Topic 1 Quantitative Chemistry

Topic Topic 1: Quantitative chemistry Stoichiometry is the study of the relationship or ratio’s between the amounts of reactants and products in a chemical reaction. Stoichiometric amounts or ratio’s are the amounts of reactant or product as given by the coefficients in the balanced equation. The following laws and ideas underpin our knowledge about the relationships between chemicals involved in reactions (see PowerPoint) 1. Law of Conservation of Mass: Lavoisier (18 th Century) concluded from studyin! reactions involvin! o"y!en that durin! any chemical reaction no atoms were destroyed. #. Law of $efinite %roportions: analytical tests showed that any compound consists of the same elements in definite proportions e.!. in every water molecule 88.88& of its mass is o"y!en. '. Law of Cominin! olumes olumes of *ases: *ay+Lussac (18,') concluded that when !ases react they do so in whole numer ratios in terms of volume e.!. ' volumes of hydro!en react with 1 volume of nitro!en to form # volumes of ammonia. -. vo!adro/s vo!adro/s Theory (1811): (1811): vo!adro vo!adro stated that e0ual volumes of !ases must must have e0ual numer of particles (provided temperature and pressure are the same) . Law of Multiple Multiple %roportions: in # different compounds of the same elements (e.!. C2 and C2 #) if the mass of 1 element is the same (e.!. caron in C2 and C2 #) than the ratio of the mass of the other element (in our e"ample o"y!en) in each compound must e a whole numer.

1. 1 The mole concept and vo!adro/s vo!adro/s constant *.*. *.*.* * *.*.

!ppl !pply y the the mole mole con conce cept pt to to subs substa tanc nces es.. 2etermine the number of particles and the amount of substance (in moles).

 !s particles are e"tremely e"tremely small chemists measure measure amounts of substance using a quantity called called the + #$%& which stands for '. " *  a number which is know as !vogadro’s !vogadro’s constant. So * mole of a substance , '. " * + units of that substance- these units can be atoms molecules ions electrons or formula units.

* mole , '. " * + atoms ions molecules electrons / Determining number of moles and the number of particles 0se the e"pression

number number of particles  

number of moles ,

'. " * + Molar ratios in compounds or formula units: Topic*notes Topic*notes

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&"amples •

in * mole of 3e $+ there are  moles of iron atoms and + moles of o"ygen-

•

in + moles of 4a 5$+ there are + moles of 5$ +6 and ' moles of 4a 7 -

•

in  moles of (48 9)+ P$9 there are ' moles of 48 97 and * moles of hydrogen atoms and so on/

•

if there are  " *  56atoms in a sample sample of ethane how many hydrogen atoms are there there in that same sample: if you have ' " *  atoms of hydrogen how how many molecules molecules of ammonia do you you have:

•

Exercises *. 8ow many moles of o"ygen o"ygen are there there in  moles moles of !l $+: . 8ow 8ow man many y mol moles es of 4$+6 are there in * mole of ;a(4$ +)+: +. >>) chloride (one mole , *+B.1g) that contains .1? of phosphorus and BB.1? of chlorine. A. Cutane (one mole , 1Ag) that contains A.A? carbon and *B.? of hydrogen. @. ! compound F (one mole , +9g) that contains *1.A? of aluminium A.*? of sulfur and 1'.*? of o"ygen. The compound forms a white precipitate when it reacts with barium nitrate solution.

1.'. >alanced e0uations *.+.* 2educe chemical equations when all reactants and products are given. *.+. >dentify the mole ratio of any two species in a chemical equation. *.+.+ !pply the state symbols (s) (l) (g) and (aq). Topic*notes *.1 hours

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 !s seen in *.* the stoichiometric amounts or molar ratios for any reaction can be obtained from a balanced equation. &"ample    → 3e $+ (s) 7 +5$ (g) 3e (s) 7 + 5$   (g) This means that * particle of 3e $+

