How many cobalt atoms are there in a cylinder of radius 2.5cm and a length of 10 cm?
The number of cobalt atoms in a cylinder of the alloy with a radius of 2.5cm and height of 10cm is approximately 1.98 × 10²⁴.
Calculation of Cobalt Atoms in Alloy Cylinder
To calculate the number of cobalt atoms in the said alloy cylinder, we first need to figure out the volume of the cylinder. Using the cylinder volume formula (πr²h), where r=2.5cm and h=10cm, the volume is approximately 196.3cm³. However, the density of the alloy is given in grams/ml, and since 1 ml equals 1 cm³, the mass of the alloy can be calculated as 8.2g/ml * 196.3ml = 1609.66g. Next, considering that cobalt constitutes 12% of the alloy, the mass of cobalt in the alloy is 12/100 * 1609.66g = 193.16g. We then convert this mass into moles using the atomic mass of cobalt (58.9g/mol), hence, the moles of cobalt are 193.16g / 58.9g/mol = 3.28 mol. Finally, by using Avogadro's number (6.022 × 10²³ atoms/mol), we can calculate the number of atoms. The number of cobalt atoms in the alloy cylinder is 3.28 mol * 6.022 × 10²³ atoms/mol ≈ 1.98 × 10²⁴ atoms.