonstrated this calculation with calcium phosphate ($Ca_3(PO_4)_2$), a compound with significant applications in medicine, agriculture, and materials science. By accurately calculating the molar mass and applying the formula, we determined that 4.50 moles of calcium phosphate has a mass of approximately 1395.81 grams. This calculation underscores the importance of stoichiometry in quantitative chemistry and its relevance in various practical applications.

Throughout this article, we have emphasized the step-by-step process of calculating molar mass, applying the conversion formula, and avoiding common mistakes. We have also provided example problems and practice exercises to reinforce the understanding of these concepts. The ability to convert between moles and mass is crucial for preparing solutions, conducting experiments, and understanding chemical reactions. Mastering these calculations not only strengthens your foundation in chemistry but also enhances your problem-solving skills in related scientific fields. Whether you are a student learning chemistry or a professional working in a scientific discipline, a solid understanding of stoichiometry and molar mass calculations is essential for success. By continuously practicing and applying these principles, you can confidently tackle various chemical calculations and deepen your understanding of the molecular world.