7

+ particles of 5$

 particles of 3e

   →

7

+ particles of 5$

 !lternatively this means that there are + times as much particles of 5$ as 3e  $+ particles- for the reaction to go to completion (,both reactants are completely used up) + times as much 5$ is needed as 3e  $+. Cy multiplying each number of particles by '. " * + the above balanced equation states the same

ratios but e"pressed in moles * mole of 3e  $+

reacts with

+ moles of 5$

to give

 moles of 3e

and

+ moles of 5$ 

>n the above equation the molar ratio of iron o"ide to carbon mono"ide is * + i.e. f or the reaction to go to completion + times more moles of 5$  are needed than 3e $+ 5omplete the following table showing other molar ratio’s in the above equation-

3e $+  3e 3e  5$ 5$  5$  3e $+  5$

   

Balancing equations >n getting an equation to alance the number of moles of each substance is changed until there are the same number of atoms of each element on each side of the equation 0nbalanced equation

5 +8A 7 $  666G 5$ 7 8$

Calanced equation

5 +8A 7

1$  666G +5$

7

98$

Conservation of mass C 5hemistry &"am 4ovember *@@A  !spirin 5@8A$9 is made by reacting ethanoic anhydride 5 98'$+ (#r  , *.*) with 6hydro"ybenEoic acid 5B8'$+ (#r  , *+A.*) according to the equation  598'$+

7

 5B8'$+

 5@8A$9

→

7

8$

(a)

if *1. g of 6hydro"ybenEoic acid is reacted with *1. g of ethanoic anhydride determine [ # mar&s ]  the limiting reagent in this reaction.

(b)

5alculate the ma"imum mass of aspirin that could be obtained in this reaction.

(c)

>f the mass obtained in this e"periment was *+.B g calculate the percentage yield of aspirin. [  mar&   ] 

[ # mar&s ] 

vo!adro/s law to calculate reactin! volumes of !ases *.9.9 !pply !vogadro’s law to calculate reacting volumes of gases. *.9.1 !pply the concept of molar volum e at standard temperature and pressure in calculations. *.9.' Solve problems involving the relationship between temperature pressure and volume for a fi"ed mass of an ideal gas. *.9.B Solve problems using the ideal gas equation P'  n*  *.9.A !nalyse graphs relating to the ideal gas equation.

;ay6%ussac noticed that there is always a very simple ratio between volumes of gases that react together. 3or instance •

* volume of hydrogen 7 an equal volume of chlorine

•

* volume of o"ygen 7  volumes of hydrogen    →

   →

 volumes of hydrogen chloride

 volumes of water vapour 

To e"plain these results !vogadro proposed that equal volumes of gases (if measured in the same conditions) must have the same number of molecules.  !s a result the above volume observation can also be considered as * molecule of hydrogen 7 * molecule of chlorine Topic*notes

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 molecules of hydrogen chloride Page * of +

vo!adro/s Law states that: 70ual volumes of different !ases at the same temperature and pressure contain the same numer of molecules (or same numer of moles) >f the same volume has the same number of particles than the same number of particles must have the same volume so * mole at s.t.p. has a volume of .9 " * 6 m+ mol6* or .9 dm + mol6* and this is called the gas molar volume. t s.t.p. (which is #@'A and 1 atm)

volume of 1 mole of a !as 5 #.#- " 1,+# m' mol+1 or ##.- dm' mol+1 >n other words if there are  x  molecules of $  in * ml of o"ygen gas then there are  x molecules of 4  in * ml of nitrogen gas and there are x  molecules of 5$  in  ml of carbon dio"ide gas.  !nother way of putting this is that the volume of a gas depends on the amount of moles n (provided the conditions are the same). $r if the volume of 8  gas is double the volume of $  than there are twice as many moles of $  as 8.  !vogadro’s %aw allows equations involving gases to be interpreted directly in terms of volumes. 3or e"ample in the equation 9.A dm + of 48+.

