Chlorophyll extracted from the crushed green leaves was dissolved in water to make $$2 \text{ L}$$ solution of Mg of concentration $$48 \text{ ppm}$$. The number of atoms of Mg in this solution is $$x \times 10^{20}$$ atoms. The value of $$x$$ is ______ (Nearest Integer) (Given: Atomic mass of Mg is $$24 \text{ g mol}^{-1}$$, $$N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$$)

We need to find the value of $$x$$ such that the number of Mg atoms in the solution is $$x \times 10^{20}$$.

The concentration of Mg is $$48 \text{ ppm}$$. For aqueous solutions, ppm means mg of solute per L of solution (since density of dilute solution $$\approx 1 \text{ g/mL}$$).

$$48 \text{ ppm} = 48 \text{ mg of Mg per litre of solution}$$

Volume of solution = $$2 \text{ L}$$

$$\text{Mass of Mg} = 48 \times 2 = 96 \text{ mg} = 0.096 \text{ g}$$

Atomic mass of Mg = $$24 \text{ g/mol}$$

$$\text{Moles of Mg} = \frac{0.096}{24} = 0.004 \text{ mol} = 4 \times 10^{-3} \text{ mol}$$

$$\text{Number of Mg atoms} = \text{Moles} \times N_A = 4 \times 10^{-3} \times 6.02 \times 10^{23}$$

$$= 4 \times 6.02 \times 10^{-3+23}$$

$$= 24.08 \times 10^{20}$$

$$\text{Number of Mg atoms} = 24.08 \times 10^{20} \approx 24 \times 10^{20}$$

So $$x = 24$$ (nearest integer).

Hence, the value of $$x$$ is 24.