Question

Question 2: An aqueous solution containing 4.23 g of an optically pure compound, (+)-Porgsareawesome (MW = 213.4 g/mol) was diluted to 700.0 mL with water and placed in a polarimeter tube 15.0 cm long. The measured rotation was +90' at 25.0'C. a) On the answer sheet provided, set up the equation to give the compound's specific T = rotation - you do not need to do any actual math! Hint: Make sure to use proper units. Use the equation at left as your guide: Separately, pure (+)-OneRingToRule Them has a known specific rotation of +120". What would be the observed specific rotation of the following mixtures? b) 25% (+)-One RingToRule Them and 75% (-)-OneRingToRule Them c) 50% (+)-OneRingToRule Them and 50% (-)-OneRingToRule Them d) 66.7% (+)-OneRingToRule Them and 33.3% (-)-OneRingToRule Them (d) +39.6°

Answer 1

The equation to calculate specific rotation is:

$[\alpha ]_{\lambda }^{\theta }=\frac{\alpha }{\gamma \cdot l}$

Where λ is the wavelength of the used light, θ is the temperature (in Celsius), α is the angle the polarized light is rotated, γ is the mass concentration of the solution and l is the optical path length.

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To calculate the rotation of a mixture, we use:

$x_{+}\cdot [\alpha ]_{+}+x_{-}\cdot [\alpha ]_{-}=[\alpha ]_{mixture}$

Where x₊ and x_- are the fraction of the + and - enantiomers, respectively.

b)

$0.25\cdot 120^{o}+0.75\cdot (-120^{o})=-60^{o}$

c)

$0.5\cdot 120^{o}+0.5\cdot (-120^{o})=0$

d)

$66.7\cdot 120^{o}+33.3\cdot (-120^{o})=40.0^{o}$