PHYSICAL CHEMISTRY

R. F. VASIL’EV and A. A. VICHUTINSKII

A CHEMILUMINESCENT METHOD FOR MEASURING RATIOS OF ELEMENTARY CONSTANTS IN REACTIONS OF LIQUID-PHASE OXIDATION OF HYDROCARBONS

(Presented by Academician V. N. Kondrat’ev, February 28, 1962)

1. We have established \((^{1})\) that the enhancement of chemiluminescence by oxygen \((^{2,3})\) is associated with the appearance of peroxide radicals in the chemical system and with high light yields upon their recombination. In carrying out the initiated oxidation of liquid hydrocarbons in a sealed vessel, a sharp attenuation occurs of the chemiluminescence accompanying this reaction. In the present work it is proposed to use this phenomenon as a method for measuring \(w_{\mathrm{O}_2}\) and \([\mathrm{O}_2]_0\).

2. The reactions of liquid-phase oxidation of hydrocarbons are chain reactions. The radicals carrying the chain are the hydrocarbon radical \(\mathrm{R}\) and the peroxide radical \(\mathrm{RO}_2\). The reaction scheme is a sequence of the following elementary processes \((^{4})\):

\[ \text{Chain initiation (appearance of radicals R) at rate } w_i \tag{1} \]

\[ \text{chain}\left\{ \begin{aligned} \mathrm{R}+\mathrm{O}_2 &\xrightarrow{k_2} \mathrm{RO}_2 \tag{2}\\ \mathrm{RO}_2+\mathrm{RH} &\xrightarrow{k_3} \mathrm{ROOH}+\mathrm{R} \tag{3} \end{aligned} \right. \]

\[ \text{chain termination}\left\{ \begin{aligned} \mathrm{R}+\mathrm{R} &\xrightarrow{k_4} \text{inactive products} \tag{4}\\ \mathrm{R}+\mathrm{RO}_2 &\xrightarrow{k_5} \text{inactive products} \tag{5}\\ \mathrm{RO}_2+\mathrm{RO}_2 &\xrightarrow{k_6} \text{inactive products}+\mathrm{O}_2 \tag{6} \end{aligned} \right. \]

For most hydrocarbons the constant \(k_2\) is so large (practically coinciding with the collision number) that even at very low \((\sim 10^{-6}\ \mathrm{mol/l})\) concentrations of \(\mathrm{O}_2\) all hydrocarbon radicals are replaced by peroxide radicals. This makes it possible not to take into account the termination reactions (4) and (5), to regard \([\mathrm{RO}_2]\) and \(w_{\mathrm{O}_2}\) as independent of the oxygen concentration down to very low values of it, and to consider that the moment of decay of the luminescence \(t_{\mathrm{sp}}\) practically coincides with the moment of complete consumption of \(\mathrm{O}_2\) in the system, i.e.,

\[ t_{\mathrm{sp}} = [\mathrm{O}_2]_0 / w_{\mathrm{O}_2}. \tag{7} \]

This equation makes it possible to use the reaction time as a measure of the reaction rate or of the oxygen concentration.

3. Determination of the ratios of elementary constants \(k_3/\sqrt{k_6}\) and of the concentration of \(\mathrm{O}_2\) in hydrocarbon oxidation reactions.* From scheme (1)—(6) it is not difficult to obtain:

\[ w_{\mathrm{O}_2} = -\frac{d[\mathrm{O}_2]}{dt} = \frac{k_3}{\sqrt{k_6}}\sqrt{w_i}\,[\mathrm{RH}] + \frac{1}{2}w_i. \tag{8} \]

This equation was used by Russell \((^{5})\) to measure the ratio \(k_3/\sqrt{k_6}\) for ethylbenzene and cumene. Substituting (8) into (7):

\[ \frac{1}{t_{\mathrm{sp}}} = \frac{w_{\mathrm{O}_2}}{[\mathrm{O}_2]_0} = \frac{k_3}{\sqrt{k_6}} \frac{\sqrt{w_i}}{[\mathrm{O}_2]_0}[\mathrm{RH}] + \frac{w_i}{2[\mathrm{O}_2]_0}. \tag{9} \]

It follows from equation (9) that, by measuring the reaction time \(t_{\mathrm{sp}}\) at different hydrocarbon concentrations and plotting a graph in the coordinates \(1/t_{\mathrm{sp}}—[\mathrm{RH}]\), one can find \(k_3/\sqrt{k_6}\) and \([\mathrm{O}_2]_0\). The ratio \(k_3/\sqrt{k_6}\) determines the oxidation rate of the given hydrocarbon (see equation (8)) and therefore is a very important kinetic characteristic of the substance.

* The authors express their gratitude to Ya. P. Stradyn’ (Institute of Organic Synthesis, Academy of Sciences of the Latvian SSR), who took part in the work.

To check the applicability of equation (9), experiments were carried out with ethylbenzene and cumene, for which the quantities of interest to us are known.

Initiation was performed by decomposition of $\alpha,\alpha'$-azobisisobutyronitrile (AIBN)

\[ \mathrm{r}_0 - \mathrm{N} = \mathrm{N} - \mathrm{r}_0 \quad \left(\mathrm{r}_0 = (\dot{\mathrm{C}}\mathrm{H}_3)_2 \dot{\mathrm{C}}\mathrm{CN}\right) \]

(the procedure for carrying out the experiments and the photometric apparatus are described in papers (1, 6)).

Fig. 1. “Cold flashes” of chemiluminescence in the chlorobenzene–ethylbenzene system—AIBN at different ethylbenzene concentrations. The mixture was saturated with oxygen by blowing with dried air. Solvent: chlorobenzene. Constant temperature of the system: 10 sec. $[\mathrm{RH}]$: $a$ — 0.078; $b$ — 0.234; $c$ — 0.391; $d$ — 0.548; $e$ — 0.704; $f$ — 0.781 mol/l.

Figure 1 shows kinetic curves of chemiluminescence recorded at different concentrations of ethylbenzene at 60° and at a constant initiation rate

\[ (w_i = 1.9 \cdot 10^{-7}\ \mathrm{mol/l\cdot sec}). \]

A gradual shortening of the reaction time is clearly observed, associated with an increase in the rate of hydrocarbon oxidation as its concentration is increased. The results of this and other series of experiments are presented in Fig. 2. The linear dependence required by equation (9) is well obeyed beginning with an ethylbenzene concentration of 0.2 mol/l. An attempt to use this equation to calculate $k_3/\sqrt{k_6}$ and $[\mathrm{O}_2]_0$, however, proved unsuccessful: the ratio of constants came out three times smaller, while the oxygen concentration was three times larger.

We assumed that the discrepancy arises because, in scheme (1)—(6), the reactions with oxygen of the primary radicals formed during decomposition of the initiator are not taken into account. If it is assumed that the radical $\dot{R}$ appears in the system as a result of the following sequence of reactions:

\[ w_i \to \mathrm{r}_0, \tag{1'} \]

\[ \mathrm{r}_0 + \mathrm{O}_2 \to \mathrm{r}_0\mathrm{O}_2, \tag{2'} \]

\[ \mathrm{r}_0\mathrm{O}_2 + \mathrm{RH} \to \mathrm{r}_0\mathrm{OOH} + \dot{\mathrm{R}}, \tag{3'} \]

Table 1

The ratio \(k_3/\sqrt{k_6}\) and the concentration of dissolved oxygen at 60°

then equations (8) and (9) take the form:

\[ w_{O_2}=\frac{k_3}{\sqrt{k_6}}\sqrt{w_i}\,[\mathrm{RH}]+\frac{3}{2}w_i, \tag{10} \]

\[ \frac{1}{t_{\mathrm{sp}}} = \frac{k_3}{\sqrt{k_6}}\frac{\sqrt{w_i}}{[O_2]_0}[\mathrm{RH}] +\frac{3}{2}\frac{w_i}{[O_2]_0}. \tag{11} \]

Calculations of the quantities \(k_3/\sqrt{k_6}\) and \([O_2]_0\) by equation (11) lead to their correct values, given in Table 1.* Thus, it may be considered established that the primary radical \(r_0\) first adds an \(O_2\) molecule, and only then does the radical \(r_0O_2\) react with a hydrocarbon molecule, abstracting an H atom from it.

Fig. 2. Dependence of the reciprocal reaction time on the concentration of ethylbenzene (1, 2), n-heptane (3), and n-decane (4) in chlorobenzene (1) and benzene (2, 3, 4) at the following values of the initiation rate (in mol/l·sec) at 60°: 1, 2 — \(1.9\cdot10^{-7}\); 3 — \(6.3\cdot10^{-7}\); 4 — \(7.5\cdot10^{-7}\).

1. If there is no hydrocarbon in the system (\([\mathrm{RH}]=0\)), then the radicals \(r_0O_2\) participate only in the recombination reaction:

\[ r_0O_2+r_0O_2 \xrightarrow{k'_6} \text{products } (+O_2?) \tag{6′} \]

and the rate of consumption of \(O_2\) is equal to \(w_i\) or \(\frac{1}{2}w_i\), depending on whether or not \(O_2\) is evolved in the elementary process (6′). We have shown (see Table 2) that \(O_2\) is not evolved in reaction (6′) \((w_{O_2}=w_i)\), and

\[ [O_2]_0=w_{O_2}t_{\mathrm{sp}}=w_i t_{\mathrm{sp}}. \tag{12} \]

1. The value of \(k_3/\sqrt{k_6}\) for the normal paraffins n-heptane and n-decane could not be determined: it is so small that the straight line runs parallel to the abscissa axis (see Fig. 2). However, the ratio of the ordinates is close to 1.5. This means that the primary peroxide radicals \(r_0O_2\) abstract an H atom from the hydrocarbon, forming the radical R, which is then converted into \(RO_2\). But the radicals \(RO_2\) are much weaker than \(r_0O_2\): they cannot abstract an H atom from the hydrocarbon at the given temperature (60°) and recombine, evolving an \(O_2\) molecule.

2. Dividing equation (11) by \(\sqrt{w_i}\), we obtain:

\[ \frac{1}{t_{\mathrm{sp}}\sqrt{w_i}} = \frac{k_3}{\sqrt{k_6}}\frac{[\mathrm{RH}]}{[O_2]_0} +\frac{3}{2}\frac{\sqrt{w_i}}{[O_2]_0}. \tag{13} \]

* In work (⁵), an inaccurate formula (8) was used; however, for the chains in question the values of \(k_3/\sqrt{k_6}\) were close to the true values, since the term \(\frac{1}{2}w_i\) played the role of a small correction.

Table 2

Determination of the concentration of \(O_2\) by the chemiluminescent method in benzene at \(60^\circ\) according to the formula \([O_2]_0 = w_i t_{\mathrm{sp}}\)

* Calculated from tables (9, 10).

Equation (13), obviously, can also be used to determine \(k_3/\sqrt{k_6}\) and \([O_2]_0\), if experiments are carried out by varying the rate of initiation and keeping the hydrocarbon concentration constant (see Table 1).

1. The rate of initiation can be found independently by means of the chemiluminescent method if the solubility of oxygen is known: for example, in an inert solvent \(w_i = [O_2]_0/t_{\mathrm{sp}}\).

2. The kinetics of the “oxygen decay” of chemiluminescence was calculated according to scheme (1)—(6) with the aid of an electronic computer (11). It was shown that the slowing of oxidation at the end of the reaction (near the decay) lowers the oxidation rate determined by the chemiluminescent method, but only very slightly (by no more than 0.5–1.5%), and this is easy to take into account. Random errors in measuring the reaction time are determined by the quality of thermostating and do not exceed 1–2% (at \(\Delta t = \pm 0.03^\circ\)).

Measurements of the kinetics of chemiluminescence intensity can be used to determine the ratio of constants \(k_2/\sqrt{k_4}\) and the relative efficiency of oxidation inhibitors.

1. Thus, the chemiluminescent method, having the same accuracy as the manometric method, in which the decrease in the pressure of \(O_2\) above the reaction mixture is used to measure the oxidation rate, has clear advantages in those cases where application of the manometric method is difficult: in viscous solvents, at high vapor pressures of the reactants, in reactions proceeding with the formation of volatile and gaseous products, etc. The simplicity of the chemical part of the apparatus should be noted: it is a glass vessel with a jacket for passing water from a thermostat and with a well-ground stopper. The measurements introduce no changes into the chemical system. The recording part of the apparatus is also not very complex, since only standard instruments produced by industry are used in it (6).

The limits of applicability of the chemiluminescent method can be shifted toward lower glow intensities (i.e., lower concentrations and temperatures) by introducing activators—substances that intensify the glow through more efficient conversion of the reaction energy into radiation (12).

Institute of Chemical Physics
Academy of Sciences of the USSR

Received
21 II 1962

CITED LITERATURE

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