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 × 10²⁰ 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 )

Solution

Chemistry ma’am · 4 steps

Read 48 ppm as 48 g of Mg in a million grams of solution, then scale it down to your 2 L.

1. Meaning of ppm. 48 ppm means 48 g of Mg in every 10⁶ g of solution. The solution is very dilute, so take its density as that of water: 2 L weighs about 2000 g.

   m_(Mg) = 48/10⁶ × 2000 g = 0.096 g

2. Grams to moles. Moles of Mg = 0.096/24 = 4 × 10⁻³ mol.
3. Moles to atoms. Number of atoms = 4 × 10⁻³ × 6.02 × 10²³ = 2.408 × 10²¹ = 24.08 × 10²⁰.
4. So. The answer is in units of 10²⁰, so x = 24.08, which rounds to 24.

The common slip: 2. Stopping at 2.408 × 10²¹ and reporting 2 ignores that the answer must be written as x × 10²⁰, which makes it 24.

The idea to keep. ppm is grams of solute per 10⁶ g of solution. For a dilute aqueous solution, 1 L weighs about 1000 g, so ppm turns into a mass in one line.

Answer from the NTA final answer key. Solution by PrepWiser.