A catalyst containing, as an essential component, molybdenum; bismuth; and cobalt, in which a sum (S) of ratios of peak intensities expressed by the following formula in an X-ray diffraction pattern obtained by using CuKα rays as an X-ray source is 42 or more and 113 or less.

S={(peak intensity at 2θ=14.1°±0.1°+(peak intensity at 2θ=25.4°±0.1°)+(peak intensity at 2θ=28.5°±0.1°)}/(peak intensity at 2θ=26.5°±0.1°)×100

A catalyst containing, as an essential component, molybdenum; bismuth; and cobalt, in which a sum (S) of ratios of peak intensities expressed by the following formula in an X-ray diffraction pattern obtained by using CuKα rays as an X-ray source is 42 or more and 113 or less.

S={(peak intensity at 2θ=14.1°±0.1°+(peak intensity at 2θ=25.4°±0.1°)+(peak intensity at 2θ=28.5°±0.1°)}/(peak intensity at 2θ=26.5°±0.1°)×100

A catalyst containing, as an essential component, molybdenum; bismuth; and cobalt, in which, with respect to a peak intensity at 2θ=25.3°±0.2° in an X-ray diffraction pattern obtained by using CuKα rays as an X-ray source, a changing rate (Q1) per 1000 hours of reaction time represented by the following formulae (1) to (4) is 16 or less.

Q1={(U1/F1−1)×100}/T×1000  (1)

F1=(peak intensity of catalyst before oxidation reaction at 2θ=25.3°±)0.2°/(peak intensity of catalyst before oxidation reaction at 2θ=26.5°±0.2°)×100  (2)

U1=(peak intensity of catalyst after oxidation reaction at 2θ=25.3°±0.2°)/(peak intensity of catalyst after oxidation reaction at 2θ=26.5°±0.2°)×100  (3)

T=time (hr) during which oxidation reaction is carried out  (4)

A catalyst containing, as an essential component, molybdenum; bismuth; and cobalt, in which, with respect to a peak intensity at 2θ=25.3°±0.2° in an X-ray diffraction pattern obtained by using CuKα rays as an X-ray source, a changing rate (Q1) per 1000 hours of reaction time represented by the following formulae (1) to (4) is 16 or less.

Q1={(U1/F1−1)×100}/T×1000  (1)

F1=(peak intensity of catalyst before oxidation reaction at 2θ=25.3°±)0.2°/(peak intensity of catalyst before oxidation reaction at 2θ=26.5°±0.2°)×100  (2)

U1=(peak intensity of catalyst after oxidation reaction at 2θ=25.3°±0.2°)/(peak intensity of catalyst after oxidation reaction at 2θ=26.5°±0.2°)×100  (3)

T=time (hr) during which oxidation reaction is carried out  (4)

There is provided a catalyst that enables the production of isobutylene with a high selectivity in the production of isobutylene by dehydration of isobutanol. The catalyst according to the present invention contains at least one metal selected from Group 6 to Group 14 metal elements in Period 4 to Period 6 of the periodic table, in alumina which includes alumina consisting of one or more crystal phases of a monoclinic crystal phase, a tetragonal crystal phase, and a cubic crystal phase.

There is provided a catalyst that enables the production of isobutylene with a high selectivity in the production of isobutylene by dehydration of isobutanol. The catalyst according to the present invention contains at least one metal selected from Group 6 to Group 14 metal elements in Period 4 to Period 6 of the periodic table, in alumina which includes alumina consisting of one or more crystal phases of a monoclinic crystal phase, a tetragonal crystal phase, and a cubic crystal phase.

A method includes supplying a gas containing acrolein to a fixed bed reactor including a reaction tube to produce acrylic acid by vapor phase catalytic oxidation of acrolein. The reaction tube is packed with catalysts having different activities in such a way that catalyst layers are formed in a tube axis direction. A catalyst X having the highest activity among the catalysts contained in all the catalyst layers is placed in the whole or a part of a section up to 30% of a length of all the catalyst layers from a rearmost portion on a gas outlet side toward a gas inlet side. A catalytically active component x in the catalyst X has Mo, V, and optionally Cu. When Cu is included, its amount is 0.8 mol or less per 12 mol of Mo. A specific surface area of the catalytically active component x is 15-40 m.sup.2/g.

An object of the present invention is to provide a catalyst capable of improving the selectivity of unsaturated aldehydes and unsaturated carboxylic acids, and a catalyst containing molybdenum, antimony, bismuth, and iron, wherein an atom ratio of the antimony to the molybdenum on a surface of the catalyst is greater than an atom ratio of the antimony to the molybdenum in the entire catalyst is provided.

A process can be used for producing methacrylic acid or a methacrylic acid ester. The process involves producing acrolein, reacting the produced acrolein with hydrogen to produce propanal, reacting the propanal with formaldehyde to produce methacrolein, and oxidizing the methacrolein in the presence of an oxygen containing gas and optionally an alcohol, to obtain methacrylic acid or methacrylic acid ester.

An improved process can be used for the production of methacrylates, in particular methacrylic acid and/or methyl methacrylate (MMA). Specific embodiments of this process can be used for the safe and efficient production of these products from C-4-based raw materials, in particular those based on isobutylene or tort-butanol as raw materials. With this novel process, it is possible to operate such processes for a longer period of time without any safety or cleaning related shutdowns. This makes it possible to carry out such processes as simple, economic, and environmentally friendly as possible.