The observed rotation of 2.0 gm of a compound iin 10 mL solution in a 25 cm long prolarimeter tube + `13.4^(@)`. The specific roration of compound is :

Options

A. `+30.2^(@)`
B. `-26.8^(@)`
C. `+26.8^(@)`
D. `+40.2^(@)`

Answer

To calculate the specific rotation of the compound, we can use the formula for specific rotation:

\[ [\alpha] = \frac{\alpha}{c \cdot l} \]

Where:
- \([\alpha]\) = specific rotation
- \(\alpha\) = observed rotation (in degrees)
- \(c\) = concentration of the solution (in grams per mL)
- \(l\) = path length of the polarimeter tube (in decimeters)

### Step 1: Identify the given values
- Observed rotation, \(\alpha = 13.4^\circ\)
- Mass of the compound = 2.0 g
- Volume of the solution = 10 mL
- Length of the polarimeter tube, \(l = 25 \text{ cm} = 2.5 \text{ dm}\)

### Step 2: Calculate the concentration \(c\)
The concentration \(c\) can be calculated using the formula:

\[ c = \frac{\text{mass of solute}}{\text{volume of solution}} \]

Substituting the values:

\[ c = \frac{2.0 \text{ g}}{10 \text{ mL}} = 0.2 \text{ g/mL} \]

### Step 3: Substitute the values into the specific rotation formula
Now we can substitute the values into the specific rotation formula:

\[ [\alpha] = \frac{13.4^\circ}{0.2 \text{ g/mL} \cdot 2.5 \text{ dm}} \]

### Step 4: Calculate specific rotation
Calculating the denominator:

\[ 0.2 \text{ g/mL} \cdot 2.5 \text{ dm} = 0.5 \text{ g} \]

Now substituting back into the formula:

\[ [\alpha] = \frac{13.4^\circ}{0.5} = 26.8^\circ \text{ g}^{-1} \text{ mL} \text{ dm}^{-1} \]

### Final Answer
The specific rotation of the compound is:

\[ [\alpha] = 26.8^\circ \text{ g}^{-1} \text{ mL} \text{ dm}^{-1} \]

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