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The 105 Trick! - Ask your friend to think of a mystery number Q between 1 and 105.
- Then ask him to work out [Q]mod3 and tell you the answer. (In other words he has to divide his mystery number by 3 and tell you what the remainder is). Call the answer x
- Ask him to work out [Q]mod5. Call the answer y
- Ask him to work out [Q]mod7. Call the answer z
- You then put the answers for x,y and z in this formula: [70x+21y+15z]mod105
- ...and you can work out Q !
Example: if the mystery number is 71 then... 71/3 = 23 remainder 2 so [71]mod3=2. This gives x=2.
71/5 = 14 remainder 1 so [71]mod5=1. This gives y=1.
71/7 = 10 remainder 1 so [71]mod7=1. This gives z=1. Your friend has told you these values for x,y and z (but not the number 71 obviously).
Put these answers in [70x+21y+15z]mod105 to get
[70x2 + 21x1 + 15x1]mod105 = [140 + 21 + 15]mod105 = [176]mod105 Finally to work out [176]mod105 you just do 176-105 =71.
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Square a 2 Digit Number, for this example 37: - Look for the nearest 10 boundary
- In this case up 3 from 37 to 40.
- Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
- Now mentally multiply 34x40
- The way I do it is 34x10=340;
- Double it mentally to 680
- Double it again mentally to 1360
- This 1360 is the FIRST interim answer.
- 37 is "3" away from the 10 boundary 40.
- Square this "3" distance from 10 boundary.
- 3x3=9 which is the SECOND interim answer.
- Add the two interim answers to get the final answer.
- Answer: 1360 + 9 = 1369
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You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first! To multiply any two digit number by 11: - For this example we will use 54.
- Separate the two digits in you mind (5__4).
- Notice the hole between them!
- Add the 5 and the 4 together (5+4=9)
- Put the resulting 9 in the hole 594. That's it! 11 x 54=594
The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627
Practice it on paper first!
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In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator. I will assume that you know your multiplication table reasonably well up to 10x10. Try this: - Take 15 x 13 for an example.
- Always place the larger number of the two on top in your mind.
- Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
- First add 15 + 3 = 18
- Add a zero behind it (multiply by 10) to get 180.
- Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
- Add 180 + 15 = 195.
That is It! Wasn't that easy? Practice it on paper first!
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Tautomers are organic compounds that are interconvertible by a chemical reaction called tautomerization. As most commonly encountered, this reaction results in the formal migration of a hydrogen atom or proton, accompanied by a switch of a single bond and adjacent double bond. In solutions where tautomerization is possible, a chemical equilibrium of the tautomers will be reached. The exact ratio of the tautomers depends on several factors, including temperature, solvent, and pH. The concept of tautomers that are interconvertible by tautomerizations is called tautomerism. Tautomerism is a special case of structural isomerism and can play an important role in non-canonical base pairing in DNA and especially RNA molecules. Tautomerizations are catalyzed by: - base (1. deprotonation; 2. formation of a delocalized anion (e.g. an enolate); 3. protonation at a different position of the anion).
- acids (1. protonation; 2. formation of a delocalized cation; 3. deprotonation at a different position adjacent to the cation).
Common tautomeric pairs are: - variations:
- Prototropic tautomerism
- refers to the relocation of a proton, as in the above examples, and may be considered a subset of acid-base behavior. Prototropic tautomers are sets of isomeric protonation states with the same empirical formula and total charge.
- Annular tautomerism
- a type of prototropic tautomerism where a proton can occupy two or more positions of a heterocyclic system. for example, 1H- and 3H-imidazole; 1H-, 2H- and 4H- 1,2,4-triazole; 1H- and 2H- isoindole.
- Ring-chain tautomerism
- occurs when the movement of the proton is accompanied by a change from an open structure to a ring, such as the aldehyde and pyran forms of glucose.
- Valence tautomerism
- is distinct from prototropic tautomerism, and involves processes with rapid reorganisation of bonding electrons. An example of this type of tautomerism can be found in bullvalene. Another example is open and closed forms of certain heterocycles, such as azide - triazirine. Valence tautomerism requires a change in molecular geometry and should not be confused with canonical resonance structures or mesomers.
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- Position of nuclei must be the same in all structures, otherwise they would be isomers with real existence.
- Total number of electrons and thus total charge must be constant.
- When separating charge (giving rise to ions), usually structures where negative charges are on less electronegative elements have little contribution, but this may not be true if additional bonds are gained.
- Resonance hybrids can not be made to have lower energy than the actual molecules.
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SEMI – MICRO QUALITATIVE ANALYSIS OF SIMPLE INORGANIC SALT
_______________________________________________________________
CATIONS: Pb 2+ ,Hg 2+ ,Cu 2+ ,Cd 2+ , Ag + , Fe 2+ , Fe 3+ , Al 3+ , Zn 2+ , Mn 2+ , Co 2+ , Sr 2+ , Ba 2+ , Mg 2+ , NH4 +
ANIONS: CO3 2- , S 2- , SO3 2- , SO4 2- , NO2 - , NO3 - , Cl - , Br 2- , PO4 3- , CH3COO -
_______________________________________________________________
PRELIMINARY TESTS
1. Note the state (amorphous or crystalline) and colour of salt.
2. Test the solubility of the salt in the following solutions:
i. Water (cold and hot)
ii. Dilute HCl (cold and hot)
iii. Dilute HNO3 (cold and hot)
_______________________________________________________________
IDENTIFICATION OF ACID RADICALS (ANIONS)
This part is the classified into three groups:
FIRST GROUP OF ACID RADICALS
The acid radicals involved in this group are carbonate(CO3 2- ), Sulphide(S 2- ), Sulphite(SO3 2- ),
Thiosulphate(S2O3 2- ) and nitrate(NO2 - ). The group reagent is dilute hydrochloric acid.
EXPERIMENT OBSERVATION INFERENCE
Effervescence or evolution of gases 1 st group of acid radicals is present.
(a) Colourless, odourless gas turns lime water
milky The acid radical may be CO3 2- or HCO3 -(
b) Colourless with rotten eggs smell and turns
lead acetate paper black. Sulphide(S 2- ) is confirmed.
(c) Colourless gas with suffocating smell. Heat
and pass the gas through acidified K2Cr2O7
solution. The solution turns green
SO3 2- is confirmed.
(d) Colourless gas with suffocating smell with a
yellow ppt. of sulphur in the test tube. Heat and
pass the gas through acidified K2Cr2O7 solution.
The solution turns dark blackish green.
S2O3 2- is confirmed.
(e) Colourless gas followed by brown gas and it
turns starch iodide paper blue. NO2 - is confirmed.
Salt + dil. HCl
(f) Colourless gas with the smell of vinegar. The acid radical may be CH3COO --
1 -?Tests to distinguish between CO3 2- and HCO3 -
EXPERIMENT OBSERVATION INFERENCE
(a) Lime water does not turn milky. CO3 2- is confirmed. Salt + water, boil and pass the
gas through lime water (b) Lime water turns milky. HCO3 - is confirmed.
Confirmation test for Acetate
EXPERIMENT OBSERVATION INFERENCE
Salt solution + Neutral FeCl3 sol. Appearance of blood red colour. Acetate is confirmed
SECOND GROUP OF ACID RADICALS
The acid radicals involved in this group are Cl - , Br - and NO3 - . The group reagent is concentrated
sulphuric acid (H2SO4).
EXPERIMENT OBSERVATION INFERENCE
Effervescence with colourless or coloured gases 2 nd group Acid radical is
present
(a) Colourless gas with a pungent smell and gives dense
white fumes when a glass rod dipped in ammonium
hydroxide (NH4OH) is exposed.
The Acid radical may be Cl -(
b) Brown gas and the solution is not blue. The acid radical may be Br -
Salt +
Concentrated
H2SO4 and heat
if necessary.
(c) Light brown gas and brown gas with pieces of copper
turnings and the solution turns blue in the test tube. The Acid radical may be NO3 -Confirmation
test for Chloride
EXPERIMENT OBSERVATION INFERENCE
(a) Chromyl – Chloride test: Salt + few
K2Cr2O7 crystals + conc. H2SO4 and heat
Pass the vapours through the test tube
which contains NaOH solution.
To this yellow solution, add dilute
CH3COOH and lead acetate solution.
Red vapours are obtained.
The solution turns yellow.
Yellow ppt. is formed
Chloride is confirmed.
(b) Silver Nitrate test: Salt solution +
AgNO3 solution + dilute HNO3
White ppt. is formed
which is soluble in NH4OH. Chloride is confirmed.
- 2 -?Confirmation test for Bromide
EXPERIMENT OBSERVATION INFERENCE
(a) Globule Test: Aqueous solution of salt + two
drops of CCl4 + 1ml chlorine water and shake
well.
An orange-red globule is
obtained Bromide is confirmed.
(b)Silver Nitrate test: Salt solution + AgNO3
solution + dilute HNO3
A pale yellow ppt. slightly soluble
in NH4OH is obtained. Bromide is confirmed.
Confirmation test for Nitrate
EXPERIMENT OBSERVATION INFERENCE
Brown ring test: Strong solution of the substance + 2 or
3 drops of conc. H2SO4, and cool. Add freshly prepared
FeSO4 solution on the sides of the test tube.
A brown ring is formed
at the junction of two
liquids.
Nitrate is confirmed.
THIRD GROUP OF ACID RADICALS
The basic radicals involved in this group are SO4 2- and PO4 3- .
EXPERIMENT OBSERVATION INFERENCE
Test for Sulphate: Aqueous solution of salt + dilute
HCl + BaCl2 solution.
A white ppt. insoluble in dilute
HCl is obtained
Sulphate (SO4 2- ) is
confirmed.
Ammonium – Molybdate Test: 2ml of soda extract 1 +
dilute HNO3 + Ammonium Molybdate solution.
A canary yellow precipitate is
obtained.
Phosphate (PO4 3- ) is
confirmed.
1 Soda extract to be prepared if the given salt is partially soluble in water.
- 3 -?ANALYSIS OF BASIC RADICALS OR CATIONS
This is classified into 6 groups. They are mentioned as below:
GROUP RADICALS GROUP REAGENTS
I Pb 2+ ,Ag + Dilute Hydrochloric acid(HCl)
II Pb 2+ ,Hg 2+ ,Cu 2+ ,Cd 2+ Dilute HCl + H2S gas.
III Al 3+ ,Fe 2+ , Fe 3+ NH4Cl(s) + NH4OH
IV Zn 2+ ,Mn 2+ ,Co 2+ ,Ni 2+ NH4Cl(s) + NH4OH + H2S gas
V Ca 2+ ,Sr 2+ ,Ba 2+ NH4Cl(s) + NH4OH + (NH4) 2CO3
VI Mg 2+ , NH4 + -Nil-
Preparation of Original solution: A suitable solvent is found for the salt as given in the preliminary test. A
few drops are used as solution.
Test for NH4 + Radicals: This test is carried out before starting the analysis for the basic radicals.
EXPERIMENT OBSERVATION INFERENCE
(a) Salt + NaOH solution and heat it.
Expose a glass rod dipped in conc.
HCl to the gas and moist red litmus
paper.
Colourless gas with a pungent smell is
obtained.
Dense white fumes and moist red
litmus paper turns blue
NH4 + may be present in the
salt
(b) Original solution + Nesseler’s
reagent. Brown solution or ppt. is obtained NH4 + is confirmed.
FIRST GROUP OF BASIC RADICALS
The basic radicals of this group are Pb 2+ & Ag + .The group reagent is dilute HCl.
EXPERIMENT OBSERVATION INFERENCE
White ppt. is formed. May be Pb 2+ & Ag +
(a) ppt. dissolves in hot water. May be Pb 2+
(1) Original solution + Dilute HCl
Filter and add water to ppt.
and heat (b) ppt. is insoluble in water. May be Ag +
- 4 -?(a) A yellow ppt. is formed. Pb 2+ is confirmed. (2) Original solution + Potassium
Chromate solution. (b) A brick red ppt. is formed. Ag + is confirmed.
(3) Original solution + KCl sol.
ppt. obtained + water and
heat it.
A yellow ppt. soluble in hot
water, on cooling reappears as
golden yellow spangles. Pb 2+ is confirmed. The yellow ppt. is insoluble
in hot water.
SECOND GROUP OF BASIC RADICALS
The basic radicals of this group are Pb 2+ , Hg 2+ , Cu 2+ and Cd 2+ .The group reagent is Dilute HCl + H2S gas.
EXPERIMENT OBSERVATION INFERENCE
May be Pb 2+ Hg 2+ & Cu 2+ (a)A Black ppt. is observed. Original solution + Dilute HCl +
H2S gas. (b)A yellow ppt. is observed. May be Cd 2+
The identification of Pb 2+ , Hg 2+ , Cu 2+ and Cd 2+ are as follows:
EXPERIMENT OBSERVATION INFERENCE
(a) Original solution + Potassium
Chromate. A yellow ppt. is observed. Pb 2+ is confirmed.
(b)Original solution + NH4OH
A bluish white ppt. soluble in excess
of NH4OH is observed which gives
rise to a deep blue solution.
May be Cu 2+
(c) Original solution + dil. acetic
acid + potassium Ferro cyanide sol. A chocolate red ppt. is observed. Cu 2+ is confirmed.
(d) Dissolve the black ppt. in aqua
regia 2 + 1ml of distilled water,
heat & add 2 drops of SnCl2
A white ppt. is observed which turns
grey. Hg 2+ is confirmed.
(e) Original solution + dilute acetic
acid + H2S gas. A yellow ppt. is formed. Cd 2+ is confirmed.
2 Aqua regia is mixture of 3 drops of HCl + 1 drop of HNO3
- 5 -?THIRD GROUP OF BASIC RADICALS
The basic radicals of this group are Al 3+ , Fe 2+ and Fe 3+ .The group reagent is NH4Cl + NH4OH
EXPERIMENT OBSERVATION INFERENCE
May be Al 3+ (a) A white gelatinous ppt. is obtained.
(b) A dirty green ppt. is obtained May be Fe 2+
(1) Original solution +
NH4Cl(s) + NH4OH in
excess (c) A reddish brown ppt. is obtained May be Fe 3+
(a) White gelatinous ppt. soluble in excess of NaOH
is obtained which gives a colourless sol. The basic radical is Al 3+
(b) Dirty green ppt. insoluble in excess of NaOH The basic radical is Fe 2+ (2) Original solution +
NaOH solution
(c) Reddish brown ppt. insoluble in excess of NaOH The basic radical is Fe 3+
(3) Clear solution of
2(a) + solid NH4Cl and
heat
The white gelatinous ppt. reappears. Al 3+ is confirmed.
(4) Original solution +
acidified KMnO4 solution
which is added drop wise.
(a) The pink colour of KMnO4 is not discharged. Fe 3+ is confirmed.
FOURTH GROUP OF BASIC RADICALS
The basic radicals of this group are Zn 2+ , Mn 2+ , Co 2+ & Ni 2+ .The group reagent is NH4Cl + NH4OH
And H2S(g).
EXPERIMENT OBSERVATION INFERENCE
May be Zn 2+ , Mn 2+ or Co 2+ (a) a white ppt. is obtained
(1) Original solution + NH4Cl(s)
+ NH4OH in excess + H2S(g) (b) Buff or pale pink or flash coloured ppt.
soluble in dilute HCl is obtained. May be Mn 2+
(a) The white ppt. is soluble in excess of
NaOH giving a colourless solution. Zn 2+ is confirmed
(2) Original solution + NaOH
solution+. (b) The white ppt. insoluble in excess of
NaOH but turns brown. Mn 2+ is confirmed
- 6 -?A Blue colour in the alcohol
layer is obtained.
FIFTH GROUP OF BASIC RADICALS
The basic radicals of this group are Ca 2+ , Sr 2+ & Ba 2+ .The group reagent is NH4Cl(s) + NH4OH and
(NH4)2 CO3.
EXPERIMENT OBSERVATION INFERENCE
(1) Original solution + NH4Cl(s) + NH4OH in
excess + (NH4)2 CO3 solution. (a) A white ppt. is obtained. May be Ca 2+ , Sr 2+ or
Ba 2+
A yellow ppt. is obtained. May be Ba 2+ .
A thin white ppt. is obtained. May be Sr 2+ .
(2) Dissolve the white ppt. obtained in small
amounts of dilute acetic acid. Divide the
solution in three parts.
Part (1) + Potassium chromate solution.
Part (2) + Calcium Sulphate Sol. and heat.
Part (3) + Ammonium exalate solution. A white ppt. is obtained. May be Ca 2+ .
(a) Apple green coloured flame is
obtained. Ba 2+ is confirmed.
(b) Crimson red coloured flame is
obtained. Sr 2+ is confirmed.
(3)Flame tests: Make a paste of the given
salt with few drops of Conc. HCl in a watch
glass. Heat a Pt. wire in non luminous flame
till no colour is imparted to the flame. Dip
the Pt. wire in the paste and hold it in the
flame. (c) Brick red coloured flame is
obtained, Ca 2+ is confirmed.
SIXTH GROUP OF BASIC RADICALS
EXPERIMENT OBSERVATION INFERENCE
(1) Original solution + excess of NH4OH +
Ammonium Hydrogen Phosphate. A white ppt. is obtained. Mg 2+ is confirmed.
______________________________________________________________
*****THE END*****
Co 2+ is confirmed
(3) Dissolve the 1(a) in aqua regia, evaporate to
Dryness, add 1ml of distilled water and divide
the resultant product into two parts.
Part (1) + 1 ml of amyl alcohol + 100 mg of solid
NH4SCN and stir it.
Part (2) + 5 drops of dimethyl glyaxime reagent +
NH4OH. A pink ppt. is obtained. Ni 2+ is confirmed.
- 7 -
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tautomarism is the tandency to exist in both ketone & enol form
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Chichibabin ReactionThe Chichibabin reaction is a method for producing 2-aminopyridine derivatives by the reaction of pyridine with sodium amide. It was reported by Aleksei Chichibabin in 1914.The direct amination of pyridine with sodium amide takes place in liquid ammonia. Following the addition elimination mechanism first a nucleophilic NH2- is added while a hydride (H-) is leaving.Before the Chichibabin reaction, only electrophilic substitution on the pyridine ring was possible, which is difficult due to the fact that pyridine is an electron-poor aromatic compound and additionally forms positive charged pyridinum ions, which further decrease the probability of an electrophile attack. The positions in the pyridine system attacked by the electrophiles are the 3rd and the 5th position.The Chichibabin reaction is a nucleophilic substitution on the pyridine ring; the 2nd and 6th positions are therefore favoured over the other positions.
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Nucleophilic substitution reactions are a general class of reactions that commonly occur with organic molecules. The general reaction is:R-L + Nuc- ® R-Nuc + L-where R-L is the organic reactant, Nuc is the nucleophile, and L is the leaving group.
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i think u must use it in +2
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Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).
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surely not for iit.but that may help u to clear aieee & bits
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Cool dancing featuring DUFFY!
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Magic Moments of India vs Pakistan cricket
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This video contains top 25 catches of all time.For more such videos log into sportsunseen.com
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Some funny cricket moments
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An animation I produced for my A-Level Art coursework, I would have rigged up the legs as well if I had worked out how!
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Vriti Edustore
