Question

Calculate the radius of a water molecule assuming to be spherical

Answer 1

As you know, density of water is 1 g/cm³
and molecular weight of water is 18g/mol , it means , 18g of water contains 6.023 × 10²³ molecules of it.

First of all we have to find volume of 1 mole of water
= mass/density = 18g/{1g/cm³} = 18 cm³
hence, volume of 1 mole of water = 18cm³ = 18 × 10⁻⁶ m³
∵ 1 mole of water = 6.023 × 10²³ molecules of water
∴ volume of 6.023 × 10²³ molecules of water = 1.8 × 10⁻⁵ m³
⇒ volume of 1 Molecule of water = 1.8/6.023 × 10⁻⁵⁻²³ m³
= 0.2988 × 10⁻²⁸ m³

Let radius of water molecule is r
Then, volume of 1 Molecule of water = 4/3 πr³
∴ 4/3 πr³ = 0.2988 × 10⁻²⁸ m³
⇒r³ = 0.2988 ×3/4π × 10⁻²⁸
⇒r = 0.1925 × 10⁻⁹ m = 0.1925 nm.

Hence, answer should be 0.1925 nm

Answer 2

I hope this answers will help you