Calculating The Mass Of Iron(III) Carbonate From Moles A Stoichiometry Guide

Jul 14, 2025 by ADMIN 77 views

Calculating the Mass of Iron(III) Carbonate Produced in a Chemical Reaction

Introduction

In the realm of chemistry, stoichiometry serves as a cornerstone for understanding the quantitative relationships between reactants and products in chemical reactions. Mastering stoichiometric calculations is crucial for predicting the amount of product formed from a given amount of reactants. This article delves into the step-by-step process of calculating the mass of iron(III) carbonate, $Fe_2(CO_3)_3$ , produced in a chemical reaction, emphasizing the importance of significant figures in scientific calculations. When dealing with chemical reactions, accurately determining the mass of products formed is essential for various applications, including industrial processes, research experiments, and environmental assessments. Understanding the stoichiometry of a reaction allows chemists to optimize reaction conditions, predict yields, and ensure the efficient use of resources. In this context, we will explore a specific scenario where 3.70 moles of iron(III) carbonate are produced and calculate the corresponding mass. This calculation will not only reinforce the fundamental principles of stoichiometry but also highlight the significance of molar mass and significant figures in obtaining precise results. The principles discussed here are broadly applicable in chemistry, making it a valuable exercise for students and professionals alike. The ability to convert between moles and mass is a fundamental skill that underpins many areas of chemical practice. From designing new materials to analyzing environmental samples, the quantitative aspects of chemistry are indispensable. The following sections will provide a detailed walkthrough of the calculation, ensuring that the reader understands each step and can apply the same methodology to similar problems. Emphasis will be placed on maintaining the correct number of significant figures, a critical aspect of scientific communication that reflects the precision of measurements and calculations.

Problem Statement

A chemical reaction produced 3.70 mol of iron(III) carbonate, $Fe_2(CO_3)_3$ . What mass of iron(III) carbonate is produced? Be sure your answer has the correct number of significant figures.

This problem requires us to convert the given moles of iron(III) carbonate into grams, using the molar mass of the compound as a conversion factor. The molar mass is a crucial concept in chemistry, representing the mass of one mole of a substance, expressed in grams per mole (g/mol). Accurate determination of molar mass is essential for stoichiometric calculations, as it directly relates the number of moles to the mass of a substance. Iron(III) carbonate, with its complex formula, presents an interesting case for molar mass calculation. It involves summing the atomic masses of all the constituent elements, taking into account the number of atoms of each element present in the compound. The correct application of molar mass not only allows us to solve the immediate problem but also provides a foundation for tackling more complex stoichiometric problems. Furthermore, the problem statement explicitly emphasizes the importance of significant figures. Significant figures are the digits in a number that contribute to its precision. In scientific measurements and calculations, it is crucial to maintain the correct number of significant figures to reflect the accuracy of the data. This means that the final answer should not imply a greater precision than the least precise measurement used in the calculation. In the given problem, the number of moles, 3.70 mol, has three significant figures, which will influence the number of significant figures in the final answer. This aspect of the problem underscores the need for careful attention to detail in scientific calculations, ensuring that the results are both accurate and meaningful. The following sections will guide you through the process of calculating the molar mass of iron(III) carbonate and using it to determine the mass produced in the reaction, all while adhering to the rules of significant figures.

Calculating the Molar Mass of Iron(III) Carbonate ( $Fe_2(CO_3)_3$ )

The molar mass of a compound is the sum of the atomic masses of all the atoms in its formula. To calculate the molar mass of $Fe_2(CO_3)_3$ , we need the atomic masses of iron (Fe), carbon (C), and oxygen (O) from the periodic table.

Atomic mass of iron (Fe) ≈ 55.845 g/mol
Atomic mass of carbon (C) ≈ 12.011 g/mol
Atomic mass of oxygen (O) ≈ 15.999 g/mol

Now, we calculate the molar mass of $Fe_2(CO_3)_3$ :

There are 2 iron atoms, so: 2 * 55.845 g/mol = 111.69 g/mol
There are 3 carbonate ( $CO_3$ ) groups, each containing 1 carbon atom, so: 3 * 12.011 g/mol = 36.033 g/mol
There are 3 carbonate ( $CO_3$ ) groups, each containing 3 oxygen atoms, totaling 9 oxygen atoms, so: 9 * 15.999 g/mol = 143.991 g/mol

Adding these values together:

Molar mass of $Fe_2(CO_3)_3$ = 111.69 g/mol + 36.033 g/mol + 143.991 g/mol = 291.714 g/mol

Considering significant figures, we should round the molar mass to a reasonable number of decimal places. In this case, retaining three significant figures is appropriate, giving us a molar mass of 291.71 g/mol. The accurate calculation of molar mass is a critical step in stoichiometry. It serves as the bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms that we can measure in the laboratory. The molar mass is a constant for a given compound and is used extensively in converting between moles and mass. In the case of iron(III) carbonate, the molar mass calculation involves accounting for the contributions of each element present in the compound. Iron, a transition metal, has a relatively high atomic mass, which significantly contributes to the overall molar mass of the compound. Carbon and oxygen, the other constituents of the carbonate group, also contribute substantially. The calculation presented here highlights the importance of using accurate atomic masses from the periodic table and carefully accounting for the stoichiometry of the compound. The subscript numbers in the chemical formula indicate the number of atoms of each element present in one formula unit of the compound. These numbers are crucial in determining the total contribution of each element to the molar mass. Furthermore, the concept of significant figures is paramount in scientific calculations. The molar mass calculated here should reflect the precision of the atomic masses used. Rounding the molar mass to an appropriate number of significant figures ensures that the final result of any calculation using this molar mass will also have the correct level of precision. In the next section, we will use this calculated molar mass to convert the given number of moles of iron(III) carbonate to mass, adhering to the principles of significant figures.

Converting Moles to Mass

To find the mass of iron(III) carbonate produced, we use the formula:

Mass = Moles * Molar Mass

We are given 3.70 mol of $Fe_2(CO_3)_3$ , and we have calculated the molar mass to be 291.71 g/mol.

Mass = 3.70 mol * 291.71 g/mol = 1079.327 g

Now, we need to consider significant figures. The given value (3.70 mol) has three significant figures, and the molar mass (291.71 g/mol) has five significant figures. According to the rules of significant figures, the result should have the same number of significant figures as the measurement with the fewest significant figures, which is three in this case.

Rounding 1079.327 g to three significant figures, we get 1080 g. Therefore, the mass of iron(III) carbonate produced is 1080 g. The conversion from moles to mass is a fundamental calculation in chemistry, often used in various contexts, from preparing solutions to determining reaction yields. This conversion relies on the molar mass as the key conversion factor, linking the number of moles, a measure of the amount of substance, to the mass, a measure of the quantity of matter. In this specific problem, we are given the number of moles of iron(III) carbonate produced in a chemical reaction and asked to calculate the mass. This calculation directly applies the definition of molar mass, which is the mass of one mole of a substance. Multiplying the given number of moles by the molar mass gives the mass of the substance. The mathematical operation involved is straightforward, but the underlying concepts are profound. It connects the macroscopic property of mass to the microscopic world of molecules and atoms. The result of the multiplication, 1079.327 g, is a precise value based on the numbers used in the calculation. However, in scientific measurements and calculations, it is crucial to consider the uncertainty associated with the measurements. This is where the concept of significant figures comes into play. Significant figures are the digits in a number that carry meaning contributing to its precision. The rules for handling significant figures ensure that the final result of a calculation does not imply a greater precision than the least precise measurement used. In this case, the given number of moles, 3.70 mol, has three significant figures, while the molar mass, 291.71 g/mol, has five significant figures. Therefore, the final answer should be rounded to three significant figures, which gives us 1080 g. This rounding reflects the inherent uncertainty in the initial measurement of 3.70 mol and ensures that the reported mass is consistent with the precision of the input data.

Conclusion

In summary, the mass of iron(III) carbonate produced in the chemical reaction is 1080 g. This result was obtained by first calculating the molar mass of $Fe_2(CO_3)_3$ and then using it to convert the given moles to mass. The final answer was adjusted to reflect the correct number of significant figures. Stoichiometric calculations are a fundamental aspect of chemistry, allowing us to quantify the relationships between reactants and products in chemical reactions. The ability to convert between moles and mass is a crucial skill for chemists, enabling them to design experiments, analyze data, and make predictions about chemical processes. In this article, we have demonstrated a step-by-step approach to solving a typical stoichiometry problem, highlighting the importance of molar mass, significant figures, and unit conversions. The molar mass calculation involves summing the atomic masses of all the elements in the compound, taking into account the stoichiometry of the formula. This calculation is a cornerstone of quantitative chemistry, providing a link between the number of moles of a substance and its mass. Accurate determination of molar mass is essential for subsequent calculations. The conversion of moles to mass is a direct application of the definition of molar mass. By multiplying the number of moles by the molar mass, we obtain the mass of the substance. This conversion is frequently used in laboratory settings for preparing solutions and determining reaction yields. Significant figures play a critical role in ensuring the accuracy and precision of scientific calculations. The final answer should reflect the uncertainty in the measurements used. By adhering to the rules of significant figures, we can ensure that our results are meaningful and reliable. In conclusion, the problem presented in this article illustrates the fundamental principles of stoichiometry and highlights the importance of careful calculation and attention to detail in chemical problem-solving. The concepts and techniques discussed here are widely applicable in chemistry and form the basis for more advanced topics. Mastering these skills is essential for anyone pursuing a career in chemistry or related fields.