A student measured the optical rotation of his sample at two different concentrations. At 0.14 g/mL, he measured áD at –12°. At 0.07 g/mL, he measured áD = +174°. What would the measurement be at 0.28 g/mL?
For 0.07 g/mL the reading is + 174.
For 0.14 (twice that) the reading would be 174+174 = 348 so the reading will be 360-348=-12 (which is listed in the problem). Therefore, the next higher concn of 2x will be -12*2 = -24 OR
348+348=696 and
696-360=336 and 336 is -24 from 360.
Check my thinking.
To find the measurement at 0.28 g/mL, we can use a mathematical relationship called the specific rotation. The specific rotation (α) is a characteristic property of a substance and is given by the equation:
α = αD / c * l
Where:
α is the specific rotation in degrees per (g/mL) * cm
αD is the observed rotation in degrees
c is the concentration in g/mL
l is the length of the tube or path length in cm
In this case, the student has measured the specific rotation (αD) at two different concentrations, 0.14 g/mL and 0.07 g/mL. We can set up a ratio to find the change in specific rotation with respect to concentration:
(αD1 / c1) = (αD2 / c2)
Let's substitute the values we know into this equation:
(–12° / 0.14 g/mL) = (+174° / 0.07 g/mL)
Now, we can solve for the change in specific rotation:
(–12° / 0.14 g/mL) = (α / 0.28 g/mL)
Cross-multiplying the equation:
–12° * 0.28 g/mL = α
α = –3.36° g/mL
Therefore, the measurement at 0.28 g/mL would be –3.36°.