easykemistry

Monday, 13 May 2024

ISOMERISM at a glance

 

ISOMERISM IN ORGANIC COMPOUNDS

Isomerism is defined as the occurrence of two or more compounds with the same molecular formular but different molecular structures. 

The different molecular structures are known as Isomers.

Isomers may belong to the same homologous series ( having the same functional group) or may belong to different homologous series (having different functional group)

Isomers with the same functional group, (i.e. belonging to the same homologous series) have similar chemical properties while isomers having different functional group (i.e. belonging to different homologous series) have different physical and chemical properties.

Example:- the formula C2H6O has two isomers 

1. Ethanol an Alkanol with molecular formula CH3CH2OH has a melting point of 78 degree celçius and is a liquid at room temperature 

     H    H
      |      |
H--C--C--OH
      |      |
    H.   H

and 

2. an Alkoxy compound with molecular formula CH3OCH3 which is a gaseous at room temperature

      H       H
      |         |
H--C--O--C--H
      |         |
      H       H

TYPES OF ISOMERISM

(i) Structural isomerism

(ii) Stereo or geometric Isomerism

(iii) Optical isomerism

 

(I) STRUCTURAL ISOMERISM

This is the occurrence of two or more compounds with the same molecular formula but different molecular structures 

TYPES OF STRUCTURAL ISOMERISM

(a) Chain isomerism: in this case, the isomer differs in the way the carbon atoms are arranged in the molecule. Eg

 CH3CH2CH2CH3  CH3CHCH3   
n-butane                                   |                                                                   
                                              CH3  
                            2-methylpropane (isobutane)

(‘n’ stands for the normal compound while ‘iso’ means the isomer of the normal compound).

NOTE: - Isomerism begins from the 4th member of the alkane homologous series, that is, butane, and as the number of carbon atoms increases the number of isomers also increases. For example, butane has two isomers normal-butane and 2-methyl propane, pentane (C5H12) has three isomers:  n-pentane, 2-methylbutane and 2,2-dimethylpropane.            

  I.  CH3CH2CH2CH2CH3.  (n-pentane)

              CH3
              |
II.  CH3CHCH2CH3  (2-methylbutane)

                                     

III.              CH3
                    |        
          CH3-C-CH3
                    |
                  CH3        2,2-dimethylpropane

Three isomers for pentane 

Another example is hexane (C6H14)

I.  CH3CH2CH2CH2CH2CH3

               n-hexane

          

              CH3
              |
II.  CH3CHCH2CH2CH3    2-methylpentane

III.                        CH3
                              |
              CH3CH2CHCH2CH3          3-methylpentane

                   CH3
                      |
IV.      CH3CCH2CH3    2,2-dimethylbutane
                  |
                  CH3

                                     

                  CH3
                    |
V.      CH3CHCHCH3    2,3-dimethylbutane
                        |
                      CH3  

Hexane has 5 isomers 

(b) position isomerism: Position isomers are those that have a substituent in different position on the same carbon skeleton. Example

                CH3CH2CH2OH             CH3CHCH3
                    propan-1-ol                             |
                                                                    OH
                                                             propan-2-ol

(c) Functional Group isomerism: These are isomers having the same molecular formular but different functional groups. They belong to different homologous series.

e.g.
                      H
                    /
(i)  CH3CH2C                          CH3-CCH3
                    \\                                ‖  
                      O                              O
     Propanal  (an aldehyde)       propan-2-one (a ketone)

(ii) CH3CH2OH                                  CH3-O-CH3 

      Ethanol  ( Alkanol)                Methoxymethane (dimethyl ether) (Alkoxy compounds)

(2) STEREO ISOMERISM OR GEOMETRIC ISOMERISM

In this type of isomerism, compounds have the same molecular formular but differ only in the way their atoms are arranged in space.

