the term &# 34 ; isoamylene &# 34 ; as used herein means 2 - methyl - 1 - butene and 2 - methyl - 2 - butene and those can be used alone or as a mixture thereof . it is preferred for this isoamylene to be diluted with hydrocarbons as described hereinafter in that the amount of o - tert - amylphenol formed is decreased . hydrocarbons which can be used to dilute the isoamylene are hydrocarbons which do not include olefins represented by the following formula ( i ) and / or dienes . olefins which cannot be used to dilute the isoamylene are represented by the formula ( i ): ## str1 ## wherein r 1 and r 2 each is an alkyl group having from 1 to 6 carbon atoms , and r 3 and r 4 each is an alkyl group having from 1 to 6 carbon atoms or a hydrogen atom . a representative example of isoamylene diluted with hydrocarbons which do not include the olefins of the formula ( i ) and / or dienes is one obtained by hydrogenating an isoprene - extracted c 5 fraction which is used in a large amount in petrochemical industries in the presence of conventional transition metal - based hydrogenation catalysts such as palladium and nickel thereby to convert dienes therein into the corresponding monolefins . the inorganic solid acid catalyst which can be used in the present invention has an acid strength h 0 of - 3 or less . this acid strength h 0 indicates an ability of an acid site on the surface of the solid acid to give a proton to a base , or to receive an electron pair therefrom , and is determined using various acid - base conversion indicators having the known pka ( see k . tanabe & amp ; t . takeshita , acid base catalysts , published by sangyo tosho co ., ltd ., pp . 161 - 162 ( 1966 )). examples of the inorganic solid acid catalysts having an acid strength of - 3 or less include composite oxides such as silica - alumina , various zeolites , titania - silica , titania - zirconia , and magnesia - silica ; clay minerals such as activated clay , bentonite , and kaolin ; mounted acids prepared by depositing sulfuric acid or phosphoric acid , for example , on silica gel or alumina ; fixed compounds such as metal sulfates , metal phosphates , and metal halides ; and heteropolyacid . in addition to the above - described inorganic solid acid catalysts , inorganic solid acid catalysts having an acid strength h 0 of - 3 or less as described in the above - described reference , &# 34 ; acid base catalyst &# 34 ;, page 160 , and also t . shimizu , metal oxide and its catalytic action , published by kodan sha co ., ltd ., page 103 ( 1978 ) can be used . of these inorganic solid acid catalysts , composite oxides such as silica - alumina , zeolite , titania - silica , and titania - zirconia , and clay minerals such as activated clay are preferred . the solid acid catalyst can be easily separated from the reaction product by techniques such as filtration . moreover , the solid acid catalyst does not produce at all alkylphenols resulting from the reaction of olefins other than isoamylene contained in the isoprene - extracted c 5 fraction which has been hydrogenated , with phenols . in addition to the inorganic solid acid catalyst , an acidic ion exchange resin can be used as the catalyst of the present invention . as such acidic ion exchange resin catalysts , strongly acidic sulfonic acid - type ion exchange resins can be used . if these ion exchange resins contain water , the resins must be heated to about 100 ° c . and vacuum dried prior to use . of course , if the water content is 1 % by weight or less , the ion exchange resin catalyst can be used without removal of water . representative examples of such ion exchange resins are amberlist 15 , amberlite xn - 1010 ( produced by rohm & amp ; haas co ., ltd . ), dowex 50 w , dowex 50 w - x4 ( produced by dow chemical co ., ltd . ), and diaion sk116 , diaion sklb ( produced by mitsubishi chemical industries limited ). as the catalyst used in the process of the present invention , the inorganic solid acid catalyst is preferred as compared to the acidic ion exchange resin catalyst in that the amounts of 2 , 4 , 6 - tri - tert - amylphenol and o - tertamylphenol formed are small . phenols which can be used in the process of the present invention include phenol , o -, p - or m - cresol , 2 , 3 -, 2 , 4 - or 2 , 6 - xylenol , 2 , 3 -, 2 , 4 - or 2 , 6 - dihalogenated phenol , 2 - methyl - 4 - tert - butylphenol , 2 - isobutyl - 6 - dodecylphenol , 2 - cyclohexyl - 6 - methylphenol , 2 , 3 , 6 - trimethylphenol , and 2 , 3 , 5 , 6 - tetramethylphenol . in accordance with the process of the present invention , the above - described isoamylene is reacted with phenols in the presence of the inorganic solid acid catalyst or acidic ion exchange resin to produce tert - amylphenols . this reaction is usual , ly carried out at a temperature ranging between 30 ° and 120 ° c . under a pressure ranging between 1 to 10 kg / cm 2 for from 1 to 7 hours . the reaction can be carried out batchwise . for example , 1 . 0 kg of phenol , from 0 . 2 to 5 kg , preferably from 0 . 