Question

For the reaction \[F{e_2}{O_3} + 3CO \to 2Fe + 3C{O_2}\]
The volume of carbon monoxide required to reduce one mole of ferric oxide is:
A) \[22.4d{m^3}\]
B) \[14.8d{m^3}\]
C) \[67.2d{m^3}\]
D) \[11.2d{m^3}\]

Answer 1

Hint: By the equation given above, it is clear that one mole of \[F{e_2}{O_3}\] is reduced in the presence of 3 moles of carbon monoxide. Since no other conditions are given, we will assume that the reaction takes place at standard temperature and pressure.

Complete Step by Step Solution:
The molar volume of a substance is defined as the amount of volume that is occupied by a single mole of substance at a given temperature and pressure.
The molar volume can be calculated based on two standards:
1) Standard temperature and pressure that is \[{0^o}\]temperature and 1-atmosphere pressure.
2) Room temperature and pressure that is \[{25^o}\] temperature and an atmospheric pressure of 1.
Based on the equation given:
\[F{e_2}{O_3} + 3CO \to 2Fe + 3C{O_2}\]
It is clear that one mole of ferric oxide is reduced in the presence of 3 moles of carbon monoxide.
Since no conditions are given, we will assume that the reaction is taking place at standard temperature and pressure.
At standard temperature and pressure, one mole of any gas will occupy the space of 22.4L .
Therefore, calculation of the volume of carbon monoxide required to reduce one mole of ferric oxide can be done by:
\[ = 3 \times 22.4\]
\[ = 67.2d{m^3}\]
Hence, option C is the correct answer

Note: Molar volume is calculated on the basis of Avogadro’s law, which states that a single mole of gas occupies the same amount of volume at the same temperature and pressure. At standard temperature and pressure, the volume occupied is 22.4L whereas at room temperature and pressure, the volume that is occupied by a substance is \[24d{m^3}\].