The unit of length convenient on the atomic scale is known as an angstrom and is denoted by A: 1 A = 10-10 m. The size of a hydrogen atom is about 0.5 A. What is the total atomic volume in m3 of a mole of hydrogen atoms?

Certainly! Understanding the atomic scale and its units is crucial in the realm of chemistry. With UrbanPro being an excellent platform for online coaching and tuition, let's delve into this problem.

Firstly, we're given that 1 angstrom (A) equals 10−1010−10 meters (m), and the size of a hydrogen atom is approximately 0.5 A. Now, to find the volume of one hydrogen atom, we'll calculate the volume of a sphere using the formula V=43πr3V=34πr3, where rr is the radius.

Given the size of a hydrogen atom (radius rr) is 0.5 A, we can substitute this into the formula:

V=43π(0.5 A)3V=34π(0.5A)3

Now, let's calculate the volume of one hydrogen atom.

V=43π(0.5×10−10 m)3V=34π(0.5×10−10m)3 V=43π(0.125×10−30 m3)V=34π(0.125×10−30m3) V=43π×0.125×10−30 m3V=34π×0.125×10−30m3 V=13π×0.5×10−30 m3V=31π×0.5×10−30m3 V=16π×10−30 m3V=61π×10−30m3

Now, to find the total atomic volume in m3m3 of a mole of hydrogen atoms, we need to multiply the volume of one atom by Avogadro's number (NANA), which is approximately 6.022×10236.022×1023 atoms per mole.

Vtotal=Vatom×NAVtotal=Vatom×NA Vtotal=16π×10−30 m3×6.022×1023 atoms/molVtotal=61π×10−30m3×6.022×1023atoms/mol

Now, let's calculate:

Vtotal=π×10−30 m3×1023 atoms/molVtotal=π×10−30m3×1023atoms/mol Vtotal=π×10−7 m3/molVtotal=π×10−7m3/mol

So, the total atomic volume of a mole of hydrogen atoms is approximately π×10−7 m3/molπ×10−7m3/mol.

This calculation is essential for understanding the spatial distribution of atoms in a given quantity, which is fundamental in various fields of chemistry and physics. If you need further clarification or assistance with similar problems, feel free to reach out for more guidance through UrbanPro's excellent online coaching services!