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 \( 9.033 \times 10^{18} \) chlorophyll molecules in 1 \( \mathrm{cm}^{2} \).

Step 1: Understand the Formula of Chlorophyll

The molecular formula for chlorophyll is \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{O}_{5} \mathrm{N}_{4} \mathrm{Mg} \). This formula describes the compound's composition, but for this problem, what is important is the amount of chlorophyll given in moles.

Step 2: Identify the Quantity of Chlorophyll

The problem states that there are \( 1.5 \times 10^{-5} \mathrm{mol} \) of chlorophyll per \( \mathrm{cm}^{2} \). This means for every \( \mathrm{cm}^{2} \) area of leaf, there exists \( 1.5 \times 10^{-5} \) moles of chlorophyll.

Step 3: Use Avogadro's Number

Avogadro's number \( 6.022 \times 10^{23} \) molecules/mol allows us to convert moles to molecules. To find out the number of molecules from moles, multiply the number of moles by Avogadro's number.

Step 4: Calculate Chlorophyll Molecules

Multiply the quantity of chlorophyll in moles by Avogadro's number:\[1.5 \times 10^{-5} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 9.033 \times 10^{18} \text{ molecules}\]

Step 5: Conclusion of Calculation

Based on the calculations, there are \( 9.033 \times 10^{18} \) chlorophyll molecules in 1 \( \mathrm{cm}^{2} \) area of the leaf.

Key Concepts

Molecular Formula

The molecular formula of a compound like chlorophyll gives us vital information about its structure and composition. Chlorophyll's molecular formula is \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{O}_{5} \mathrm{N}_{4} \mathrm{Mg} \). This notation tells us that each molecule of chlorophyll consists of:

• 55 carbon atoms \( (\mathrm{C}_{55}) \)
• 72 hydrogen atoms \( (\mathrm{H}_{72}) \)
• 5 oxygen atoms \( (\mathrm{O}_{5}) \)
• 4 nitrogen atoms \( (\mathrm{N}_{4}) \)
• 1 magnesium atom \( (\mathrm{Mg}) \)

Breaking down the molecular formula helps in understanding the chemical structure and the types of elements present. Each element plays a significant role in the function and color of the chlorophyll molecule. Understanding this composition is crucial, especially in chemical reactions where specific elements may interact and change.

Avogadro's Number

Avogadro's Number is a fundamental constant in chemistry, denoted as \( 6.022 \times 10^{23} \) particles per mole. This large number allows chemists to count and relate atoms, molecules, and ions to a tangible quantity. When dealing with substances like chlorophyll, Avogadro's Number becomes essential in converting between the number of moles and the number of molecules. This concept links microscopic measurements in chemistry to macroscopic phenomena we observe. In practice, when we are given the number of moles of a substance, multiplying it by Avogadro's Number provides the exact number of molecules present. For example, in the context of chlorophyll in a leaf, knowing the moles per \( \mathrm{cm}^2 \) area allows the calculation of the actual number of chlorophyll molecules present.

Mole Concept

The mole concept is a core principle in chemistry that measures the amount of substance. One mole includes precisely \( 6.022 \times 10^{23} \) elementary entities, such as molecules or atoms, as determined by Avogadro's Number. For the leaf's chlorophyll example, the presence of \( 1.5 \times 10^{-5} \ \text{mol} \) per \( \mathrm{cm}^{2} \) means that within each square centimeter of leaf, this specific quantity of chlorophyll is available. The mole serves as a bridge connecting the atomic scale with the real world measurements. When moles are multiplied by Avogadro's Number, we achieve a graspable quantity—like counting the number of molecules—making complex chemical quantities understandable and usable in experiments and calculations.

Chemical Composition

Understanding chemical composition involves recognizing the elements and their ratios within a compound. The composition dissects a molecule into its constituent atoms and provides insight into chemical behavior and properties.For chlorophyll, its composition \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{O}_{5} \mathrm{N}_{4} \mathrm{Mg} \) illustrates both its complexity and functionality. Each element contributes uniquely:

• Carbon and Hydrogen: Form a backbone and are common in organic molecules.
• Oxygen and Nitrogen: Contribute to polarity and potential for interactions.
• Magnesium: Central in the chlorophyll’s ability to capture light energy.

This chemical composition aids students in appreciating how molecules like chlorophyll support life processes, such as photosynthesis, by understanding their functional components.