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Chapter 14: Problem 6

The chlorophyll-a molecule \(\left(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\right)\) is important in photosynthesis. (a) Determine its molecular mass (in atomic mass units). (b) What is the mass (in grams) of 3.00 moles of chlorophyll-a molecules?

Short Answer

Expert verified
(a) 893.62 u; (b) 2680.86 g

Step by step solution

01

Identify Atomic Masses

To calculate the molecular mass, we need the atomic masses of each element in the molecular formula. These are typically: Carbon (C) = 12.01 u, Hydrogen (H) = 1.01 u, Magnesium (Mg) = 24.31 u, Nitrogen (N) = 14.01 u, Oxygen (O) = 16.00 u.
02

Calculate Individual Contributions

For each element in the formula \(\text{C}_{55} \text{H}_{72} \text{Mg} \text{N}_{4} \text{O}_{5}\), calculate the contribution to the molecular mass: - Carbon: \(55 \times 12.01 = 660.55\)- Hydrogen: \(72 \times 1.01 = 72.72\)- Magnesium: \(1 \times 24.31 = 24.31\)- Nitrogen: \(4 \times 14.01 = 56.04\)- Oxygen: \(5 \times 16.00 = 80.00\).
03

Calculate Total Molecular Mass

Add all the contributions together: \[660.55 (C) + 72.72 (H) + 24.31 (Mg) + 56.04 (N) + 80.00 (O) = 893.62\ \text{u}\]. Thus, the molecular mass of chlorophyll-a is 893.62 u.
04

Use Avogadro's Number

Now, to find the mass of 3.00 moles of chlorophyll-a, use the relation that 1 mole of a substance has a mass equivalent to its molecular mass in grams, by using Avogadro's number \(6.022 \times 10^{23} \text{ entities per mole}\).
05

Calculate Mass of 3.00 Moles

The mass of one mole of chlorophyll-a is 893.62 grams. Therefore, the mass of 3 moles is calculated as follows: \[3.00 \times 893.62 \text{ g} = 2680.86 \text{ g}\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Mass Units (AMU)
Atomic Mass Units (AMU) are a standard way of expressing the masses of atoms and molecules. They allow us to compare the weight of different atoms by providing a unified mass scale.
  • An atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom.
  • It's a very small unit, which makes it suitable for dealing with atoms and molecules.
  • Each element has its unique atomic mass in AMU, reflecting its isotopic composition and natural abundance.
In the context of chlorophyll-a, knowing the atomic masses (like Carbon = 12.01 u, Hydrogen = 1.01 u, etc.) helps calculate the total molecular mass by adding the contributions of each atom in the chemical formula.
Moles Calculation
Moles are a fundamental concept in chemistry. They provide a bridge between the atomic scale and the macroscopic world we observe.
  • A mole is a specific number of particles, represented by Avogadro's number: approximately \(6.022 \times 10^{23}\).
  • This is similar to how we use the term "dozen" to mean 12 items.
  • In chemistry, moles are used to express amounts of a chemical substance.
In the exercise, to find the mass of 3.00 moles of chlorophyll-a, we multiply the number of moles by the molecular mass. This conversion is essential for practical applications in laboratory settings, such as weighing chemical substances.
Chemical Formula Interpretation
Interpreting a chemical formula is crucial for understanding the composition of a molecule. It tells us how many of each type of atom are present.
  • For example, the chlorophyll-a molecule is given as \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\).
  • This indicates 55 Carbon atoms, 72 Hydrogen atoms, 1 Magnesium atom, 4 Nitrogen atoms, and 5 Oxygen atoms per molecule.
  • Understanding the formula enables calculations like determining the molecular mass or reactants required in a chemical reaction.
These interpretations are essential for converting between different chemical units and predicting the behavior of molecules in different environments.
Avogadro's Number
Avogadro's Number is a fundamental constant in chemistry that represents the number of atoms, ions, or molecules in one mole of a substance.
  • This number is \(6.022 \times 10^{23}\), which is astronomically large.
  • It allows chemists to count particles by weighing them.
  • By knowing how many molecules are in a mole, chemists can easily convert measurements from the molecular scale to the macroscopic scale.
In our example, using Avogadro's number allows us to find the mass of several moles of chlorophyll-a by acknowledging that the molecular mass in AMU matches the mass in grams for one mole. This connection is vital for experiments and calculations in both laboratory and industrial chemistry.

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Most popular questions from this chapter

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