Calculating Mass Fraction Of Calcium Chloride In A Mixture A Chemistry Problem Solution

In the realm of chemistry, quantitative analysis plays a pivotal role in determining the composition of mixtures. One common technique involves selectively precipitating a component of the mixture and then converting the precipitate into a stable compound with a known chemical formula. By carefully measuring the mass of this final compound, we can deduce the amount of the original component present in the mixture.

This article delves into a classic chemistry problem involving a mixture of calcium chloride ($CaCl_2$) and sodium chloride (NaCl). Our goal is to determine the mass fraction of $CaCl_2$ in the mixture. To achieve this, we'll walk through a step-by-step solution, highlighting the key concepts and calculations involved. Understanding mass fraction calculations is crucial in various chemical applications, ranging from environmental analysis to pharmaceutical formulation. By mastering this concept, you'll gain a solid foundation for tackling more complex stoichiometric problems.

Problem Statement

Let's begin by clearly stating the problem we aim to solve:

A sample of a mixture of $CaCl_2$ and NaCl weighing 2.22 grams was treated to precipitate all the calcium as calcium carbonate ($CaCO_3$). The $CaCO_3$ was then heated and quantitatively converted to 0.84 grams of calcium oxide (CaO). Calculate the mass fraction of $CaCl_2$ in the mixture.

This problem exemplifies a typical gravimetric analysis scenario, where we use mass measurements to determine the quantity of a specific component in a mixture. The strategy here is to relate the mass of CaO produced to the original mass of $CaCl_2$ in the mixture. To do this effectively, you need a strong understanding of stoichiometry and chemical reactions.

Solution

Step 1: Write the Balanced Chemical Equations

The first step in solving any stoichiometry problem is to write the balanced chemical equations for the reactions involved. This ensures that we have the correct mole ratios for our calculations. In this case, we have two key reactions:

1. Precipitation of Calcium Carbonate: $CaCl_2(aq) + Na_2CO_3(aq) \rightarrow CaCO_3(s) + 2NaCl(aq)$

   Here, calcium chloride reacts with sodium carbonate to form a precipitate of calcium carbonate. While sodium carbonate isn't explicitly mentioned in the problem, it's a common reagent used to precipitate calcium ions as calcium carbonate. The balanced equation is essential for understanding the stoichiometric relationships between reactants and products.

2. Thermal Decomposition of Calcium Carbonate: $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$

   This reaction involves the decomposition of calcium carbonate upon heating, yielding calcium oxide and carbon dioxide gas. This is a classic example of a thermal decomposition reaction, where a compound breaks down into simpler substances upon heating. The balanced equation shows that one mole of $CaCO_3$ decomposes to produce one mole of CaO.

Step 2: Calculate Moles of CaO

Next, we need to determine the number of moles of CaO produced. This is a crucial step as it links the mass of the final product (CaO) to the amount of calcium originally present in the mixture. To do this, we use the molar mass of CaO:

Molar mass of CaO = 40.08 g/mol (Ca) + 16.00 g/mol (O) = 56.08 g/mol

Now, we can calculate the moles of CaO:

Moles of CaO = Mass of CaO / Molar mass of CaO Moles of CaO = 0.84 g / 56.08 g/mol Moles of CaO ≈ 0.015 mol

This calculation demonstrates the importance of molar mass in converting between mass and moles. Accurate molar mass values are essential for precise stoichiometric calculations. The result, 0.015 moles of CaO, will be used in the subsequent steps to determine the amount of $CaCl_2$ in the original mixture.

Step 3: Determine Moles of $CaCl_2$

From the balanced chemical equations, we know that 1 mole of $CaCO_3$ produces 1 mole of CaO, and 1 mole of $CaCl_2$ produces 1 mole of $CaCO_3$. Therefore, the moles of CaO are equal to the moles of $CaCO_3$, which are also equal to the moles of $CaCl_2$ in the original mixture.

Moles of $CaCl_2$ = Moles of CaO ≈ 0.015 mol

This step highlights the significance of the mole ratio derived from the balanced chemical equations. The 1:1:1 mole ratio between $CaCl_2$, $CaCO_3$, and CaO simplifies the calculation, allowing us to directly equate the moles of CaO to the moles of $CaCl_2$. Understanding mole ratios is fundamental to stoichiometric calculations.

Step 4: Calculate Mass of $CaCl_2$

Now that we know the moles of $CaCl_2$, we can calculate its mass using its molar mass:

Molar mass of $CaCl_2$ = 40.08 g/mol (Ca) + 2 * 35.45 g/mol (Cl) = 110.98 g/mol

Mass of $CaCl_2$ = Moles of $CaCl_2$ * Molar mass of $CaCl_2$ Mass of $CaCl_2$ = 0.015 mol * 110.98 g/mol Mass of $CaCl_2$ ≈ 1.66 g

This calculation emphasizes the practical application of molar mass in converting moles back to mass. The result, 1.66 grams of $CaCl_2$, represents the mass of calcium chloride present in the original 2.22-gram mixture. Accurate molar mass values are crucial for obtaining reliable results.

Step 5: Calculate Mass Fraction of $CaCl_2$

Finally, we can calculate the mass fraction of $CaCl_2$ in the mixture. The mass fraction is defined as the mass of the component divided by the total mass of the mixture:

Mass fraction of $CaCl_2$ = (Mass of $CaCl_2$ / Total mass of mixture) * 100% Mass fraction of $CaCl_2$ = (1.66 g / 2.22 g) * 100% Mass fraction of $CaCl_2$ ≈ 74.77%

Therefore, the mass fraction of $CaCl_2$ in the mixture is approximately 74.77%.

This final step illustrates the calculation of mass fraction, a common way to express the composition of a mixture. The mass fraction provides a clear indication of the relative amount of a specific component within the mixture. In this case, the high mass fraction of $CaCl_2$ indicates that it is the major component of the mixture.

Conclusion

In this article, we successfully calculated the mass fraction of $CaCl_2$ in a mixture with NaCl using a step-by-step approach. We began by understanding the problem statement and outlining the overall strategy. Then, we wrote balanced chemical equations for the reactions involved, calculated the moles of CaO produced, determined the moles of $CaCl_2$ in the original mixture, calculated the mass of $CaCl_2$, and finally, calculated the mass fraction of $CaCl_2$.

This problem demonstrates the practical application of stoichiometry and gravimetric analysis in determining the composition of mixtures. By mastering these concepts, you can confidently tackle a wide range of chemistry problems. Remember, the key to success in stoichiometry lies in understanding the mole concept, balanced chemical equations, and molar mass calculations. This approach can be applied to various analytical chemistry problems. Furthermore, this type of quantitative analysis is crucial in various fields, including environmental science, pharmaceutical chemistry, and materials science. The ability to accurately determine the composition of mixtures is essential for quality control, research, and development in these fields.

By understanding the principles behind these calculations, students can apply them to a broader range of quantitative analysis problems, solidifying their understanding of chemical principles and analytical techniques. This problem-solving approach also encourages critical thinking and problem-solving skills, which are valuable assets in any scientific discipline. Furthermore, practicing similar problems will help students develop confidence in their ability to tackle complex chemical calculations and interpret experimental results accurately.