At STP the volume of nitrogen gas required to cover a sample...

At STP the volume of nitrogen gas required to cover a sample of silica gel, assuming Langmuir monolayer adsorption, is found to be $1.33 \mathrm{~cm}^{3} \mathrm{~g}^{-1}$ of the gel. The area occupied by a nitrogen molecule is $0.15 \mathrm{~nm}^{2}$. What is the surface area per gram of silica gel? a. $5.568 \mathrm{~m}^{2} \mathrm{~g}^{-1}$ b. $1.5 \mathrm{~m}^{2} \mathrm{~g}^{-1}$ c. $5.343 \mathrm{~m}^{2} \mathrm{~g}^{-1}$ d. $1.33 \mathrm{~m}^{2} \mathrm{~g}^{-1}$

At STP the volume of nitrogen gas required to cover a sample of silica gel, assuming Langmuir monolayer adsorption, is found to be $1.33 \mathrm{~cm}^{3} \mathrm{~g}^{-1}$ of the gel. The area occupied by a nitrogen molecule is $0.15 \mathrm{~nm}^{2}$. What is the surface area per gram of silica gel?
a. $5.568 \mathrm{~m}^{2} \mathrm{~g}^{-1}$
b. $1.5 \mathrm{~m}^{2} \mathrm{~g}^{-1}$
c. $5.343 \mathrm{~m}^{2} \mathrm{~g}^{-1}$
d. $1.33 \mathrm{~m}^{2} \mathrm{~g}^{-1}$

Key Concepts

Surface Area Determination from Gas Adsorption

Calculating the surface area per gram of a material through gas adsorption involves determining the number of molecules that form a monolayer on the surface and then multiplying by the area occupied by each individual molecule. This process relies on accurate measurements of gas volume adsorbed and the known cross-sectional area of the adsorbate molecules, providing a practical method to evaluate the specific surface area of porous materials.

Ideal Gas Law and Avogadro's Number

These fundamental principles relate the macroscopic measurements of gases (such as volume and pressure) to the number of particles present. The ideal gas law allows conversion of a given gas volume at STP into moles, and Avogadro's number is then used to determine the total number of molecules. This connection is essential for calculating the surface area when each adsorbed molecule occupies a known area.

Unit Conversion

An important aspect of these calculations is the conversion between different units, such as converting volumes in cubic centimeters to liters, areas from square nanometers to square meters, and maintaining consistency in the use of mass. Mastering unit conversion is crucial for obtaining meaningful and accurate results in surface area and adsorption computations.

Langmuir Monolayer Adsorption

This concept pertains to the adsorption of molecules onto a solid surface such that only one layer of adsorbate is formed. It assumes that each adsorption site on the surface can hold only one molecule and that all sites have equal energy. This model is crucial when determining the surface area of a material from gas adsorption data because it links the volume of gas adsorbed to the number of molecules that cover the surface.

Standard Temperature and Pressure (STP)

STP provides a standard set of conditions (typically 0°C and 1 atm) under which the properties of gases, such as molar volume, are well defined. Using STP conditions allows for the consistent conversion between the volume of gas and the number of moles, serving as a reference point in many calculations, including those involving gas adsorption measurements.

Please give Ace some feedback