5 to 2 kg of a catalyst , and a hydrogenated isoprene - extracted c 5 fraction containing from 1 to 8 moles , preferably from 2 to 4 moles , per mole of phenol of isoamylene are placed an an autoclave and then reacted with stirring at a temperature of from 30 ° to 120 ° c ., preferably from 50 ° to 80 ° c ., for from 1 to 7 hours , preferably from 2 to 5 hours . after the reaction is completed , the catalyst is removed from the reaction mixture by filtration and the major portion of the unreacted c 5 fraction is removed . the thus - obtained concentrate is distilled to separate and purify the desired product , tert - amylphenol . in accordance with the process of the present invention , when the above - described hydrogenated isopreneextracted c 5 fraction is used , only isoamylene contained therein can be reacted with phenols , so that p - tert - amylphenol and 2 , 4 - di - tert - amylphenol can be produced selectively . thus , high purity tert - amylphenols can be produced inexpensively . the present invention is described in greater detail by reference to the following non - limiting examples and comparative example . unless otherwise indicated , all percents , parts , ratios and the like are by mol . a mixture of 400 g of an isoprene - extracted c 5 fraction having a composition shown in table 1 below and 4 . 0 g of a 0 . 3 % palladium / alumina catalyst was placed in a 1 . 0 - liter sus autoclave and the autoclave was then closed . hydrogen was charged to the autoclave at a gauge pressure of 5 . 0 kg / cm 2 , and hydrogenation was conducted with stirring at 85 ° c . for 1 . 0 hour . after the reaction was completed , hydrogen was withdrawn , and the catalyst was removed by filtration to obtain a hydrogenated c 5 fraction . the composition of the c 5 fraction thus obtained is shown in table 2 below . table 1______________________________________ amount (%) ______________________________________isopentane 31 . 3n - pentane 33 . 41 - pentene 7 . 0trans - 2 - pentene 2 . 4cis - 2 - pentene 1 . 22 - methyl - 1 - butene 10 . 02 - methyl - 2 - butene 1 . 4isoprene 0 . 9piperylene 4 . 7other compounds 7 . 7______________________________________ table 2______________________________________ amount (%) ______________________________________isoprene 28 . 6n - pentane 34 . 61 - pentene 1 . 8trans - 2 - pentene 9 . 2cis - 2 - pentene 3 . 42 - methyl - 1 - butene 7 . 92 - methyl - 2 - butene 5 . 2isoprene 0piperylene 0cyclopentane 0 . 2other compounds 9 . 1______________________________________ a 50 ml autoclave was charged with 0 . 91 g ( 9 . 64 millimoles ) of phenol , 10 . 3 g of the c 5 fraction as prepared above , and 1 . 00 g of activated clay ( strong ) ( produced by nippon kassei hakudo co ., ltd .) which had been burned at 200 ° c . for 6 hours , and the autoclave was then closed . the acid strength of the activated clay ( as determined using a hammet indicator ) was as follows : - 5 . 6 & lt ; h 0 ≦- 3 . 6 . the closed autoclave was maintained at 70 ° c . for 3 hours while stirring at about 800 rpm to conduct a reaction . the gauge pressure , therein was 2 . 0 kg / cm 2 . after the reaction was completed , the reaction mixture was cooled to room temperature , and the activated clay was removed by filtration . gas chromatographic analysis according to the internal standard method showed that the proportion of the unreacted phenol was 1 . 1 %, and 0 . 08 g ( 5 . 1 %) of o - tert - amylphenol , 0 . 40 g ( 25 . 3 %) of p - tert amylphenol , and 1 . 54 g ( 68 . 2 %) of 2 , 4 - di - tert - amylphenol were formed . the structure of each compound was confirmed by nmr , ir , and mass spectral analyses . the procedure of example 1 was repeated except that 1 . 00 g ( 10 . 6 millimoles ) of phenol , 11 . 4 g of the same c 5 fraction as used in example 1 , and 1 . 00 g of silica - alumina &# 34 ; is - 28 &# 34 ; ( produced by shokubai kasei kogyo co ., ltd .) which had been burned at 500 ° c . for 10 hours were used . the acid strength of the silica alumina ( as determined in the same manner as in example 1 ) was as follows : h 0 ≦- 8 . 2 . the proportion of the unreacted phenol was 5 . 0 %, and 0 . 05 g ( 2 . 9 %) of o - tert - amylphenol , 0 . 22 g ( 12 . 6 %) of p - tertamylphenol , 1 . 73 g ( 69 . 6 %) of 2 , 4 - di - tert - amylphenol , and 0 . 01 g ( 0 . 3 %) of 2 , 4 , 6 - tri - tert - amylphenol were formed . the procedure of example 1 was repeated except that 1 . 04 g ( 11 . 1 millimoles ) of phenol , 11 . 8 g of the same c 5 fraction as used in example 1 , and 1 . 00 g of the same silica - alumina as used in example 2 but which had not been burned were used . tert - amylphenols were not formed at all , and only the starting material , phenol , was recovered . the acid strength of the silica - alumina ( as determined in the same manner as in example 1 ) was as follows : - 3 . 0 & lt ; h 0 ≦+ 1 . 5 . a 50 ml glass autoclave was charged with 1 . 14 g ( 12 . 1 millimoles ) of phenol , 12 . 9 g of the same c 5 fraction as used in example 1 , and 1 . 00 g of amberlist 15 , and the autoclave was then closed and maintained at 40 ° c . for 3 hours while stirring at about 800 rpm . the gauge pressure therein was 1 . 0 kg / cm 2 . the reaction mixture was analyzed in the same manner as in example 1 . 100 % of the phenol was converted , and 0 . 21 g ( 10 . 7 %) of o - tert - amylphenol , 0 . 59 ( 29 . 4 %) of p - tert - amylphenol , 1 . 45 g ( 51 . 7 %) of 2 , 4 - di - tertamylphenol , and 0 . 13 g ( 3 . 5 %) of 2 , 4 , 6 - tri - tert - amylphenol were formed . while the invention has been described in detail and with reference to specific embodiments thereof , it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof .