The volume of nitrogen gas vm (measured at 1.013 bar and 0^∘ C ) required to form a complete mon

step 1 This problem asks us to find service area given specific conditions such as pressure. So our job

The volume of nitrogen gas vm (measured at 1.013 bar and 0^∘...

The volume of nitrogen gas $v_{\mathrm{m}}$ (measured at 1.013 bar and $0^{\circ} \mathrm{C}$ ) required to form a complete monolayer on a sample silica gel is $129 \mathrm{cm}^{3} \mathrm{g}^{-1}$ of gel. Calculate the surface area per gram of the gel if each nitrogen molecule occupies $16.2 \times$ $10^{-20} \mathrm{m}^{2}$

Key Concepts

Monolayer Adsorption

Monolayer adsorption refers to the formation of a single, molecule-thick layer on a solid's surface. This concept assumes that once every surface active site is occupied by an adsorbate molecule, the surface is completely covered without any additional layers forming. It is a fundamental assumption in surface area analyses based on adsorption techniques and is directly used to relate the amount of adsorbed gas to the total accessible surface area of a material.

Gas Adsorption Methods for Surface Area Measurement

Gas adsorption techniques, such as those using nitrogen at standard conditions, are widely employed to measure the surface area of porous materials. By determining the volume of gas that forms a complete monolayer on a solid, scientists can estimate the number of adsorbate molecules that cover the surface. This method, which often underpins BET (Brunauer–Emmett–Teller) theory, links adsorbed gas volume to the total surface area available for adsorption.

Ideal Gas Law and Mole Conversions

The Ideal Gas Law provides a relationship between the volume, temperature, and pressure of a gas, enabling conversion from a measured gas volume to the number of moles. When an experiment is conducted at standard temperature and pressure (STP), these conversions become straightforward and are essential for linking macroscopic measurements (like gas volume) to the microscopic number of molecules present on a surface.

Molecular Cross-sectional Area

The molecular cross-sectional area quantifies the physical space that an individual molecule occupies when adsorbed onto a surface. This value is critical in calculating the total surface area, as it allows for a direct conversion from the number of adsorbed molecules (obtained from the gas volume and mole calculations) to the overall area covered on the material’s surface.

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