To determine the molecular formula of the new drug Alanine (C\(_5\)H\(_8\))\(_n\)O\(_5\) with a relative molecular mass of 284, we need to find the molar mass of the repeating unit and how many of those units fit into the given molecular mass.
First, let's calculate the molar mass of the repeating unit (C\(_5\)H\(_8\)O\(_5\)):
- Carbon (C): 12.01 g/mol × 5 = 60.05 g/mol
- Hydrogen (H): 1.008 g/mol × 8 = 8.064 g/mol
- Oxygen (O): 16.00 g/mol × 5 = 80.00 g/mol
Now, summing these values gives us the molar mass of the repeating unit:
\[ \text{Molar mass of } C_5H_8O_5 = 60.05 + 8.064 + 80.00 = 148.114 \text{ g/mol} \]
Next, we determine how many of these repeating units (n) make up the molecular mass of 284:
\[ n = \frac{284 \text{ g/mol}}{148.114 \text{ g/mol}} \approx 1.916 \]
This tells us that the structure might contain two repeating units (since n typically must be an integer).
To find out the total molecular formula, we multiply the number of each atom in the repeating unit by 2:
\[ \text{Molecular formula} = C_{5 \times 2}H_{8 \times 2}O_{5 \times 2} = C_{10}H_{16}O_{10} \]
Thus, the molecular formula of Alanine is:
\[ \text{C}{10}\text{H}{16}\text{O}_{10} \]
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