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6.5:Ⅹ=3.25:4
6.5:Ⅹ=3.25:4
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.5:Ⅹ=3.25，本题已解答、，你好:4x=6.5x4÷3.25x=8
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-1/2,2/5,-3/10,4/17,6/37我已解决部分为,（-1）^n*(n)/(1+n^2),但是不知到第六项的分子是否可能是8,不知原因,后来想一想,也认为孩子老师出的题可能错了.不过也要感谢丁配龙的答案.
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楼主的题目明显错了,第五项应该是 5/26.楼主通项公式是对的,按公式计算第六项为6/37,所以分子当然不可能是8.如果题目没错,根本不可能,那就总结不出通项公式了,所以题目肯定错了.
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Journal of ChemistryVolume ), Article ID
pagesResearch Article
-Promoted Solvent-Free Synthesis of Benzoxazoles, Benzimidazoles, and Benzothiazole Derivatives,1 ,2 and 11Research and Development Division, RA Chem Pharma Limited, Prasanth Nagar, Hyderabad 500072,
India2Department of Chemistry, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur 522510,
IndiaReceived 10 June 2012; Revised 17 August 2012; Accepted 21 August 2012Academic Editor: Antonio Romerosa Copyright (C) 2013 K. Ravi Kumar et al. This is an open access article distributed under the , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.An efficient protocol has been developed for the preparation of a library of benzoxazole, benzimidazole, and benzothiazole derivatives from reactions of acyl chlorides with o-substituted aminoaromatics in the presence of catalytic amount of silica-supported sodium hydrogen sulphate under solvent-free conditions. Simple workup procedure, high yield, easy availability, reusability, and use of ecofriendly catalyst are some of the striking features of the present protocol.1. IntroductionMolecules with benzoxazole, benzimidazole, and benzothiazoles moieties are attractive targets for synthesis since they often exhibit diverse and important biological properties. These heterocycles have shown different pharmacological activities such as antibiotic [], antifungal [], antiviral [], anticancer [], antimicrobial [], and anti-Parkinson [] properties. They have also been used as ligands for asymmetric transformations []. Benzimidazole derivatives are a unique and broad spectrum class of antirhino/enteroviral agents such as antiulcerative [] and antiallergic []; they are effective against the human cytomegalovirus [] and are also efficient selective neuropeptide Y Y1 receptor antagonists []. A number of methods are reported for the synthesis of these heterocycles by using different catalysts such as Pd-catalyzed oxidative cyclization [], ionic liquid-mediated synthesis [], base-assisted reaction of 1,1-dibromoethanes [], SiO2-ZnCl2 [], ZrOCl2·8H2O [], In(OTf)3 [], polyethylene-glycol-mediated catalysts [], and different heteropolyacid catalysts [], which include condensation of orthoesters [–], nitriles [], aldehydes [–], carboxylic acids [–], acid chlorides [], amides [] and esters [] with o-substituted aminoaromatics in the presence of different acids and catalysts. Beckmann rearrangement of o-acylphenol oximes [], photocyclization of phenolic Schiff bases [], and benzimidazole, synthesis in solvent-free conditions [] were also used. More recently benzoxazole, benzimidazole, and benzothiozoles were prepared from condensation of aldehydes with o-substituted aminoaromatics in the presence of Indion 190 resin []. However, many of these methods suffer from one or more of the drawbacks such as requirement of strong acidic conditions, long reaction times, low yields, tedious workup procedures, requirement of excess amounts of reagents, and use of toxic reagents, catalysts or solvents. Therefore, there is a strong demand for a highly efficient and environmentally benign method for the synthesis of these heterocycles.In recent years, heterogeneous catalysts [–] have gained importance in several organic transformations due to their interesting reactivity as well as for economic and