You want to plate a steel part having a surface area of 240 with a 0.002--thick layer of silver. The atomic mass of silver is 107.868 . The density of silver is 10.49 . How many atoms of silver are required

This question is incomplete, the complete question is;

You want to plate a steel part having a surface area of 240 in² with a 0.002-in thick layer of silver.

The atomic mass of silver is 107.868 g/mol .

The density of silver is 10.49 g/cm³.

How many atoms of silver are required?

4.6 × 10²³ atoms of silver are required

Explanation:

Given the data in the question;

first, we determine the volume of silver layer  

volume of silver layer = surface area × thickness

we substitute

volume of silver layer =  240 in² × 0.002-in = 0.48 in³

we know that 1 in³ = 16.387 cm³

so, volume of silver layer  = 0.48 × 16.387 = 7.87 cm³

Next we calculate mass of silver;

⇒ density × Volume

mass of silver = 10.49 g/cm³ × 7.87 cm³ = 82.5563 g

Now, number of atoms of silver are required will be;

Number of atoms = (mass/atomic mass) × Avogadro number

we know that A.v no. is 6.02214 × 10²³ mol⁻¹

so

Number of atoms = (82.5563 g / 107.868 g/mol . ) × 6.02214 × 10²³ mol⁻¹

= 0.7653 × 6.02214 × 10²³

= 4.6 × 10²³ atoms

Therefore; 4.6 × 10²³ atoms of silver are required

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