Question

Chlorophyll contains \(2.68 \%\) of magnesium. The number of magnesium atoms present in 2 g of chlorophyll is (1) \(1.34 \times 10^{21}\) (2) \(6 \times 10^{20}\) (3) \(5.34 \times 10^{22}\) (4) \(5.34 \times 10^{23}\)

Short answer

(1) 1.34 \times 10^{21}

Step-by-step solution

- Calculate the Mass of Magnesium in Chlorophyll

First, calculate the mass of magnesium in 2 g of chlorophyll. Since chlorophyll contains 2.68% magnesium, the mass of magnesium in 2 g of chlorophyll can be calculated as: \[ \text{Mass of Mg} = 2 \text{ g} \times \frac{2.68}{100} = 0.0536 \text{ g} \]

- Convert Mass to Moles

Next, convert the mass of magnesium obtained to moles. The molar mass of magnesium is 24.305 g/mol. The number of moles of magnesium is calculated by: \[ \text{Moles of Mg} = \frac{0.0536 \text{ g}}{24.305 \text{ g/mol}} \approx 0.002205 \text{ moles} \]

- Calculate the Number of Magnesium Atoms

Finally, calculate the number of magnesium atoms using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol. The number of magnesium atoms is given by: \[ \text{Number of Mg atoms} = 0.002205 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 1.33 \times 10^{21} \text{ atoms} \]

Key concepts

Percentage Composition

Percentage composition is an important concept in chemistry. It tells us how much of each element is present in a compound based on its mass.
In the context of chlorophyll, we're concerned with magnesium's percentage composition.
When we say that chlorophyll contains 2.68% magnesium, it means that in every 100 grams of chlorophyll, there are 2.68 grams of magnesium.
This percentage allows us to calculate the mass of magnesium when we know the total mass of chlorophyll.
Let's walk through the calculation from the exercise:

• First, we knew the mass of chlorophyll (2 grams). Using the percentage (2.68%), we calculated the mass of magnesium: \(\text{Mass of Mg} = 2 \text{g} \times \frac{2.68}{100} = 0.0536 \text{g}\)

Mole Concept

The mole concept is a fundamental aspect of chemistry, allowing us to count particles (like atoms or molecules) by weighing them. It's a bridge between the atomic and macroscopic worlds.
A mole (abbreviated as mol) is a quantity that contains exactly \(6.022 \times 10^{23}\) entities (Avogadro's number).
When we have the mass of a substance and its molar mass (mass of one mole), we can find the number of moles.
For magnesium, with a molar mass of 24.305 g/mol, we can determine the number of moles in 0.0536 grams: \(\text{Moles of Mg} = \frac{0.0536 \text{g}}{24.305 \text{g/mol}} \approx 0.002205 \text{moles}\).

Avogadro's Number

Avogadro's number, \(6.022 \times 10^{23}\) atoms/mol, is essential for linking moles to actual numbers of atoms. This large number helps chemists understand quantities on a microscopic level.
Once we know the number of moles of a substance, Avogadro's number allows us to find the exact number of atoms or molecules.

• For example, in the exercise, we calculated the moles of magnesium to be 0.002205. Multiplying by Avogadro's number gives us the number of atoms: \(0.002205 \text{moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \approx 1.33 \times 10^{21} \text{ atoms}\).

This large number represents the actual atoms in 2 grams of chlorophyll containing 2.68% magnesium.