Calculate the number of molecules present in one litre of water assuming that the density of water is 1 g/cm^3

The correct option is 3.346 x 10²⁵.

Let us calculate the number of molecules present in one litre of water step-by-step.

Step 1: Find the mass of one litre of water
We are given:
Volume of water, $$V=1\text{ litre}=1000{\text{ cm}}^3$$
Density of water, $$d=1{\text{ g/cm}}^3$$
Using the relationship between mass, density, and volume: $$\text{Mass}=\text{Density}\times \text{Volume}$$
$$m=1{\text{ g/cm}}^3\times 1000{\text{ cm}}^3=1000\text{ g}$$

Step 2: Determine the molar mass of water (H₂O)
Water consists of two Hydrogen atoms and one Oxygen atom.
Atomic mass of Hydrogen (H) ≈ 1 g/mol
Atomic mass of Oxygen (O) ≈ 16 g/mol
Therefore, the molar mass of water (M) is: $$M=(2\times 1)+16=18\text{ g/mol}$$

Step 3: Calculate the number of moles of water in 1000 g
The number of moles (n) is given by: $$n=\frac{\text{Given Mass (m)}}{\text{Molar Mass (M)}}$$
$$n=\frac{1000}{18}\approx 55.56\text{ moles}$$

Step 4: Calculate the total number of molecules
According to Avogadro's law, one mole of any substance contains Avogadro's number of molecules: $$N_A=6.022\times {10}^{23}\text{ molecules/mol}$$
Thus, the total number of molecules (N) in 55.56 moles is: $$N=n\times N_A$$
$$N=55.56\times 6.022\times {10}^{23}$$
$$N\approx 334.6\times {10}^{23}=3.346\times {10}^{25}\text{ molecules}$$

Hence, the number of molecules present in one litre of water is indeed 3.346 x 10²⁵.