TYPES   STEREO ISOMERISM

(a) Geometrical isomerism: This type of isomerism is found in compounds having either a double bond, triple bond or a ring structure. These multiple bonds prevent the free rotation about a carbon=carbon atom. that is, the carbon atoms are not cylindrically symmetrical. There are two forms of geometric isomers, the Cis and Trans isomer. For example, but-2-ene has two geometric isomer which are trans-but-2-ene and cis-but-2-ene as shown below.

when naming geometric isomers, you look at the substituents, where the substituents (group other than Carbon atoms) are on the same side of the double bond, that isomer is named the Cis isomer and when the substituents are on opposite sides of the double bond, we put a trans- isomer, but the names are the same

   H               CH3                          H             H         
        \           /                                   \         /
          C=C                                       C=C
        /         \                                    ∕         ∖
  CH3          H                                CH3       CH3

Trans-but-2-ene                          Cis-but-2-ene

 

      H          Br                   H           H
        \         /                         \        /
          C=C                            C=C
        /       \                          /      \  
  Br              H                    Br      Br
Trans-1,2-dibromoethene       Cis-1,2-dibromoethene                    

   C1OOH.  C4OOH               H           COOH
      \           /                             \         /      
        C2=C3                              C=C   
      ∕         ∖                            /        \
COOH       H                      H             H
Trans-butenedioic acid            Cis-butenedioic acid

(b) Optical isomerism: Optical isomers   are isomers that have the same molecular and structural formular but cannot be superimposed on each other. In other words, an optical isomer is one which is not super-imposable on its mirror image. An optical isomer has at least one carbon atom which has four different groups or atoms attached to it. Such a carbon atom (surrounded by four different atoms /group) is called chiral carbon or chiral center. E.g. 2-hydroxylpropanoic acid (Lactic acid).


                           CH3
                            |
             HO — *CH
                            |
                           COOH

                  The Asterix C-atom is called a chiral C-atom because it is surrounded by four (4) different groups.

            In glucose, there are several chiral carbon atoms.

                                          H
                                          ∣
                                          C = O
                                          |
                                H — *C —OH
                                            |
                              OH —*C —H
                                            |
                                H — *C— OH
                                          |
                                H —*C —OH
                                          |
                                H — C—H
                                          |
                                          OH

Optical isomers are also called Enantiomers.

Isomers that belong to the same homologous series (same functional group) have similar chemical properties but may have different physical properties. But isomers which belong to different homologous series (different functional group) have different chemical and physical properties.

Friday, 19 April 2024

HYDROCARBONS at a glance

Organic Chemistry is the study of Carbon and its compounds.

Organic compounds are compounds containing Carbon, hydrogen and any one or two other elements like Sulphur, Nitrogen, Oxygen, Phosphorus and even metals like Sodium and potassium.


 General Properties of Organic Compounds 

1.The solid ones  have low melting and low boiling points.

2. They are soluble in non-polar solvents.

3. They are thermally unstable ( i.e easily decompose/ breakdown on heating)

4. They combustible

5. They are mostly covalent in nature.


              HYDROCARBONS

Hydrocarbons are compounds containing only two elements, that is, Hydrogen and Carbon.


There are three main families of hydrocarbons 

****The Alkanes 

****The Alkenes and 

****The Alkynes 


Sources of hydrocarbons


There are three main sources of hydrocarbons, 

i. Crude oil or petroleum

ii. Natural gas 

iii. Coal


I. Crude oil/petroleum: - Crude oil is a viscous dark liquid that is found in deposits underground. It is formed from animal remains and marine vegetation, algae e.t.c when these are subjected to pressure, heat and bacterial activity they gradually change to this dark viscous liquid known as crude oil. 


Crude oil exploration and drilling 


Crude oil-bearing rocks and areas are located and explored by the following processes.

I. Taking an aerial photograph of the place. 

II. Examining and testing the surface rocks.

III. Drilling large holes/core into the ground 

IV. Exploding dynamite in the deep holes drilled into the earth's crust taking recordings and reflections of shock waves resulting from the explosions in the rocks.




ii. Natural gas: - Natural gas is a naturally occurring hydrocarbon mixture composed mainly of methane (CH4 about 65% -90%)). Along with methane are other hydrocarbons like ethane, propane and butane. 


It is formed from the decomposition and compression of organic matter, like dead plants and animals, over thousands of years and is usually found in deep underground deposits.


It is extracted from these underground deposits (reservoirs) by drilling pipes into the reservoirs. It is then separated and purified into its various components by fractional distillation.


Uses

i. it is used mainly for heating as fuel,

ii. it is used for generating electricity 

iii. it used as fuel for transportation in the form of liquified natural gas 


Even though we consider natural gas as a relatively clean fossil fuel, its extraction, transportation and various uses can still affect our environment (such as water pollution, methane emissions and land disturbance). 



