Question

Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 L solution of Mg of concentration 48 ppm. The number of atoms of Mg in this solution is \(x × 10^{20}\) atoms. The value of \(x\) is ________. (Nearest integer)
(Given : Atomic mass of Mg is 24 g mol^–1; N_A = 6.02 × 10²³ mol^–1)

Answer 1

Correct Answer: 24

To determine the number of Mg atoms in a 2 L solution with a concentration of 48 ppm, follow these steps:

1. Calculate the total mass of Mg in the solution: The concentration is 48 ppm, which means 48 mg of Mg per 1 L of solution. Therefore, in 2 L of solution, the mass of Mg is:
   \(48\, \text{mg/L} \times 2\, \text{L} = 96\, \text{mg}\).
2. Convert the mass of Mg to grams:
   \(96\, \text{mg} = 0.096\, \text{g}\).
3. Calculate moles of Mg: Given the atomic mass of Mg is 24 g/mol, calculate moles of Mg:
   \(\frac{0.096\, \text{g}}{24\, \text{g/mol}} = 0.004\, \text{mol}\).
4. Calculate number of atoms using Avogadro's number (N_A = 6.02 × 10²³ mol^–1):
   \(0.004\, \text{mol} \times 6.02 \times 10^{23}\, \text{atoms/mol} = 2.408 \times 10^{21}\, \text{atoms}\).
5. Express in terms of \(x \times 10^{20}\) atoms:
   \(2.408 \times 10^{21}\) atoms = \(24.08 \times 10^{20}\) atoms.
6. Find \(x\), rounding to the nearest integer:
   \(x = 24\).

The calculated value of \(x\) is within the given range (24,24). Thus, \(x = 24\).