Question

What is the surface area of a solid material (in m²/g) if it has a nitrogen gas adsorption of 0.52 cm³/g at a relative pressure of 0.1 and assuming a monolayer coverage?

Answer 1

To calculate the surface area of a solid material using nitrogen gas adsorption, we can use the Brunauer-Emmett-Teller  BET  theory. However, since the problem assumes monolayer coverage, we can use the simpler Langmuir isotherm model.First, we need to convert the nitrogen gas adsorption volume from cm/g to m/g:0.52 cm/g *  1 m / 1,000,000 cm  = 5.2  10 m/gNext, we need to know the cross-sectional area of a nitrogen molecule. The diameter of a nitrogen molecule is approximately 0.36 nm. Therefore, the cross-sectional area  A_N2  can be calculated as:A_N2 =  *  diameter / 2 A_N2 =  *  0.36 nm / 2 A_N2 =  *  0.18 nm A_N2  0.1018 nmNow, we need to convert the cross-sectional area from nm to m:0.1018 nm *  1 m / 1,000,000,000 nm  = 1.018  10 mFinally, we can calculate the surface area  S  of the solid material using the monolayer coverage:S =  adsorption volume * Avogadro's number * cross-sectional area of N2  / molecular weight of N2S =  5.2  10 m/g * 6.022  10 molecules/mol * 1.018  10 m  / 28.02 g/molS  1.13  10 m/gSo, the surface area of the solid material is approximately 113 m/g.