The diameter of the hydrogen molecule is about 0.27 nm . If an adsorbent has a surface of 850 m^

step 1 The very first thing that we need to do in this problem is convert our nanometers into meters. W

The diameter of the hydrogen molecule is about 0.27 nm . If...

The diameter of the hydrogen molecule is about 0.27 $\mathrm{nm} .$ If an adsorbent has a surface of $850 \mathrm{m}^{2} \mathrm{cm}^{-3},$ what volume of $\mathrm{H}_{2}\left(\text { measured at } 25^{\circ} \mathrm{C} \text { and } 1 \text { bar }\right)$ could be adsorbed by $100 \mathrm{mL}$ of the adsorbent? It may be assumed that the adsorbed molecules just touch in a plane and are arranged so that four adjacent spheres have their centers at the corners of a square.

Key Concepts

Ideal Gas Law

The ideal gas law provides a relationship among pressure, volume, temperature, and the number of moles of a gas. It is used to predict the behavior of a gas under particular conditions and is essential for calculating the volume an ideal gas would occupy at specified temperature and pressure conditions. This principle is particularly useful in adsorption studies when estimating the volume of gas that could be adsorbed versus when it is in the free state.

Adsorption

Adsorption is the process by which atoms, ions, or molecules from a substance adhere to a surface of another material. This process creates a coating or a thin film on the surface, and it is central to areas such as catalysis, gas storage, and separation technologies, where the interaction between the adsorbate and the adsorbent determines the efficiency of these processes.

Surface Area in Adsorption Processes

The effectiveness of an adsorbent is largely determined by its available surface area. A higher surface area allows for more adsorbate molecules to adhere, thereby increasing the material's capacity to store gases or liquid molecules. This concept emphasizes that the total area over which adsorption occurs is directly correlated with the overall adsorption capacity of the material.

Molecular Packing

Molecular packing describes the geometric arrangement of molecules on a surface or within a confined space. In adsorption, molecules are often modeled as spheres that pack in regular arrangements (such as square or hexagonal patterns) on a surface. This arrangement affects the density of the adsorbed layer and is crucial for estimating how many molecules can be accommodated given the physical size of the molecules.

Dimensional Analysis and Unit Conversion

Dimensional analysis and unit conversion involve ensuring that all quantities in a calculation are expressed in compatible units. This technique is vital when dealing with different measurement scales—such as nanometers for molecular dimensions, square meters for surface area, and liters or cubic meters for volume—ensuring that final results are accurate and meaningful in the context of the problem.

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