Answer all questions in this section.

1.

The following reactions occur in the gas phase:

$$\mathrm{CH_3NO_{2(g)}} + \mathrm{HNO_{3(g)}} \rightarrow 2\m... ...3OH_{(g)}} \eqno{\Delta\bar{H}^\circ = 66.48\,\mathrm{kJ/mol}}$$

$$\mathrm{CH_3NO_{2(g)}} + \mathrm{HCl_{(g)}} \rightarrow \mat... ..._3OH_{(g)}} \eqno{\Delta\bar{H}^\circ = 8.95\,\mathrm{kJ/mol}}$$

When NO₂ and hydrogen chloride react in the gas phase, the products are HNO₃ and NOCl. What is the enthalpy change in this reaction? [5 marks]

2.

Silver (I) oxide dissociates into its elements. Calculate the partial pressure of oxygen which would be in equilibrium with silver oxide at $25^\circ\mathrm{C}$. [8 marks]

3.

Calcium carbonate decomposes under certain conditions to calcium oxide and carbon dioxide.

(a)

Is calcium carbonate stable with respect to calcium oxide and carbon dioxide at $25^\circ\mathrm{C}$ under normal atmospheric conditions? The pressure of carbon dioxide in normal air is $3.3\times 10^{-4}\,\mathrm{bar}$. [7 marks]

(b)

Calcium oxide is an enormously important industrial chemical used in steel production, in water treatment, and in the pulp and paper industry, among other applications. It has traditionally been produced by heating calcium carbonate to a high temperature. Assuming that the partial pressure of carbon dioxide is $3.3\times 10^{-4}\,\mathrm{bar}$, what is the minimum temperature (in degrees Celsius) at which the decomposition reaction becomes spontaneous? [10 marks]

Hints: Although the operating temperature may seem rather high, an approximation which we have used for temperatures near standard still gives very good results. You need to simultaneously consider two factors which affect spontaneity to solve this problem.

4.

Suppose that a nitrogen molecule is traveling at 500m/s and that its speed has been measured to an accuracy of 1%. Estimate the resulting minimum uncertainty in the position. Considering that molecules have typical dimensions of about $10^{-10}\,\mathrm{m}$, is this a large uncertainty? [5 marks]

5.

The Lyman series is a series of lines in the emission spectrum of hydrogen corresponding to transitions to the ground state of the atom. The longest wavelength line in the Lyman series has a wavelength of 121.57nm. What is the value of Rydberg's constant? [7 marks]

6.

Recall that $K_\alpha$ X rays result from a transition in which an electron's principal quantum number changes from n=2 to n=1 in a multielectron atom. The frequency of $K_\alpha$ radiation obeys the following empirical relationship:

$$\nu = a(Z-b)^2$$

where Z is the atomic number and $b\approx 1$. Give a rationalization for this value of b based on your knowledge of atomic structure. [3 marks]

7.

Predict the ground-state electronic configuration of rhenium (Re). Also predict the stable ions of this metal. Are the ions paramagnetic? [6 marks]

8.

The Bohr theory of the atom makes some correct predictions but also gets some things wrong. Give an example of something that is correctly predicted by the Bohr theory. Also present an example of something which the Bohr theory does not correctly describe. Briefly explain each of your examples. [6 marks]

9.

Use a simple argument based on LCAO theory to predict whether or not He₂⁺ is likely to be a stable molecule under normal conditions. [4 marks]

10.

Does N₂ have a vibrational absorption spectrum? Briefly explain your reasoning. [2 marks]

11.

The rotational Raman spectrum of $\isotope{1}{}{H}_2$ consists of a series of lines separated by 3649.3GHz while the rotational Raman spectrum of $\isotope{2}{}{H}_2$ displays a line separation of 1825.3GHz. The isotopic masses of $\isotope{1}{}{H}$ and of $\isotope{2}{}{H}$ are, respectively, 1.007825 and 2.014102amu. Compute the bond lengths of both of these molecules. Are they significantly different? [12 marks]