Determining Empirical Formula Iron Oxide Compound Oxygen Content

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Introduction

In the realm of chemistry, one of the fundamental concepts is the empirical formula. The empirical formula of a compound represents the simplest whole-number ratio of atoms of each element present in the compound. Determining the empirical formula is a crucial step in understanding the composition and properties of chemical substances. In this article, we will delve into the concept of empirical formulas and walk through the process of determining the empirical formula of a compound containing only iron and oxygen, given its oxygen content.

Defining the Empirical Formula

The empirical formula provides the most basic representation of the elemental composition of a compound. It does not necessarily indicate the actual number of atoms in a molecule, which is described by the molecular formula. For instance, the molecular formula of glucose is C6H12O6, indicating that each molecule contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. However, the empirical formula of glucose is CH2O, representing the simplest whole-number ratio of these elements (1:2:1).

Determining the empirical formula involves several key steps, which we will illustrate through the example of an iron oxide compound.

Problem Statement: Determining the Empirical Formula of an Iron Oxide

Let's consider the problem of finding the empirical formula of a compound that contains only iron (Fe) and oxygen (O) and is 2.27% oxygen by mass. This means that in a 100-gram sample of the compound, 2.27 grams are oxygen, and the remaining mass is iron. Our goal is to use this information to determine the simplest whole-number ratio of iron and oxygen atoms in the compound.

Step-by-Step Solution

Step 1: Convert Percentages to Grams

Assume we have 100 grams of the compound. This makes the percentage directly equivalent to grams. Therefore:

  • Mass of oxygen (O) = 2.27 grams
  • Mass of iron (Fe) = 100 grams - 2.27 grams = 97.73 grams

Step 2: Convert Grams to Moles

To convert grams to moles, we use the molar masses of the elements. The molar mass of oxygen (O) is approximately 16.00 g/mol, and the molar mass of iron (Fe) is approximately 55.85 g/mol.

  • Moles of oxygen (O) = (2.27 grams) / (16.00 g/mol) = 0.142 moles
  • Moles of iron (Fe) = (97.73 grams) / (55.85 g/mol) = 1.75 moles

Step 3: Determine the Mole Ratio

Divide each mole value by the smallest mole value to obtain the simplest mole ratio.

  • Divide both by 0.142:
    • Iron (Fe) ratio = (1.75 moles) / (0.142 moles) = 12.32
    • Oxygen (O) ratio = (0.142 moles) / (0.142 moles) = 1

Step 4: Convert to Whole Numbers

The ratio we obtained is approximately Fe12.32O1. Since empirical formulas require whole numbers, we need to find a multiplier to convert 12.32 to a whole number. Multiplying by 1 does not work, multiplying by 2 gives 24.64 which is close to 24 or 25, but not close enough. We might need to consider larger multipliers or recognize that 12.32 is very close to 12 1/3 (or 37/3). If we consider that multiplying both by 3, we get Fe36.96O3 which implies something near Fe37O3. But considering the options given, it could also be a rounding error and the number is closer to 12 1/2, or 25/2. Multiplying 12.32 by 2 gives us 24.64, which is very close to 25. This hints at a possible ratio if we considered Fe25O2, yet that is not an option given. Multiplying by 7 gives 86.24 which is not close to a whole number. We must recognize the error lies in the original problem, or choices, and must proceed given the answer choices. Given the numbers involved and the simplicity sought in empirical formulas, let's reassess our approach to see if we missed something or can simplify it differently.

It appears there was an error in the original percentage of oxygen. A compound containing only iron and oxygen with 2.27% oxygen would result in an unusual empirical formula not represented in the options. A more typical iron oxide formula (such as FeO, Fe2O3, or Fe3O4) would have a significantly higher oxygen percentage.

Given the options provided, let’s work backward to see which formula aligns with a reasonable oxygen percentage.

Assessing the Options

A. FeO:

  • Molar mass of FeO = 55.85 g/mol (Fe) + 16.00 g/mol (O) = 71.85 g/mol
  • % of O in FeO = (16.00 g/mol / 71.85 g/mol) * 100% = 22.27%

B. FeO2:

  • Molar mass of FeO2 = 55.85 g/mol (Fe) + 2 * 16.00 g/mol (O) = 87.85 g/mol
  • % of O in FeO2 = (32.00 g/mol / 87.85 g/mol) * 100% = 36.43%

C. Fe2O:

  • Molar mass of Fe2O = 2 * 55.85 g/mol (Fe) + 16.00 g/mol (O) = 127.70 g/mol
  • % of O in Fe2O = (16.00 g/mol / 127.70 g/mol) * 100% = 12.53%

D. Fe7O2:

  • Molar mass of Fe7O2 = 7 * 55.85 g/mol (Fe) + 2 * 16.00 g/mol (O) = 423.95 g/mol
  • % of O in Fe7O2 = (32.00 g/mol / 423.95 g/mol) * 100% = 7.55%

Conclusion Based on Options

Given the significant discrepancy between the provided oxygen percentage (2.27%) and the calculated percentages for common iron oxides, it is likely that there was an error in the initial problem statement. However, if we were to select the option that is closest to a possible iron oxide based on typical stoichiometry, FeO (option A) is the most likely answer, although its oxygen percentage (22.27%) is far from 2.27%.

In this scenario, we must acknowledge the high likelihood of an error in the initial problem data or the answer choices provided. In a real-world setting, such a discrepancy would prompt a reevaluation of the experimental data or the problem's premise.

Understanding Common Iron Oxides

Iron oxides are compounds composed of iron and oxygen, and they play a crucial role in various natural and industrial processes. These compounds exhibit diverse chemical formulas, each with unique properties and applications. The most common iron oxides include:

  • Iron(II) Oxide (FeO): Also known as ferrous oxide, FeO is a non-stoichiometric compound with a black color. It is thermodynamically unstable below 575 °C and tends to disproportionate into metallic iron and Fe3O4. However, it can be stabilized in its pure form at high pressures and temperatures. FeO is used in the production of iron and steel.
  • Iron(III) Oxide (Fe2O3): Also known as ferric oxide, Fe2O3 exists in several polymorphs, the most common being α-Fe2O3 (hematite). Hematite is a reddish-brown solid and is the primary ore of iron. It is widely used in pigments, coatings, and catalysts. Another polymorph, γ-Fe2O3 (maghemite), is ferromagnetic and is used in magnetic recording media.
  • Iron(II,III) Oxide (Fe3O4): Also known as magnetite, Fe3O4 is a black magnetic solid. It is one of the main iron ores and exhibits ferrimagnetism. Fe3O4 is used in magnetic recording, pigments, and as a catalyst. It also has applications in biomedicine due to its magnetic properties.

Formation of Iron Oxides

Iron oxides can form through various chemical reactions, including:

  • Direct Reaction of Iron with Oxygen: Iron reacts with oxygen at high temperatures to form a mixture of iron oxides, with the specific product depending on the reaction conditions, such as temperature and oxygen concentration.
  • Thermal Decomposition of Iron Compounds: Heating iron-containing compounds, such as iron hydroxides or carbonates, can lead to the formation of iron oxides. For example, heating iron(III) hydroxide (Fe(OH)3) results in the formation of Fe2O3.
  • Corrosion of Iron: Iron can corrode in the presence of oxygen and moisture, forming hydrated iron oxides, commonly known as rust. The composition of rust is complex and varies depending on environmental conditions.

Applications of Iron Oxides

Iron oxides have a wide range of applications due to their diverse properties. Some key applications include:

  • Pigments: Iron oxides are widely used as pigments in paints, coatings, and plastics. Hematite (α-Fe2O3) provides a red color, while other iron oxides can produce yellow, brown, and black pigments.
  • Magnetic Recording: Magnetite (Fe3O4) and maghemite (γ-Fe2O3) are used in magnetic recording media, such as audio tapes and hard drives.
  • Catalysis: Iron oxides are used as catalysts in various chemical reactions, including the Haber-Bosch process for ammonia synthesis and the water-gas shift reaction.
  • Biomedicine: Magnetic iron oxide nanoparticles have applications in drug delivery, magnetic resonance imaging (MRI), and hyperthermia cancer therapy.
  • Iron and Steel Production: Iron oxides, particularly hematite, are the primary ores used in the production of iron and steel.

Importance of Stoichiometry

The stoichiometry of iron oxides is crucial in determining their properties and applications. The ratio of iron to oxygen atoms in the compound dictates its crystal structure, magnetic behavior, and chemical reactivity. Non-stoichiometric iron oxides, which deviate from ideal stoichiometric ratios, can exhibit unique properties and are used in specialized applications.

Conclusion

In conclusion, determining the empirical formula of a compound is a fundamental skill in chemistry, providing insight into its elemental composition. While the initial problem presented here had inconsistencies, the process of converting percentages to moles, finding mole ratios, and simplifying to whole numbers is a universally applicable method. Additionally, we've explored common iron oxides and their applications, highlighting the significance of understanding chemical stoichiometry and empirical formulas in the broader field of chemistry.