The mineral magnetite is an iron oxide ore that has a density of 5.20 g/cm³. At high temperature, magnetite reacts with carbon monoxide to yield iron metal and carbon dioxide. When 2.660 g of magnetite is allowed to react with sufficient carbon monoxide, the CO₂ product is found to have a volume of 1.136 L at 298 K and 751 mm Hg pressure. (a) What mass of iron in grams is formed in the reaction? (b) What is the formula of magnetite?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the reaction of magnetite (Fe₃O₄) with carbon monoxide (CO) to produce iron (Fe) and carbon dioxide (CO₂).

Step 2: Use the ideal gas law, PV = nRT, to calculate the number of moles of CO₂ produced. Convert the pressure from mm Hg to atm and use R = 0.0821 L·atm/mol·K.

Step 3: Use stoichiometry to determine the moles of iron produced. From the balanced equation, find the mole ratio between CO₂ and Fe.

Step 4: Calculate the mass of iron produced using the moles of iron and the molar mass of iron (55.85 g/mol).

Step 5: Determine the formula of magnetite by recognizing it as Fe₃O₄, a common iron oxide mineral.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry will help calculate the mass of iron produced from the given mass of magnetite and the volume of carbon dioxide generated.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for converting the volume of carbon dioxide produced into moles, which can then be used in stoichiometric calculations. Understanding this concept is crucial for determining how much iron is formed from the reaction involving magnetite and carbon monoxide.

Chemical Formula of Magnetite

The chemical formula of magnetite is Fe₃O₄, indicating that it is composed of three iron (Fe) atoms and four oxygen (O) atoms. Recognizing the formula is important for understanding the composition of the mineral and for performing stoichiometric calculations in the reaction with carbon monoxide. This knowledge is fundamental to answering part (b) of the question regarding the formula of magnetite.

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A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (b) Use the data in Figure 5.19 to identify the alkali metal.

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A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (c) What are the densities of the solid and the vapor in g>cm3?