Ninhydrin having molecular formula `C_9H_6O_4`, is commonly used by forensic scientists to detect and analyse fingerprints. The number of molecules in 7.4 g of ninhydrin is
(Atomic mass of C = 12 u, H = 1 u, O = 16 u)

Options

A. `1.5 xx 10^(22)`
B. `2.5 xx 10^(23)`
C. `2.5 xx 10^(22)`
D. `4.2 xx 10^(23)`

Explanation

To find the number of molecules in 7.4 g of ninhydrin (C₉H₆O₄), we will follow these steps:

### Step 1: Calculate the Molar Mass of Ninhydrin
The molecular formula of ninhydrin is C₉H₆O₄. We need to calculate its molar mass using the atomic masses provided.

- Carbon (C): 9 atoms × 12 u = 108 u
- Hydrogen (H): 6 atoms × 1 u = 6 u
- Oxygen (O): 4 atoms × 16 u = 64 u

Now, add these values together to find the molar mass:
\[ \text{Molar Mass} = 108 + 6 + 64 = 178 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles in 7.4 g of Ninhydrin
To find the number of moles (n) in 7.4 g of ninhydrin, use the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ n = \frac{7.4 \text{ g}}{178 \text{ g/mol}} \approx 0.04157 \text{ moles} \]

### Step 3: Calculate the Number of Molecules
To find the number of molecules, use Avogadro's number (Nₐ = 6.022 × 10²³ molecules/mol):
\[ \text{Number of molecules} = n \times N_a \]
Substituting the values:
\[ \text{Number of molecules} = 0.04157 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 2.5 \times 10^{22} \text{ molecules} \]

### Final Answer
The number of molecules in 7.4 g of ninhydrin is approximately \(2.5 \times 10^{22}\) molecules.

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