Coal: - Coal is a solid fossil fuel that is mainly composed of carbon, as well as various amounts of other elements such as hydrogen, oxygen, sulfur, and nitrogen (see carbon and its compounds)




Fractional Distillation Of Petroleum

Unless it is refined, crude oil will just be a viscous liguid with very limited use. But when it undergoes fractional Distillation, it is separated into various compounds.


Fractions from fractional Distillation of Petroleum

Table: -showing various petroleum fractions and their uses


Fractions

Number of C-atoms

Uses

1.

Petroleum gas 

C1 - C4

Used mainly as fuel and manufacturing of other organic compounds like chloromethane

2.

Ether

C4 – C6

Used as solvents

3.

Petrol

C7 -C10

Used mainly as fuel for motor car engines

4

Kerosene

C10 – C18

Fuel for cooking, for lighting and used for jet engines

5

Diesel oil

C18 – C25

It is used as a raw material for cracking process, used as fuel for diesel engines

6

Lubricating oils

C20 – C35

Used for

i. oiling / lubricating moving parts of machines, engines and generators

ii. Raw material for making candles, hair cream and body creams products

7.

Bitumen

Above C35

Used for road construction



Classification of Hydrocarbons


Hydrocarbons are classified into 

I. Aliphatic and

II. Aromatic Hydrocarbons


ALIPHATIC HYDROCARBONS: - These are straight chain, branched chain or cyclic hydrocarbons that are saturated or unsaturated. 

Examples of aliphatic hydrocarbons are (CH3CH2CH3) propane, (CH3CH2CH=CH2) butane, pentyne


AROMATIC HYDROCARBON: - These are hydrocarbons that contain the benzene ring (C6H6) in its structure. Aromatic Hydrocarbons are unsaturated.

ALIPHATIC HYDROCARBONS: - these are straight chain, branched chain or cyclic hydrocarbons that are saturated or unsaturated. 

Examples of aliphatic hydrocarbons are (CH3CH2CH3) propane, (CH3CH2CH=CH2) butene, CH3CH2CH2C≡CH) pentyne, CH3CH2CH2C≡CH)

Straight Chain hydrocarbons

        H   H  H

        ׀ ׀      ׀ 

H – C – C – C −H

        ׀     ׀      ׀

       H H H

Propane

   

 

      H  H   H  

      ׀    ׀ ׀     

H−C – C – C= C– H

     ׀      ׀          ׀

    H H        H

Butene

 

   

 

       H    H  H

        ׀     ׀     ׀

H – C – C– C –C ≡ C –H

        ׀    ׀    ׀      

        H  H   H

Pentyne

 

Branched chain hydrocarbon

 

    H H H

       ׀      ׀      ׀

H− C – C – C −H

       ׀            ׀       

      H       H

       H – C – H

              ׀

             H

 

2-methyl propane

benzene

Cyclic hydrocarbon

                   H

                    ׀

                   C

                 ∕ \

       H − C   −   C – H


Cyclopropane

 

AROMATIC HYDROCARBON: - These are hydrocarbons that contain the benzene ring (C6H6) in its structure. Aromatic Hydrocarbons are unsaturated.

 

Terminologies in Organic Chemistry.

 

I. CATENATION- this is the ability of an element to form single and multiple bonds with itself and other elements.


2. OCTANE NUMBER: - This is the measurement of the efficiency of combustion of petrol in car engines.

It is based on the proportion of branched chain alkanes to straight chains in a given fuel.

For instance, a sample of petrol that contains a high proportion of normal (straight chain) heptane than 2,2,4 trimethylpentane has a low octane number of below 50.


         3. HYBRIDIZATION: - This is the mixing of orbitals to get the same number of hybrid orbitals.

4. HOMOLOGOUS SERIES: - This is a family of organic compounds that conforms to a general molecular formular, and successive members differs by a -CH2- group.

Examples of homologous series include the alkanes, alkenes and alkynes

Characteristics of a Homologous Series 

i. Members differs by a -CH2- group

. Members have the same general molecular formular

iii. Members have similar chemical properties 

iv. Members have the same general method of preparation

v. There is a gradual change in the physical properties of members as you go down the group.


ALKYL GROUP: - This is a homologous series of hydrocarbons formed by the loss of a hydrogen atom by a corresponding alkane.

     The following table shows the first five alkyl members and their corresponding alkane.

Alkyl group

Corresponding Alkane

Formula

CH3

CH4

  H    

        ׀     

H – C –

        ׀    

       H  

C2H5

C2H6

  H   H    

        ׀ ׀     

H – C – C –

        ׀     ׀    

       H H  

C3H7

C3H8

    H   H H

        ׀ ׀      ׀ 

H – C – C – C −

        ׀     ׀      ׀

       H H

C4H9

C4H10

  H   H H   H

        ׀ ׀      ׀     ׀

H – C – C – C – C −

        ׀     ׀      ׀     ׀

       H H H   H

 

C5H11

C5H12

  H   H H   H   H

        ׀ ׀      ׀     ׀     ׀

H – C – C – C – C – C −

        ׀     ׀      ׀     ׀     ׀

       H H H   H   H

The alkyl groups are generally represented by the letter R


FUNCTIONAL GROUP: - A functional group is an atom, a bond or a group of atoms that is present in all the members of a homologous series, and it determines the chemical properties of the family.

The table below shows some functional groups and their names as sufixes and prefixes


Functional groups

Name as Suffix

Name as Prefix

−OH

R-OH

     

      -Ol

Hydroxy-

−        COOH

             O   

          ∕∕

 — C

        ∖

          H 

 

 

      -Oic acid

 

 

  -

−COOR

           O

        ∕

  − C

        \

         OR

 

 

Alkanoate

 

 

   -

− CONH2

          O

       ∕

 − C

       \

         NH2

 

 

-amide

 

 

   -

−C=O

          O

     ∕∕

−C

    \

    

 

 

-One

 

 

-oxo-

-CHO

         O

    ∕∕

−C

     \

      H

 

 

-al

 

 

Oxo-

−NH2

   −N 

 

-amine

 

 

amino

−CN

  −C≡N

 

 -carbonitrile

 

cyano

 

−Cl

 

 

-Chloro

 

 −Br

 

 

-bromo

 

 −I

 

 

-iodo

 

   −

 

       -ane

 

 

   =

 

       -ene

 

 

   ≡

 

      -yne

 

 

 The three main hydrocarbons (that is, the alkane, the alkene and the alkyne are discussed separately in different posts. 




 OBJECTIVE QUESTIONS 

1. Octane number is highest in petrol containing a high proportion of

a. heptane 

b. octane

c. 2-methylpentane

d. 2,2,4-trimethylpentane


2. Compounds containing only hydrogen and carbon are called 

a. hydrocarbons

b. alkanes 

c. isomers 

d. organic 

3.



Sunday, 14 April 2024

Rates of Chemical Reactions

During a chemical reaction, reactants collide with one another to form products and the formation of these  products do not  occur at the same rates. Hence 

Rate of a chemical reaction can be defined as the number of moles of  reactants that are converted, or products that are formed per unit time.

Mathematically 

Rate =      mass in grammes 
                      time taken

For instance, if 6g of zinc metal is placed in dilute tetraoxosulphate (VI) acid and it takes 3 mins to completely react,  then the rate of chemical reaction is given by. 

Rate =      6g     = 2g/mins
                3min
That is, 2g of the zinc was converted to ZnCl2 per minute 

Factors used for Measuring Rates Of Reaction
The rate of a chemical reaction can be measured or can be  determine by any one of the following.
i.   decrease in mass of reactants.
ii.  increase in volume of a gaseous product 
iii. change in pH
iv. change in colour intensity 
v. Change in pressure
 
These are all measurable factors.

 Factors Affecting the Rate of Chemical Reactions.
The following factors will a reaction to be fast or slow.

i. Nature of reactants
ii. Temperature
iii.. Concentration 
iv. Pressure 
v.  Presence of light
vi. Surface area 
vii. Presence of a catalyst

Before we discussed how each of these factors will affect the rate of a chemical reaction. It is important that we understand the concept of collision theory.

Collision theory assumes that for a chemical reaction to occur, there must be Collision between reactants particles and these Collisions must be effective.

A collision is said to be  effective when it leads to formation of products

What this concept is actually implying is that, all collisions do not  lead to the formation of a product, only the ones that are effective. So the various factors that affect a chemical reactions are factors that actually increase the number of effective collisions.


