Chemistry 3730 Fall 2000 Quiz 4

Name:

Note: You should start the computations for questions 1-3 while you work on question 4.

1.

Perform a geometry optimization on trans-2-butene

at the 3-21G level. Report the energy, bond lengths, and the C-C=C bond angle. [7 marks]

Suggestion: To avoid disasters, save your structure to disk after the computation.

$E = \underline{\hspace{3.5cm}}$kcal/mol	C-C: Å
CH3 C-H: Å	C=C: Å
=C-H: Å	C-C=C angle: $^\circ$

 

2.

Repeat the calculation for cis-2-butene:

Are there significant quantitative differences (other than the obvious change in stereochemistry) between the two structures? Discuss briefly. [10 marks]

$E = \underline{\hspace{3.5cm}}$kcal/mol	C-C: Å
CH3 C-H: Å	C=C: Å
=C-H: Å	C-C=C angle: $^\circ$

3.

Compute $\Delta E$ for the reaction $\textrm{cis-2-butene}\rightarrow\textrm{trans-2-butene}$. For a simple gas-phase isomerization such as this one, $\Delta H = \Delta E$. The experimental value of $\Delta H$ for this reaction is $-1.0\,\mathrm{kcal/mol}$. How does your value compare? Is the agreement (or lack thereof) expected? [5 marks]  

4.

The rotational absorption spectrum of 1H35Cl consists of a series of roughly equally spaced lines separated by $20.51\pm 0.19\,\mathrm{cm}^{-1}$. What is the bond length? [10 marks]

Notes: Don't bother propagating the uncertainty unless you're curious about the uncertainty in the bond length. The rotational selection rule is $\Delta J=\pm 1$. The rotational energy of a diatomic molecule is given by

$$E_J = J(J+1)\frac{\hbar^2}{2\mu R^2}.$$

The isotopic masses of 1H and of 35Cl are, respectively, 1.0078250321 and 34.96885271amu. The reduced mass is defined by

$$\frac{1}{\mu} = \frac{1}{m_1}+\frac{1}{m_2}.$$

Finally, $\hbar = 1.054\,571\,60\times 10^{-34}\,\mathrm{J\,s}$, the atomic mass unit corresponds to $1.660\,538\,73\times 10^{-27}\,\mathrm{kg}$ and $1\,\mathrm{cm}^{-1}$ is $1.986\,445\,44\times 10^{-23}\,\mathrm{J}$.