To determine the actual number of atoms contained in a given mass of an element, you need to use Avogadro's number and the molar mass of the element.
Avogadro's number (represented by the symbol "Nₐ") is approximately 6.022 × 10^23 atoms per mole. This means that one mole of any element contains 6.022 × 10^23 atoms.
The molar mass of chlorine (Cl) is approximately 35.45 grams per mole. This means that one mole of chlorine has a mass of 35.45 grams.
To find the number of moles in a given mass of chlorine, you can use the formula:
moles = mass / molar mass
In this case, the mass is given as 2.8 dm³. However, dm³ is a unit of volume, not mass. To proceed, we need to know the density or convert the volume to mass using the density of chlorine.
Assuming the density of chlorine gas at room temperature and pressure (STP) is approximately 3.2 g/dm³, we can calculate the mass of chlorine in 2.8 dm³ as follows:
mass = volume × density = 2.8 dm³ × 3.2 g/dm³ = 8.96 grams
Now that we have the mass of chlorine (8.96 grams), we can calculate the number of moles:
moles = mass / molar mass = 8.96 g / 35.45 g/mol ≈ 0.253 mol
Finally, we can determine the actual number of chlorine atoms by multiplying the number of moles by Avogadro's number:
number of atoms = moles × Avogadro's number ≈ 0.253 mol × (6.022 × 10^23 atoms/mol) ≈ 1.52 × 10^23 atoms
Therefore, in 2.8 dm³ of chlorine (assuming the given density), there are approximately 1.52 × 10^23 chlorine atoms.