I. Effect of Nature of reactants:- this is one of the factors that affects the rate of a reaction, since different elements/ compounds behave differently.
The reactivity of metals varies as you go down the activity series and so when metals react with acids for example the reactions are not the same.
Example by virtue of their nature (their high reactivity) sodium and potassium will react explosively with dilut acids while metals like zinc and iron will react moderately with dilute acids.

II. Effect of Temperature: - An increase in temperature will cause reactants particles to gain more kinetic energy leading to an incr1ease in effective collision and hence, an increase in the rate of reaction. An increase in temperature will also lead to an increase in the energy of the system.

III. Effect of Concentration: - An increase in the concentration of the reactants will lead to an increase in the number of reactants per unit area (the reactants becomes closer) thus, leading to overcrowding and increase in the effective collision of the reactants and hence an increase in the rate of the reaction.

IV. Effect of pressure: - An increase in pressure will lead to a decrease in volume that is, a decrease in the intermolecular space between the reactants particles leading to an increase in the effective collision and hence an increase in the rate of reaction. And vice versa 

V. Effect of presence of light: - Some reactions are photochemical, that is, affected by light. When such reactions are exposed to light the reactants, particles become more activated and collide more increasing the number of effective collisions and hence an increase in the rate of reaction.

VI. Effect of a catalyst: - A catalyst increases the rate of a reaction by creating a different pathway with a lower activation energy.

ACTIVATION ENERGY: see definition in chemistry.
  For a collision to be effective, the reactants must possess the minimum amount of energy needed to overcome the energy barrier (activation energy for the reaction) for that reaction. The higher the activation energy, the slower the rate of reaction; positive catalyst helps to lower the activation energy.


 Energy Profile Diagram 

This is a diagram / graph that shows the pathway of a chemical reaction. whether the reaction is exothermic or endothermic.












Energy profile diagram for an Exothermic reaction










Energy profile diagram for an Endothermic reaction











       Rate Curve
A rate Curve is the graph which shows the rate of a reaction. It is a graph of reaction against time.( that is, change in concentration against time, decrease in mass against time, e.t.c) 
The slope or the gradient of the curve is steep at the beginning because the reaction is fastest ( since  , it becomes less steep as the reaction progresses and slows down, then it finally becomes horizontal. 
The point at which the graph becomes horizontal indicates the end point of the reaction, when one of the reactants is completely used up











OBJECTIVE QUESTIONS 

1. 




THEORY QUESTIONS.

1.(a)(i) Define rate of a chemical reaction?
     ii). mention three factors that can affect the rate of a chemical reaction
     iii). state the collision theory

b).  A sample of carbon is burnt at a rate of 0.50gper second for 30 minutes to generate heat.
    (i). write a balanced equation for the reaction
   (ii). determine the    I. volume of carbon (IV) oxide produced at s.t.p.  II. moles of oxygen used up in the process at s.t.p. [ C= 12.0, O= 16.0, Molar volume Vm = 22.4dm3

c. State how each of the following affects the rate of chemical reactions  (i) surface area (ii) catalyst  [waec]

2.a(I) What is meant by the rate of chemical reaction? 
(ii). Explain in terms of collision theory, the effect of temperature increase on reaction rate.
(b) When hydrogen peroxide is exposed to air, it decomposes  (I) write an equation for the reaction (ii). Outline an experiment to illustrate the effect of a named catalyst on the rate of decomposition. 
(iii).         

3a(i) Sketch an energy profile diagram to show the effect of a catalyst on the reaction rate, given that it is exothermic.
b. The graph below is the ratio curve for the following reaction carried out in an open vessel 

MgCO3(aq) + 2HCl → MgCl2(aq) +H2O(l) + CO2(g)

(i)  For how long the reaction occurred 
(ii) why was there a loss in mass?
(iii) State whether the reaction rate was fastest at the beginning, the middle  or towards the end of the reaction.  Give reason for your answer.
(iv) List three reaction conditions that can affect the slope of the curve.(waec)

4(a)In an experiment, excess 0.050mol/dm3 HCl was added to 10g of granulated zincin a beaker. Other conditions remaining constant state how the reaction rate would be affected in each case if the experiment was repeated using 
(i) 1.0mol/dm3 HCl
(ii) 8.0g of granulated zinc
(iii) 10g of zinc dust 
(iv) a higher volume of 0.5mol/dm3 HCl 
(v) a reaction vessel dipped in crushed ice 
(vi) equal volumes of water and 0.50mol/dm3 HCl.
b. 



