An octapeptide (Mol.wt `= 516 g`) on complete hydrolysis given glycine and alanine (Mol. Mass `= 89 g`). Alanine contributes `41.59 %` to total weight of hydrolysed product. How many number of alanine unit present in octapeptide.

Explanation

To determine the number of alanine units present in the octapeptide, we will follow these steps:

### Step 1: Understand the Composition of the Octapeptide
An octapeptide consists of 8 amino acids linked by peptide bonds. When hydrolyzed, it will yield a total of 9 amino acids (8 original amino acids + 1 additional from hydrolysis).

### Step 2: Calculate the Total Weight of Hydrolyzed Product
The molecular weight of the octapeptide is given as 516 g. During hydrolysis, 8 molecules of water (each with a molecular weight of 18 g) are added to the total weight. Therefore, the total weight of the hydrolyzed product is:

\[ \text{Total weight} = \text{Molecular weight of octapeptide} + \text{Weight of water} \]
\[ \text{Total weight} = 516 \, \text{g} + (8 \times 18 \, \text{g}) = 516 \, \text{g} + 144 \, \text{g} = 660 \, \text{g} \]

### Step 3: Determine the Contribution of Alanine
We know that alanine contributes 41.59% to the total weight of the hydrolyzed product. Therefore, the weight of alanine in the mixture can be calculated as follows:

\[ \text{Weight of alanine} = 41.59\% \times 660 \, \text{g} = \frac{41.59}{100} \times 660 = 274.51 \, \text{g} \]

### Step 4: Calculate the Number of Alanine Units
The molecular weight of alanine is given as 89 g. To find the number of alanine units, we divide the total weight of alanine by its molecular weight:

\[ \text{Number of alanine units} = \frac{\text{Weight of alanine}}{\text{Molecular weight of alanine}} = \frac{274.51 \, \text{g}}{89 \, \text{g}} \approx 3.08 \]

Since the number of alanine units must be a whole number, we round it to 3.

### Conclusion
The number of alanine units present in the octapeptide is **3**.

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