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Calculate the specific rotation of (R)-2-methylbutanol given the observed rotation, mass, volume, and path length.

Chemistry

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Answer

A\text{A}

Step-by-step solution

6 steps
  1. Identify the given values.

    Observed rotation (α\alpha) = +2.3∘+2.3^\circ
    Mass of (R)-2-methylbutanol = 10.0 g10.0 \text{ g}
    Volume of solution = 50 mL50 \text{ mL}
    Path length of polarimeter tube (ll) = 20 cm20 \text{ cm}

  2. Convert the path length to decimeters (dm).

    l=20 cm×1 dm10 cm=2 dml = 20 \text{ cm} \times \frac{1 \text{ dm}}{10 \text{ cm}} = 2 \text{ dm}
  3. Calculate the concentration (cc) of the solution in g/mL.

    c=mass of solutevolume of solution=10.0 g50 mL=0.2 g/mLc = \frac{\text{mass of solute}}{\text{volume of solution}} = \frac{10.0 \text{ g}}{50 \text{ mL}} = 0.2 \text{ g/mL}
  4. 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.

  5. Substitute the values and calculate the specific rotation.

    [α]=+2.3∘2 dm×0.2 g/mL[\alpha] = \frac{+2.3^\circ}{2 \text{ dm} \times 0.2 \text{ g/mL}} [α]=2.30.4[\alpha] = \frac{2.3}{0.4} [α]=5.75[\alpha] = 5.75

    The specific rotation of (R)-2-methylbutanol is 5.75∘ dm−1(g/mL)−15.75^\circ \text{ dm}^{-1} (\text{g/mL})^{-1}.

  6. Compare the result with the given options.

    The calculated specific rotation is 5.75. This matches option (A).

    The final answer is A\text{A}

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