Saturday, 13 April 2024

NATURE OF MATER

What is Matter: -
 Mater is defined as anything that has mass and occupies space.

Composition
 of matter: - matter consist of any one of the following particles. To
1. Atoms.  
2. Molecules.  Or
 3. Ions

1. An Atom is the smallest particle of an element that can take part in a chemical reaction.

2. A molecule is the smallest particle of a substance that exist alone and still possess the properties of the substance. E.g H2O, O


3. An Ion is a charged particle; it is formed when an atom loses or gains electrons.  E.g Na+, Cl- 

Radicals are group of atoms with a single charge.  E.g NO-, SO42-, OH-

Matter generally is made up of any one or more of the particles mentioned above.

States of matter
matter can exist in three states.
i. the solid
ii. the liquid and
iii. the gaseous state.

SOLID: - In solids the particles of matter are densely packed and are held by strong forces of attraction (force of cohesion).
Properties of solids 
i., solids have fixed, or definite volumes
ii. solids also have fixed shapes.
iii solids cannot be compressed
                                      Solid state (particles are tightly packed and are held by strong forces

LIQUIDS: -In liquids the molecules (particles) are close together in an orderly manner with little freedom of movement.  Molecules in a liquid are close together but are not held so
rigidly in position and can move past one another.

Properties of Liquids
i.  a liquid no fixed or definite shape but it takes the shape of its container, 
ii. liquids have a fixed or definite volume 
iii. liquids cannot be compressed.

                                              
                                              Liquid state (particles are not held tightly together)

GAS: - In a gas, the particles/molecules are separated by distances that are large compared with the size of the molecules.
Properties of gases
i.; gasses have no fixed or definite volume (will occupy entire volume of its container) 
ii. gases have no fixed shape.
iii.   gases can be compressed
 Gases differ from liquids and solids in the distances between their individual particles.

 Gases (particles of gases are wide apart)

The three states of matter can be inter-convertible without changing the composition of the substance. Upon heating, a solid it will change into a liquid form at a particular temperature.
The temperature at which this transition occurs is called the melting point of the solid. Further heating will convert the liquid into a gas at a particular temperature called the boiling point of the liquid. Cooling a gas on the other hand, will cause it to change into a liquid, this process is called Condensation. When the liquid is cooled further, it will change into the solid form, and the process is known as Freezing. 
Some solids change directly to the gaseous without passing through the liquid state and vice Versal. These processes are both known Sublimation and Deposition.


          Changes in the state of Matter
   
  Now remember we defined chemistry as the study of the composition, properties and the uses of mater as well as the principle that underlies the changes that matter undergoes, and so far, we are told that mater consist of one or any two of atoms, molecules or ions. now the properties of matter can be divided into two, that is, physical properties and chemical properties.

PROPERTIES OF MATTER 
    The properties of matter can be grouped into two
i. Physical properties are those properties that a substance (matter) shows by itself (i.e those properties that you see when you look at, touch or smell the substance) these include Temperature, Pressure, Colour, Smell, Density, Solubility, Melting and boiling points.

ii. Chemical properties on the other hand are those properties that matter exhibits when it comes in contact with other substances like acids, bases, even water to form new substances.


Physical and Chemical change

A physical change is one that is easily reversible and in which no new substance is formed.
example of physical changes is.
i. Dissolving sodium chloride in water
ii. Changing water to ice
iii. Evaporation of liquids
iv. Melting of candle wax

A chemical change
 is one which is not easily reversible and in which a new substance is always formed.
example of changes is.
i.   burning of wood, paper, or clothe.
ii.  rusting of iron when exposed to air and moisture.
iii. decomposition of organic matter.
iv. dissolving a metal like calcium or magnesium in dilute acids.
v.   the hardening of cement   when exposed to air.


OBJECTIVE QUESTIONS
1. Which of the following is a physical change 
a). Dissolving sugar on water
b). Addition of acid to base 
c). Burñing of wood
d). Rusting of iron

2. 




THEORY QUESTIONS
1(i). State two differences between the properties of solids and gasses
 (ii). What process does each of X, Y and Z represent in the changes shown below?






2.