Question

Caffeine (molecular weight \(=194\) ) contains \(28.9 \%\) nitrogen. The number of nitrogen atoms in caffeine molecule is (1) 2 (2) 4 (3) 7 (4) 8

Short answer

There are 4 nitrogen atoms in a caffeine molecule.

Step-by-step solution

Understand Given Values

We are given the molecular weight of caffeine ( weight = \(194 \text{ g/mol} \) and the percentage of nitrogen in caffeine ( 28.9\text{%} ). Our goal is to find the number of nitrogen atoms.

Calculate the Weight of Nitrogen in One Molecule of Caffeine

To determine the weight of nitrogen, multiply the molecular weight of caffeine by the percentage of nitrogen: Weight of Nitrogen = \ = (\(194 \text{ g/mol} \)) \times (\( \frac{28.9}{100} \)) = \(56.066 \text{ g/mol} \)

Find the Number of Nitrogen Atoms

The atomic weight of nitrogen is approximately \(14 \text{ g/mol} \). To find the number of nitrogen atoms:\[ \text{Number of Nitrogen Atoms} = \frac{\text{Weight of Nitrogen}}{\text{Atomic Weight of Nitrogen}} \] Substituting the values: \ Number of Nitrogen Atoms = \( \frac{56.066 \text{ g/mol}}{14 \text{ g/mol}} \) \approx 4 There are 4 nitrogen atoms in a caffeine molecule.

Key concepts

Calculating Molecular Weight

Molecular weight is the sum of the atomic weights of all atoms in a molecule. For caffeine, we are given the molecular weight as 194 g/mol. The molecular weight is crucial for finding other properties like the weight of individual elements within the molecule.
To better understand this, imagine caffeine as a Lego structure where each piece has a specific weight. When combined, these pieces add up to the total molecular weight. Recognizing the molecular weight helps simplify various calculations.

Percentage Composition

Percentage composition helps us understand what portion of a molecule is made up of a specific element. In our problem, 28.9% of caffeine's molecular weight is nitrogen. This is found by identifying the fraction of nitrogen and then expressing it as a percentage:
\[ \text{Percentage of Element =} \frac{\text{Weight of Element in a Molecule}}{\text{Molecular Weight of the Molecule}} \times 100 \]
Understanding this concept is analogous to finding out how much flour is in a cake recipe. It tells us about the relative amounts of components within the molecule, making it easier to pinpoint the molecular contribution of each atom.

Number of Atoms Calculation

To find the exact number of atoms of an element in a molecule, we use both the molecular weight and the percentage composition. For nitrogen in caffeine, we were given that nitrogen makes up 28.9% of caffeine's weight.
We start by calculating the actual weight of nitrogen in one mole of caffeine.
\[ \text{Weight of Nitrogen} = \text{Molecular Weight of Caffeine} \times \frac{\text{Percentage of Nitrogen}}{100} \]
Next, we find out how many nitrogen atoms are present by dividing this weight by the atomic weight of a single nitrogen atom.
\[ \text{Number of Nitrogen Atoms} = \frac{\text{Weight of Nitrogen}}{\text{Atomic Weight of Nitrogen}} \]
This helps us break down the molecule into its elemental components, much like counting individual playing cards.

Atomic Weight

Atomic weight, also known as atomic mass, is the average mass of atoms of an element. For calculations in chemistry, we use the atomic weight to convert between masses and number of atoms. In our problem, nitrogen's atomic weight is 14 g/mol.
This value is essential because it allows us to connect mass (measured in grams) to the actual number of atoms through Avogadro's number (6.022 × 10²³ atoms/mol). Through this conversion, we comprehend how many atoms of a specific element make up a given mass.
Think of atomic weight as the weight of individual nuts in a bag. Knowing the weight of each nut helps us figure out how many nuts are in the bag if we know its total weight.