Kuestion

5l 

7 8

4  7 +8

   →

   →

48+ for .9 dm + of 4  B. dm + of 8 is needed to give

  85l

8ydrogen and chlorine react according to the equation above. unitsHHH See http==www.chm.davidson.edu=5hemistry!pplets=;as%aws=;as5onstant.html  for determining the gas constant. See http==resources.schoolscience.co.uk=C!#!=*'plus=aerosch+pg*.html

9hen carryin! out calculations usin! the ideal !as e0uation we need to ensure we can cancel units=== >etter to use f the pressure is in atm then • •

&ither change to Pa (* atm , *.*+ " * 1 Pa) $r use .A+ % atm O 6* mol6*

The ideal gas equation can be used to solve a variety of problems such as •

calculate the pN or T values of a gas in a particular condition provided  of the + quantities are known

•

calculate the molar mass of a gas o

o

o

•

we need to know the conditions it is in and the mass of the sample of the gas we can then calculate n and then using n , mass=# r  calculate the # r  we can also use this calculation to identify an unknown gas e"perimentally HHH

calculate the new value of either p N or T provided we know what the other  have changed into. >f we are assuming that when we change * or  conditions and the mass or amount gas stays the same then in pN , nIT both n and I are constants and n , pN=T should be the same for both sets of conditions. So N * P*

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, T*

T

!or"ed example   units *.+ atm , *.+ " *.*+ " * 1 Pa , *.+9 " * 1 Pa 9. !pply pN , nIT *.+9 " * 1 " N , 9.@* " * 6+ " A.+*9 " @9

N , A.@' " * 61 m+ (, A@.' cm+)

!or"ed example  ! gas occupies *B cm + at a pressure of .A+ atm and at A °5. (a) f the percentage by mass of nitrogen in the indigo sample is *.B1? determine the empirical formula of indigo. +U (c) >f the molar mass is appro"imately ' g mol 6* determine the molecular formula of indigo.

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*. (4) ! balloon which can hold a ma"imum of ** cm + of air before bursting contains @11 cm + of air at 1X5 . 2etermine whether the balloon will burst if the temperature is increased to 1 5. !ssume that the pressure of the gas in the balloon remains constant. +U

*+. (4) !n element F reacts with o"ygen to form the o"ide F $+ . (a) f .*@@ g of the o"ide was obtained from *.+@ g of F calculate the relative atomic mass of F and identify the element.

1U

(c) 4itrogen also forms an o"ide on reaction with o"ygen. This o"ide contains 1.@ ? of nitrogen and B9.* ? of o"ygen by mass. 5alculate the empirical formula of this second o"ide.

+U

*9. (#) ! student is asked to prepare some copper(>>) nitrate by reacting nitric acid with copper(>>) o"ide. (a) >) o"ide to +'. of cm *.*1 mol dm6+ nitric acid solution. 5alculate the amount (in mol) of nitric acid.

+

*U

(c) 0se the information in (a) and (b) to identify the limiting reagent and determine the amount (in mol) of copper(>>) nitrate formed. U

*1. The value of F in 4a!l(S$ 9). - 8$ can be found by determining the number of moles of sulphate in the compound quantitatively. ! 1.*Ag sample was dissolved and e"cess Ca5l  was added. The precipitate of CaS$ 9 was separated dried and found to weigh 1.+*1g. (use integer mass numbers). (a) (b) (c) (d)

5alculate the number of moles of CaS$ 9 in the 1.+*1g sample. 8ow many moles of sulphate are there in the 1.*Ag of 4a!l(S$ 9).F8$: 5alculate the number of moles of !l in the 1.*Ag of 4a!l(S$ 9).F8$. 2etermine the total mass of sulphate sodium and aluminium that are present in the 1.*Ag sample of 4a!l(S$ 9).F8$ (e) 2etermine the number of moles of water in the 1.*Ag sample of 4a!l(S$ 9).F8$ (f) 2etermine the value of F in 4a!l(S$ 9).F8$

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#ark scheme P!P&I * *  + 9 1 ' B A @ *

** * *+ *9 *1 *' *B *A *@ 

*  + 9 1 ' B A @ +

+* + ++ +9 +1 +' +B +A +@ 9

9* 9 9+ 99 91 9' 9B 9A 9@ 1

P!P&I  *. (#B) . (41)

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*.

(#')

.

(4')

9.(#*) Topic*notes

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1. (4*)

'.

(4)

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