Problem 101 - Chemistry Matter and Change

Question

Chlorophyll The green color of leaves is due to the presence of chlorophyll, \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{O}_{5} \mathrm{N}_{4} \mathrm{Mg}\) . A fresh leaf was found to have \(1.5 \times 10^{-5} \mathrm{mol}\) of chlorophyll per \(\mathrm{cm}^{2} .\) How many chlorophyll molecules are in 1 \(\mathrm{cm}^{2} ?\)

Step-by-Step Solution

Answer

There are approximately \(9.033 \times 10^{18}\) chlorophyll molecules in 1 cm² of a fresh leaf.

Step 1: Understand the given data

The exercise provides us with the amount of chlorophyll present in a fresh leaf in moles per cm². We have 1.5 x 10⁻⁵ mol of chlorophyll per cm². We need to find the number of chlorophyll molecules in that 1 cm².

Step 2: Use Avogadro's number to find the number of molecules

Avogadro's number, denoted as \(N_A\), is equal to approximately \(6.022 \times 10^{23}\) particles per mole. To find the number of chlorophyll molecules in 1 cm², we'll multiply the given moles of chlorophyll by Avogadro's number: Number of chlorophyll molecules = (moles of chlorophyll) x \(N_A\)

Step 3: Calculate the number of chlorophyll molecules in 1 cm²

Now, we will plug in the given moles of chlorophyll and Avogadro's number in the formula: Number of chlorophyll molecules = \((1.5 \times 10^{-5}\, \text{mol}) \times (6.022 \times 10^{23}\, \text{molecules/mol})\) To perform this multiplication, we multiply the coefficients and add the exponents: Number of chlorophyll molecules = \(1.5 \times 6.022 \times 10^{-5+23}\) Number of chlorophyll molecules = \(9.033 \times 10^{18}\)

Step 4: Write the final answer

There are approximately \(9.033 \times 10^{18}\) chlorophyll molecules in 1 cm² of a fresh leaf.

Key Concepts

Understanding Avogadro's Number

When studying chemistry, Avogadro's number emerges as a fundamental aspect that links the microscopic world of atoms and molecules to the macroscopic world we interact with daily. Named after Amedeo Avogadro, this number is crucial in the mole concept and relates the number of particles to the amount of substance in moles.

Avogadro's number, denoted as \(N_A\), is approximately \(6.022 \times 10^{23}\) entities per mole. It is a dimensionless quantity, meaning it has no units associated with it because it is a count of individual particles, like atoms, ions or molecules, in a given sample. Whether it's molecules of water or chlorophyll, one mole of any substance contains Avogadro's number of those entities.

This constant enables us to perform calculations that convert between the mass of a substance and the number of molecules or atoms it contains. This linking of mass and count at the atomic scale is indispensable in the study of chemistry and forms the backbone for complex chemical quantification and reactions.

Mole Concept Simplified

Diving deeper into chemistry, the mole concept is pivotal for understanding chemical quantities. The mole, often abbreviated as mol, is the SI unit of measurement for the amount of substance. One mole is defined as exactly Avogadro's number of particles, which can be atoms, molecules, electrons, or any other specified entities.

The beauty of the mole concept lies in its ability to simplify chemical equations and reactions. For example, knowing that one mole of carbon atoms equates to \(6.022 \times 10^{23}\) carbon atoms makes it easier to conceptualize large quantities and take part in stoichiometric calculations. Because Avogadro's number is exceedingly large, utilizing moles allows chemists to deal with the vast numbers of atoms and molecules in a more manageable way, turning the inconceivably small scale of atoms into amounts that can be practically measured and used in the laboratory.

In the context of chlorophyll molecules in leaves, using moles allows us to quantify how many molecules are present in a small area, which directly informs us about the intensity of the green color, as chlorophyll is the pigment responsible for photosynthesis and gives plants their green hue.

Chemical Composition of Chlorophyll

Chlorophyll is an essential pigment found in the chloroplasts of green plants and is a critical component of photosynthesis, the process plants use to convert light energy into chemical energy. The green color of leaves and the very sustenance of most life on Earth can be attributed to this molecule.

The chemical formula for chlorophyll is usually represented as \(C_{55}H_{72}O_{5}N_{4}Mg\), indicating a composition of 55 carbon atoms, 72 hydrogen atoms, 5 oxygen atoms, 4 nitrogen atoms, and a central magnesium atom. By knowing the chemical composition, scientists can delve into the molecular structure and the role of each atom within the molecule. For instance, the magnesium atom at the center of the chlorophyll molecule plays a key role in capturing light.

To understand the massive scale of how many chlorophyll molecules reside in a single square centimeter of a leaf, we rely on calculations using both Avogadro's number and the mole concept. As illustrated in the textbook exercise, we can calculate the number of chlorophyll molecules by understanding these concepts, which underpin many aspects of chemistry and plant biology.