When precipitates are washed with a definite quantity of water or some other solvent, it's not recommended to use the washings at the same time. The principle also applies to the extraction between two liquid phases. In almost all analytical textbooks this principle is introduced with the next formula : [numerical formula] In some of them such special numbers, for instance, as n=4 and 5 are put in the formula to show C_5  <C_n

KIHARA, Kiyoshi

OHARA, Yoshiro

After two centuries after the fall of the last Sumerian dynasty of Ur in 2003BC, the first kingdom of Babylon did appear. The Amorites who were Semitic people who had lived in the west of middle Mesopotamia brought the collapse of Ur itself. They appeared as nomadic clans ruled by fierce tribal chiefs, who forced themselves into lands where they needed to graze their herds. There was no Amorite invasion of southern Mesopotamia as such, but the Amorites ascended smoothly to power in many places, especially during the reign of the last kings of the Ur III dynasty, and so the following Amorite dynasty took over the rule of long-extant city-states such as Isin, Larsa, Eshnunna, and Kish and also established new ones. After a brief periods of an Elamites and old Assyrian empire dominations that took place for only 46 years the Amorite kingdom was firmly established in 2004 BC in Babylon and continued until 1595 BC, known in Mesopotamia’s history as the "Amorite Period". Babylon became the major power in the ancient world during the reign of Hammurabi. It was from then that all parts of southern Mesopotamia came to be known as Babylonia. It was during the reign Babylonia witnessed the great care he had devoted to maintain and expand irrigation networks and keep the prosperity of the empire and even so successfully constructing new canals and dams. When Hammurabi established control over the whole region of Mesopotamia by 1760, and especially the city-states of Sumeria, he restored the irrigation canals there to their best conditions and brought water back to areas of the south that were previously deprived of it. His unification of the entire south and the lands north of Babylon allowed him to dig long canals to the various cities of these lands. The canal he called “Hammurabi-is-the-abundance-of-the-people”, for example, ran by Nippur, Isin, Uruk, Larsa, Ur, and Eridu, and covered a stretch of land extending for a distance of some 160 kilometers. These works brought economic development and increased the wealth of the population to unprecedented levels. Hammurabi’s achievement as a lawmaker is specifically highlighted; as he was famous for his “Legal Code” which he had promulgated.Validerad;2020;Nivå 1;2020-04-24 (alebob)</p

Adamo, Nasrat

Al-Ansari, Nadhir

Digitala Vetenskapliga Arkivet - Academic Archive On-line

In Old Babylonia : Irrigation and Agriculture Flourished Under the Code of Hammurabi (2000-1600 BC)

AIT Associated Repository of Academic Resources (Aichi Institute of Technology) / 愛知工業大学学術情報リポジトリ

ON THE THEORY OF W ASHING AND EXTRACTION Kiyoshi KIHARA * andYoshiro OHARA料When precipitates are washed with a definite quantity of water or some other solvent， it's not recommended to use the washings at the same time. The principle also applies to the extraction between two liquid phases. In almost all analytical textbooks this principle is introduced with the next formula: f' _ C。，管-，一一1 一一而11+一二一i¥ 叫晶 IIn some of them such special numbers， for instance， as n=4 and 5 are put in the formula to show C5くC生 practically. But the authors thought this is not the best way for the advanced students and tried to give a proof of C n+Iえ C"・1. WASHING 97 If the total quantity of washings is divided in equal日 partsand each of them is used for washing one after the other successively， the concentration of solution which remains absorbed by precipitates after the nth washing is to be expressed as follows: C"=. Co a= 1) -7寸-τ下 ，a=V I~I 一一ーー一一一一 l¥ n a I Co original concentration of solution which remains with precipitates. υconstant volume absorbed hy precipitates‘ V total volume of washings. 2. E玄TRACTIONLike the process in washing described in 1， the total extraction medium is divided in equal n parts and each of them is used for extraction one aft巴rthe other successively. Then th巴 presentamount of solute which remains not extracted after the nth extraction， is to be expressed with the following formula: W"一一 w0__ h = _!_j_ rlニ W1V n (1十」dn， u v， w 仰肌 w1) n b I d : distribution constant. ρ: constant volume of solution. V total quantity of extraction medium. w 0 : original amount of solute. 1.. 1 1 \n十"~ 1.， 1 ¥" 3. PROOF OF 1十一一一一・一一I >11十一一一l¥-. n+1 αI ~ ¥-. 1lα/ C" and W n belong to the same types of formula as observed in 1 and 2. And the authors atternpted te give the proof of C"+IぐC"by two di任erentmathematical methods， using the binomial theorem and differential calculus. * Department of Applied Ch自mistry，Aichi Technical College， Wakamizucho 1 chome， Chikusaku， Nagoya， Japan 料 Departmentof Mathematics， Faculty of Science， Nagoya University. Furocho Chikusaku， Nagoya， Japan. 98 Kiyoshi Kihara and Y oshiro Ohara 3.1 PROOF BY BINOMIAL THEOREM ( 1十寸aY=岳山(寸J(Hj i;)n+17+!(H14:)h 1十一一 =L:"1Ck (~工下.~': _ {1 1 ¥k {1 1 ¥"十1=エn+1Ck ¥ --=-~- ・一一! 十1一一一・一一l~~+1Vk \n+1- . aJ I ¥n十r'a}戸 I1 ¥ k 叩-1 n-k十1 1 n'-'k ¥nfi} 12 ……一一五一一・7肩「" I 1 1 ¥k 問時-k十2 1 n+lvk ¥n干l'a}=五平1 一匹-1-・7両!n-k+1 12ィ1 _1 k-l k-l 一一一一一園一一一一 1一一一一一一一 ←一一一一一一>0 (k>l) 12 n-k十2 n2-(k-2)四 n'-(k-2)nk-l 0< 12"ー (k-2)叩n+1 I 1 1、k n 1 ¥ k L:n+:LCkトニー・二一I>L:nCk I一二←i';;:'ôT ム ~， n十1 a I ~ ';:i -~ ，冗 aI 3.2 PROOF BY DIFFERENTIAL CALCULUS Put t=土 i泊nlい糾1十よ斗jYz，Jth加e叩n f(t)οωのか←山日)=(ベ1引(σ山¥ 12 a I Put g(t) in place of a log f(t)， then g(t)=J堕旦土1L-andgF(t)=1一(1十t)log(1+t) t -~~- O "/ t2(1+t) From h(t)=tー (1十t)log(l十t)，h'(t)=-log(lィt)，O<tえ∞ andh(O)=O 目 h'(t)く0，h(t)くOg'(t)くO. From the result obtained above g(t) is a decreasing function in the range 0くtく∞.1， 1 ¥ n Then each of log f(t)， f(t) andll十 1is also a decreasing function. ¥ n a I Cn= .. _C~ n {" 1 ¥ n was proved to be an increasing function. 1十一一ー l1 担 aI The outline of this paper was presented at the association meeting of the Japanese Chemical Society， the Japan Analyst Society， and other related chemical societies held at Nagoya on 18， October 1967. 

ON THE THEORY OF WASHING AND EXTRACTION

Luleå University of Technology Publications

http://repository.aitech.ac.jp/dspace/bitstream/11133/233/1/%e7%b4%80%e8%a6%815%e5%8f%b7%28P97-98%29.pdf

ON THE THEORY OF WASHING AND EXTRACTION

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