environmental reasons. In continuation of our work to develop new methodologies for organic transformations [–], we observed that silica-supported sodium hydrogen sulphate is highly efficient catalyst for the synthesis of substituted benzoxazole, benzimidazole, and benzothiazole derivatives through the reaction of o-substitued aminoaromatics with different acyl chlorides under solvent-free conditions. The catalyst NaHSO4-SiO2 can easily be prepared [] from the readily available NaHSO4 and silica gel (230&#x mesh) and these are inexpensive and nontoxic. Besides, as the reaction is heterogeneous in nature, the catalyst can easily be removed by simple filtration (Scheme ).Scheme 12. Results and DiscussionsIn order to find the optimum reaction conditions for the condensation reaction, preliminary efforts were mainly focused on the evaluation of different solvents. The model reaction has been carried out between o-phenylenediamine and benzoyl chloride in the presence of NaHSO4-SiO2 catalyst under different solvents and at different temperatures, and results are shown in Table .Table 1: Preparation of 2-phenyl benzimidazole using various solvents and temperauresa.The effect of solvent, reaction temperature, and time on the reaction was systematically investigated, and the results were summarized in Table . The optimized reaction conditions for the reaction were found to be NaHSO4-SiO2 under solvent-free condition for 12 hr at the temperature of 100°C. Thus, we used NaHSO4-SiO2 as a catalyst in the present work. In order to elucidate the role of NaHSO4-SiO2 as catalyst, a controlled reaction was conducted using o-phenylenediamine and benzoyl chloride under solvent-free condition in the absence of catalyst. This resulted in the formation of only 7% of the fused product after 12 hr at 100°C. However, reaction with same substrate using 25%/wt of NaHSO4-SiO2 at 100°C for 12 hr afforded the product in quantitative yield. Lower temperatures required more time for the completion of the reaction and obtained low yields compared to the optimized reaction condition.As shown in Table , different acyl chlorides reacted with different o-substituted aminoaromatics without any significant difference in the reaction time to give the corresponding 2-substituted benzoxazole, benzimidazole, and benzothiazole derivatives in good yield. The method has the ability to tolerate other functional groups such as methoxy, methyl, and halides. The products were synthesized in good to excellent yields and characterized by 1H NMR, LCMS, and physical constant. Physical and spectral data of known compounds are in agreement with those reported in literature [–].Table 2: Synthesis of 2-substituted benzoxazoles, benzimidazoles, and benzothiazolesa.The reusability of catalyst is important for the large-scale operation and industrial point of view. Therefore, the recovery and reusability of NaHSO4-SiO2 was examined. The catalyst was separated and reused after washing with EtOAc and drying at 100°C. The reusability of catalyst was investigated in the reaction of o-phenylenediamine with benzoyl chloride (Figure ). The results illustrated in Figure
showed that the catalyst can be used four times with consistent yield.3. ConclusionIn conclusion, NaHSO4-SiO2 was found to be an efficient catalyst for the formation of benzoxazole, benzimidazole, and benzothiazole derivatives. The use of this inexpensive, easily available, and reusable catalyst makes this protocol practical, environment friendly, and economically attractive. The simple workup procedure, high yields of products, and nontoxic nature of the catalyst are other advantages of the present method.4. Experimental SectionAll 1H NMR spectra were recorded on 400 MHz Varian FT-NMR spectrometers. All chemical shifts are given as
