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Calculate the specific rotation of glucose given the observed rotation, mass, volume, and path length.

Chemistry

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Answer

A\text{A}

Step-by-step solution

5 steps
  1. Identify the given values.

    Observed rotation (α\alpha) = +13.6∘+13.6^\circ
    Mass of glucose = 8 g8 \text{ g}
    Volume of methanol = 100 mL100 \text{ mL}
    Path length of polarimeter tube (ll) = 2 dm2 \text{ dm}

  2. Calculate the concentration (cc) of the glucose solution.

    The concentration is given in g/mL.

    c=mass of solutevolume of solution=8 g100 mL=0.08 g/mLc = \frac{\text{mass of solute}}{\text{volume of solution}} = \frac{8 \text{ g}}{100 \text{ mL}} = 0.08 \text{ g/mL}
  3. Use the formula for specific rotation.

    The specific rotation [α][\alpha] is calculated using the formula:

    [α]=αl⋅c[\alpha] = \frac{\alpha}{l \cdot c}

    where α\alpha is the observed rotation, ll is the path length in decimeters (dm), and cc is the concentration in g/mL.

  4. Substitute the values and calculate the specific rotation.

    [α]=+13.6∘2 dm×0.08 g/mL[\alpha] = \frac{+13.6^\circ}{2 \text{ dm} \times 0.08 \text{ g/mL}} [α]=13.60.16[\alpha] = \frac{13.6}{0.16} [α]=85[\alpha] = 85

    The specific rotation of glucose is 85∘ dm−1(g/mL)−185^\circ \text{ dm}^{-1} (\text{g/mL})^{-1}.

  5. Compare the result with the given options.

    The calculated specific rotation is 85. This matches option (A).

    The final answer is A\text{A}

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