Question

Chlorophyll, the substance responsible for the green color of leaves, has one magnesium atom per chlorophyll molecule and contains \(2.72 \%\) magnesium by mass. What is the molar mass of chlorophyll?

Short answer

Answer: The molar mass of chlorophyll is approximately 892.98 g/mol.

Step-by-step solution

Given information and molar mass of Magnesium

We are given that the mass percentage of magnesium in chlorophyll is \(2.72 \%\). Also, we know that there is 1 magnesium atom (Mg) per chlorophyll molecule. The molar mass of magnesium is 24.31 g/mol.

Set up the equation with mass percentage

Let's denote the molar mass of chlorophyll as M_chl. Since the mass percentage of magnesium in chlorophyll is \(2.72 \%\), we can write: 2.72 = (mass of magnesium in a chlorophyll molecule)/(molar mass of chlorophyll) * 100 We are also given that there is 1 magnesium atom per chlorophyll molecule: mass of magnesium in a chlorophyll molecule = (1 * molar mass of magnesium) Combining the two equations, we get: 2.72 = (1 * 24.31)/M_chl * 100

Solve for the molar mass of chlorophyll

Now, we just need to solve for M_chl: M_chl = (1 * 24.31 * 100) / 2.72 M_chl ≈ 892.98 g/mol So, the molar mass of chlorophyll is approximately 892.98 g/mol.

Key concepts

Molecular Composition

Understanding the molecular composition of a substance involves identifying the types and numbers of atoms it contains. In the case of chlorophyll, which imparts the green color to leaves, its molecular composition is highly complex, involving a long carbon chain, a porphyrin ring structure, and a magnesium atom at its core. Each molecule of chlorophyll contains exactly one atom of magnesium, which is vital for capturing light energy during the process of photosynthesis.

When studying substances like chlorophyll, chemists use molecular formulas that represent the numbers and types of atoms in each molecule. Although we don't have the full molecular formula for chlorophyll in this exercise, knowing that each molecule includes one magnesium atom is crucial. This information allows us to calculate the mass percent composition and, eventually, the molar mass of the entire chlorophyll molecule.

Mass Percent Composition

Mass percent composition is a way of expressing the concentration of an element within a compound. It indicates what percentage of the total mass of the compound is due to a particular element. In the example of chlorophyll, we are given that magnesium makes up 2.72% of the compound's mass.

Let's take a closer look at the concept with chlorophyll as an example. If you have 100 grams of chlorophyll, the mass of magnesium would be 2.72 grams because it is 2.72% of the total mass. This principal facilitates the connection between the mass of pure elements within a compound and the total molar mass of the compound. This connection then helps in determining the molar mass of the compound based on the known molar mass of its constituent elements.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental practice in chemistry. Molar mass, defined as the mass of one mole of a substance, is expressed in grams per mole (g/mol). It is the summation of the molar masses of all the atoms in a single molecule of the substance.

In this case, to calculate the molar mass of chlorophyll (M_chl), you start by establishing the known mass percent of magnesium (2.72%) and magnesium's molar mass (24.31 g/mol). From the mass percent composition, we can set up an equation that leads to the molar mass of chlorophyll by rearranging and solving:
\[ M_{chl} = \frac{1 \times 24.31 \times 100}{2.72} \approx 892.98 \, g/mol \]
This step illustrates the inverse relationship between the mass percent of an element in a compound and the molar mass of the compound. A lower mass percent means a higher molar mass for the compound, assuming one mole of the element is present.