What volume of oxygen, measured at 25^∘ C and 1 bar, is required to form an oxide film on 1 m^2

step 1 Let's note that the effective area of our array in which our atoms will arrange themselves is 1

What volume of oxygen, measured at 25^∘ C and 1 bar, is...

What volume of oxygen, measured at $25^{\circ} \mathrm{C}$ and 1 bar, is required to form an oxide film on $1 \mathrm{m}^{2}$ of a metal with atoms in a square array $0.1 \mathrm{nm}$ apart? Assume that one oxygen atom combines with each metal atom.

Key Concepts

Surface Atomic Density

Surface atomic density refers to the number of atoms per unit area on a solid surface. It is determined by the arrangement of atoms in a lattice and the spacing between them. This concept is crucial for calculating how many atoms are present on a given surface area, which is necessary when relating microscopic structures (like a monolayer of atoms) to stoichiometric requirements in reactions or film formations.

Avogadro's Number and the Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance in terms of number of particles, with Avogadro's number (approximately 6.022 x 10^23) representing the number of atoms or molecules in one mole. Using this concept, one can convert the total number of atoms determined from a surface density calculation into moles, which is essential for linking atomic-scale quantities to bulk measurements such as gas volume.

Ideal Gas Law and Molar Volume

The ideal gas law relates pressure, volume, temperature, and number of moles of a gas, providing a framework to predict a gas's behavior under various conditions. Under defined conditions, such as 25°C and 1 bar, a gas occupies a specific molar volume. This concept is vital for converting the moles of gas (derived from the stoichiometric requirements) into the corresponding volume, thereby connecting the microscopic reaction requirements to macroscopic gas measurements.

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