value with reference to Tetra methyl silane (TMS) as an internal standard. Melting points were taken in open capillaries. The IR spectra were recorded on a PerkinElmer 257 spectrometer using KBr discs. Products were purified by flash chromatography on 100&#x mesh silica gel. The chemicals and solvents were purchased from commercial suppliers either from Aldrich, Spectrochem, and they were used without purification prior to use.5. FT-IR Spectrum of NaHSO
The FT-IR spectrum of the catalyst is shown in Figure . The catalyst is solid, and its solid-state IR spectrum was recorded using the KBr-disc technique. For silica (SiO2), the major peaks are broad antisymmetric Si-O-Si stretching from 1000&#x cm−1 and symmetric Si-O-Si stretching near 798 cm−1, and bending modes of Si-O-Si lie around 467 cm−1. The spectrum also shows a broad Si-OH stretching absorption from 3300 to 3500 cm−1.Figure 1: FT-IR spectra of silica-supported sodium hydrogen sulphate.6. X-Ray Diffraction (XRD) Spectrum of NaHSO
Powder X-ray diffraction measurement was performed using D8 advance diffractometer. The strongest peaks of XRD pattern correspond to the SiO2 plane with the other peaks indexed as the [, , ] planes of supported sodium hydrogen sulphate (Figure ).Figure 2: XRD spectra of silica-supported sodium hydrogen sulphate.Figure 3: Investigation of reusability of NaHSO4-SiO2.7. General Experimental ProcedureA mixture of 2-amino phenols or o-phenylenediamines (1 mmol) and acyl chloride (1 mmol) were place in a sealed vessel containing NaHSO4-SiO2 (25%/wt) the reaction mixture was stirred at 100°C for 12 hrs. The progress of the reaction was monitored by TLC Hexane: EtOAc (4 : 1) after completion of the reaction, the reaction mixture was cooled and treated by dilution with EtOAc and the catalyst was removed by filtration. Obtained filtrate was evaporated under reduced pressure to get the crude product, which was purified by column chromatography to give 2-substituted benzoxazoles, benzimidazole, and benzothioazole derivatives.8. Representative Spectral Data2-Phenyl-1H-benzo [d]Imidazole (Table , Entry 1).1H NMR (DMSO-d6):
13.02 (br s, 1H), 8.20 (d, J = 7.6 Hz, 2H), 7.67&#x (m, 1H), 7.56&#x (m, 4H), 7.22&#x (m, 2H); (LC-MS)
: 195.08 [M + H]+; IR (KBr, cm−1): , , , , 738. Anal. Calcd. For C13H10N2: C, 80.39; H, 5.19; N, 14.42. Found: C, 80.11; H, 5.01; N, 14.38.2-Heptyl-1H-benzo [d]Imidazole (Table , Entry 9). 1H NMR (DMSO-d6): δ12.11 (br s, 1H), 7.49 (d, J = 8 Hz, 1H), 7.38 (d, J = 6.4 Hz, 1H), 7.09&#x (m, 2H), 2.78 (t, J = 7.6 Hz, 2H), 1.77&#x (m, 2H), 1.31&#x (m, 8H), 0.85 (t, J = 6.4 Hz, 3H); (LC-MS)
: 217.21 [M+H]+; IR (KBr, cm−1): , , , . Anal. Calcd. For C14H20N2: C, 77.73; H, 9.32; N, 12.95. Found: C, 77.70; H, 9.28; N, 12.86.2-Heptyl-5-methyl-1H-Benzo [d]Imidazole (Table , Entry 10).1H NMR (DMSO-d6): δ11.98 (br s, 1H), 7.36&#x (m, 2H), 6.93-6.89 (m, 1H), 2.74 (t, J = 7.6 Hz, 2H), 2.37 (s, 3H), 1.78&#x (m, 2H), 1.30&#x (m, 8H), 0.85 (t, J = 6.4 Hz, 3H); (LC-MS)
: 231.18 [M+H]+; IR (KBr, cm−1): , , , 803. Anal. Calcd. For C15H22N2: C, 78.21; H, 9.63; N, 12.16. Found: C, 78.19; H, 9.58; N, 12.15.2-Phenyl Benzo [d]Oxazole (Table , Entry 11).1H NMR (CDCl3): δ 8.27&#x (m, 2H), 7.79&#x (m, 1H), 7.60&#x (m, 1H), 7.54&#x (m, 3H), 7.38&#x (m, 2H); (LC-MS)
: 196.20 [M+H]+; IR (KBr, cm−1): , , . Anal. Calcd. For C13H9NO: C, 79.98; H, 4.65; N, 7.17. Found: C, 79.86; H, 4.61; N, 7.14; O.2-Phenyl Benzo [d]Thiazole (Table , Entry 24).1H NMR (CDCl3): δ8.11&#x (m, 3H), 7.91 (d, J = 8.4 Hz, 1H), 7.51-7.40 (m, 4H), 7.39-7.37 (m, 1H); (LC-MS)
: 212.12 [M+H]+; IR (KBr, cm−1): , , , 961, 766, 685. Anal. Calcd. For C13H9NS: C, 73.90; H, 4.29; N, 6.63. Found: C, 73.87; H, 4.27; N, 6.59.AcknowledgmentsWe sincerely thank the RA chem. Pharma Ltd for financial support and encouragement. Support from the analytical department is also acknowledged.References
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