Question

For the reaction \(\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \rightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2}\), the vol- ume of carbon monoxide required to reduce one mole of ferric oxide is a. \(67.2 \mathrm{dm}^{-1}\) b. \(44.8 \mathrm{dm}^{3}\) c. \(21.5 \mathrm{dm}^{2}\) d. \(89.7 \mathrm{dm}^{1}\)

Short answer

The required volume of CO is \(67.2 \, \text{dm}^3\), option a.

Step-by-step solution

Understand the Chemical Equation

The given chemical reaction is \( \text{Fe}_2\text{O}_3 + 3 \text{CO} \rightarrow 2 \text{Fe} + 3 \text{CO}_2 \). This represents the reduction of iron(III) oxide (\( \text{Fe}_2\text{O}_3 \)) by carbon monoxide (\( \text{CO} \)) to produce iron (\( \text{Fe} \)) and carbon dioxide (\( \text{CO}_2 \)). Notice that 3 moles of \( \text{CO} \) are required to react with 1 mole of \( \text{Fe}_2\text{O}_3 \).

Moles of CO Required

From the balanced equation, we understand that for each mole of \( \text{Fe}_2\text{O}_3 \), 3 moles of \( \text{CO} \) are required. Thus, if you have 1 mole of \( \text{Fe}_2\text{O}_3 \), you will need 3 moles of \( \text{CO} \) to completely react with it.

Molar Volume at STP

Under standard temperature and pressure (STP), 1 mole of any ideal gas occupies a volume of 22.4 liters (equivalent to 22.4 \( \text{dm}^3 \)). This principle is applied here to determine the volume occupied by 3 moles of \( \text{CO} \).

Calculate the Volume of CO

Calculate the volume occupied by 3 moles of \( \text{CO} \) using the molar volume: \[ \text{Volume of 3 moles of CO} = 3 \times 22.4 \, \text{dm}^3 = 67.2 \, \text{dm}^3. \] This is the volume of carbon monoxide required to reduce one mole of ferric oxide.

Key concepts

Understanding Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. In a given reaction, reactants are converted to products, showcasing the rearrangement of atoms. This forms the essence of a chemical reaction.
In the reaction \( \mathrm{Fe}_2 \mathrm{O}_3 + 3 \mathrm{CO} \rightarrow 2 \mathrm{Fe} + 3 \mathrm{CO}_2 \), iron(III) oxide (\( \mathrm{Fe}_2 \mathrm{O}_3 \)) reacts with carbon monoxide (\( \mathrm{CO} \)) to yield iron (\( \mathrm{Fe} \)) and carbon dioxide (\( \mathrm{CO}_2 \)).
The carbon monoxide reduces the iron oxide to produce free iron, illustrating the concept of reduction and support.

• Reactants: \( \mathrm{Fe}_2 \mathrm{O}_3 \) and \( \mathrm{CO} \)
• Products: \( \mathrm{Fe} \) and \( \mathrm{CO}_2 \)
• This balanced reaction follows the Law of Conservation of Mass, meaning the number of each type of atom is the same on both sides of the equation.

Molar Volume and Its Importance

Molar volume is a fundamental concept in chemistry, referring to the volume that one mole of any gas occupies at a given temperature and pressure. Under standard temperature and pressure (STP), defined as 0°C (273.15 K) and 1 atm pressure, one mole of an ideal gas occupies 22.4 liters or 22.4 \( \text{dm}^3 \).
Molar volume helps in calculating the volume of gases involved in reactions. For example, if you know the amount of substance in moles and the conditions are STP, you can easily determine the volume that gas occupies:

• Molar Volume at STP: 22.4 \( \text{dm}^3/\text{mol} \)
• Conversion: Moles \( \times \) Molar Volume \( = \) Volume in \( \text{dm}^3 \)

This is particularly useful when working with gaseous reactants or products, as seen in determining the volume of carbon monoxide required in the given reaction.

Ideal Gases and Their Behavior

Ideal gases follow the Ideal Gas Law, which is an equation of state for a hypothetical gas. This law approximates the behavior of real gases under a range of conditions and is expressed by the equation:\[\text{PV} = n\text{RT}\]Where \(P\) is pressure, \(V\) is volume, \(n\) is moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.

• Assumes no interactions between molecules.
• Molecules occupy no space.
• Useful at high temperature and low pressure.

This concept is crucial when calculating the effects of changing conditions on gas volume and directly applies in the calculated volume of carbon monoxide in the iron oxide reduction reaction.

Deciphering Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants transforming into products and provide a framework to balance the quantity of atoms, adhering to the Law of Conservation of Mass. A balanced chemical equation provides crucial quantitative information essential for stoichiometric calculations.
Such equations highlight proportion, allowing for the calculation of the amounts of substances involved.In the reaction equation:
\(\mathrm{Fe}_2 \mathrm{O}_3 + 3 \mathrm{CO} \rightarrow 2 \mathrm{Fe} + 3 \mathrm{CO}_2\), each molecule is associated with a coefficient which represents the number of moles.

• \(\mathrm{Fe}_2 \mathrm{O}_3\): 1 mole
• \(\mathrm{CO}\): 3 moles
• \(\mathrm{Fe}\): 2 moles
• \(\mathrm{CO}_2\): 3 moles

From these coefficients, stoichiometry links the proportions of reactants and products, enabling the calculation of necessary reactant quantities or resulting product volumes, as illustrated by the volume of CO necessary for reduction in the exercise problem.