Narcotics are chemical substances which produce sleep and unconsciousness. Morphine diacetate is most widely used analgesic . How many double bond equivalents are present in morphine diacetate ?

Answer

To determine the number of double bond equivalents (DBE) in morphine diacetate, we can follow these steps:

### Step 1: Identify the molecular formula of morphine diacetate.
Morphine diacetate has the molecular formula C21H23N O5.

### Step 2: Use the formula for calculating double bond equivalents.
The formula for calculating double bond equivalents (DBE) is:

\[ DBE = C + 1 - \frac{H}{2} - \frac{X}{2} + \frac{N}{2} \]

Where:
- \(C\) = number of carbon atoms
- \(H\) = number of hydrogen atoms
- \(X\) = number of halogen atoms (which is 0 in this case)
- \(N\) = number of nitrogen atoms

### Step 3: Substitute the values into the formula.
From the molecular formula C21H23N O5:
- \(C = 21\)
- \(H = 23\)
- \(X = 0\) (no halogens)
- \(N = 1\)

Now substituting these values into the DBE formula:

\[ DBE = 21 + 1 - \frac{23}{2} - \frac{0}{2} + \frac{1}{2} \]

### Step 4: Simplify the equation.
Calculating step-by-step:

1. Calculate \( \frac{23}{2} = 11.5\)
2. Calculate \( \frac{0}{2} = 0\)
3. Calculate \( \frac{1}{2} = 0.5\)

Now substituting these values back into the equation:

\[ DBE = 21 + 1 - 11.5 + 0 + 0.5 \]

\[ DBE = 22 - 11.5 + 0.5 \]

\[ DBE = 22 - 11 = 10 \]

### Step 5: Conclusion
The number of double bond equivalents in morphine diacetate is **10**.

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