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27.9: Ion-Cyclotron Resonance

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  • A gaseous ion in a magnetic field moves in a circular orbit with an angular frequency \(\omega_c\) such that \(\omega_c = \left( e/m \right) \left( H_0/c \right)\), in which \(e/m\) is the ratio of charge to mass, \(H_0\) is the applied magnetic field, and \(c\) is the velocity of light. The frequency \(\omega_c\) is called the "cyclotron frequency" and is the basis of the cyclotron particle accelerator used in nuclear physics. Now suppose a radio-frequency field is imposed on the ions from a variable oscillator, as shown in Figure 27-15. When the frequency of the oscillator \(\omega\) equals \(\omega_c\), the ions absorb energy and move faster through larger orbits, but at the same frequency \(\omega_c\).

    Figure 27-15: Detection of ion-cyclotron resonance. When \(\omega = \omega_c\), energy is absorbed by the ions and the ammeter registers a current.

    Ion-cyclotron resonance combines features of mass spectroscopy in that the ratio \(e/m\) is involved, and of NMR spectroscopy in that detection depends on absorption of energy from a radio-frequency oscillator. The chemical applications depend on reactions between the ions during the time they remain in the cyclotron, which may be many seconds. Suppose then that we generate \(\ce{OH}^\ominus\) by electron bombardment of a gaseous mixture of water and 2-methyl-2-propanol (tert-butyl alcohol). The \(\ce{OH}^\ominus\) ion can be detected by its characteristic frequency \(\omega = \left( e/m \right) \left( H_0/c \right)\), in which \(e/m = 1/17\). Now, because the reaction \(\ce{(CH_3)_3COH} + \ce{OH}^\ominus \rightarrow \ce{(CH_3)_3CO}^\ominus + \ce{H_2O}\) occurs, a new ion of \(e/m = 1/73\) appears. The reverse reaction, \(\ce{(CH_3)_3CO}^\ominus + \ce{H_2O} \rightarrow \ce{(CH_3)_3COH} + \ce{OH}^\ominus\), does not occur to a measurable extent. From this we can infer that \(\ce{(CH_3)_3COH}\) is a stronger acid than \(\ce{H_2O}\) in the gas phase. These experiments clearly are related to chemical-ionization mass spectroscopy (Section 27-7), and provide the basis for determining the gas-phase acidities of alkynes and water, discussed in Section 11-8. A detailed gas-phase acidity scale has been established by this means.

    Many unusual reactions occur between ions and neutral molecules in the gas phase, which can be detected by ion-cyclotron resonance; a few examples are

    \[\ce{CH_3F^+} \: \text{(from electron impact)} + \ce{CH_3F} \rightarrow \ce{CH_3} \overset{+}{\ce{F}} \ce{H} + \cdot \ce{CH_2F} \: \text{(} \ce{H} \cdot \: \text{atom transfer)}\]

    \[\ce{CH_3FH^+} + \ce{N_2} \rightarrow \ce{CH_3N_2^+} + \ce{HF} \: \: \: \: \: \text{(nucleophilic displacement)}\]

    \[\ce{CH_3FH^+} + \ce{Xe} \rightarrow \ce{CH_3Xe^+} + \ce{HF} \: \: \: \: \: \text{(nucleophilic displacement)}\]

    Clearly, in gas-phase reactions \(\ce{HF}\) is an extremely good leaving group in being rapidly displaced both by \(\ce{Xe}\) and \(\ce{N_2}\). From our discussions of leaving groups in Section 8-7C, we can infer that \(\ce{H_2F}^\oplus\) must be a very strong acid in the gas phase and the available evidence indicates that this is so.

    It is possible to measure the concentrations of the ions as a function of time and thus determine the rates of reaction of ions with neutral molecules in the gas phase. Figure 27-16 shows the results of a typical experiment wherein a sequence of reactions occurs that involves chloromethane as the neutral molecule and begins with the ion \(\ce{CH_3Cl}^\oplus\) formed by a short burst \(\left( 10 \: \text{msec} \right)\) of \(16 \: \text{KeV}\) electrons. The originally formed \(\ce{CH_3Cl}^\oplus\) ions react with \(\ce{CH_3Cl}\) to yield \(\ce{CH_3ClH}^\oplus + \cdot \ce{CH_2Cl}\). The buildup of \(\ce{CH_3ClH}^\oplus\) and the disappearance of \(\ce{CH_3Cl}^\oplus\) clearly are coupled. A slower reaction, \(\ce{CH_3ClH}^\oplus + \ce{CH_3Cl} \rightarrow \ce{(CH_3)_2Cl}^\oplus + \ce{HCl}\), then takes over the action.

    Figure courtesy of Dr. J. L. Beauchamp)

    Contributors and Attributions

    John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."