Chemistry Chapter (10) Solutions

 ·  Solution: The homogeneous mixture of two or more substances is known as solution.

  · Solvent: The substance which is present in large proportion in solution is known as solvent.

 · Solute: The substance which is present in smaller proportion in solution is known as solute.

 ·  Concentration: The amount of solution present in a given amount of solution is known as concentration.

 · Concentrated Solution: Solution containing relatively higher concentration of solute is known as concentrated solution.

 · Dilute Solution: Solution containing relatively lower concentration of solute is known as dilute solution.

Type of Solution

     Depending upon the physical state of solute and solvent, types of solution are:

SOLVENT  STATE	SOLUTE  STATE	EXAMPLE
Gas	Gas	Air
Liquid	Gas	CO2 in water
Solid	Gas	Hydrogen in Pd
Liquid	Liquid	Alcohol in water
Gas	Liquid	Water vapour in air
Solid	Liquid	Hg in Au
Gas	Solid	Sublimation of solid into gas
Liquid	Solid	Sugar in water
Solid	Solid	Alloys

        Aqueous Solution: Solution of substances in water is known as aqueous solution.

Amalgam: Solution of metals in mercury is called amalgam.

Concentration Units:

           Percentage Composition: It is expressed by four different ways:

i)                  Percentage weight/ weight: It is the weight of solute dissolved per 100 parts by weight of solution.10% w/w salt solution means 10g of salt dissolved in 100g of solution in water . This contains 90g of water.

                % by weight = mass of solute/ mass of solution × 100

ii)               Percentage weight/ volume: It is the weight of solute dissolved per 100 parts by volume of solution. 10g of sugar dissolved in 100 cm³ of solution is 10% w/v solution of sugar.

iii)            Percentage volume/ weight: It is the number of cm³ of solute dissolved per 100g of the solution. If 10 cm³ of alcohol are dissolved in water and the total weight of solution is 100g then it is 10% v/w solution alcohol in water.

iv)            Percentage volume/volume: It is the volume of solute dissolved per 100 cm³ of the solution.

  ·       Morality (M): It is the number of moles of solute present in dm³ of solution.

           Number of mole = mass (g) / formula mass

  ·       Morality (m): It is the number of moles of solute present in kg or 1000g of solvent.

  ·       Normality (N): It is the number of gram equivalents of solute in dm³ of solution.

     Relation between Molarity and Normality:

  ·       Formula weight × Molrity =Normality × Equivalent weight

Or

       Molarity = Normality × equivalent weight/formula weight

  ·       Mole fraction (x): The mole fraction of any component in a mixture is the ratio of the number of moles of it to the total number of moles of all the components present.

  ·       The sum of the mole fractions of all components of a solution must be equal to one. There is no formal units of moles fraction. Anyhow, sometimes mole fraction is multiplied 100 to get mole percent.

  ·       Parts per million (ppm): It is defined as the number of parts (by weight or volume) of a solute per million parts (by weight or volume) of the solution.

  ·       This unit is used for very low concentration of solution.

  ·       Ideal solution: A solution is said to be ideal, if there is no energy change (ΔH =0) and no volume change (Δv = 0) when the solute is dissolved in the solvent.

  ·       In an ideal solution, there is no intermolecular forces of attraction between the solute and the solvent particles i.e. the components have zero heat of mixing and zero volume change.

  ·       Ideal solutions obey Raoult’s law exactly at all concentrations and temperatures.

  ·       Raoult’s Law:

i)                  For binary solution of volatile liquid: According to this law, “the partial vapour pressure of any volatile component in a solution is equal to the product of the vapour pressure of pure component and its mole fraction in the solution”.

             P_A = P⁰_A X_A   and     P_B = P⁰_B X_B

        Where P_A and P_B are the partial pressures of  component A and B.X_A  and X_B are the mole fraction of component A and B. P⁰_A and P⁰_B are the vapour pressure of two pure liquids.

ii)               For solutions containing non-volatile solutes: In non-volatile solute, there is only contribution of solvent in the vapour pressure. So, the vapour pressure of the solution of a non-volatile solute is equal to the vapour pressure of the pure solvent.

             P_A = P⁰_A X_A      i.e.     P = P⁰_A  X_A

           Where P = Pressure of solution; P⁰_A = Partial pressure of pure solvent and X_A = mole fraction of solvent.

Thus, Raoult’s law may be stated as:

          “At a given temperature, the vapour pressure of a solution containing non-volatil solute is directly proportional to the mole fraction of solvent”.

Limitations of Raoult’s Law:

             It should be applied only for every dilute solutions.

             The solute should be non-volatile.

              The solute should be non-electrolyte.

Non-Ideal Solutions: The solutions which do not obey Raoult’s law i.e. show positive of negative deviation from Raoult’s law are called non-ideal solution. In non-ideal solutions,

                                   ΔH_mixing ≠ 0 & ΔV_mixing  ≠ 0

Positive deviations: positive deviation from Raoult’s law occurs if weaker interaction forces of attraction exist between unlike binary molecules ( A & B ) in comparison to like binary molecules ( A & A or B & B ).

The extent of positive deviation depends upon following factors:

i)                  Difference in polarity of the molecule.

ii)               Difference in intermolecule forces of attraction.

iii)            Difference in length of hydrocarbon.

iv)            Association of either of the constituents in liquid state.

v)               ΔH_mixing = +ve (endothermic)

vi)            ΔH_mixing = +ve

vii)         Solubility increases by heating.

viii)      P_A > P⁰_A X_A and P_B > P⁰_B X_B.

Negative deviation: Negative deviation from Raoult’s law occurs if stronger interaction of attraction exist in unlike molecule ( i.e. between A and B) in comparison to like molecule ( i.e. either between A & A or A & B).

i)-  ΔH_mixing = -ve (exothermic)        ii)-  ΔV_mixing = +ve

iii)- Solubility decreases by heating.  iv)-  P_A < P⁰_A X_A and P_B < P⁰_B  X_B. 

  ·       Azeotropes: The mixture of two or more solvents, which have definite composition and boiling point is called azeotropes or azeotropic mixture. The azeotropes which show positive deviation from ideal behavior i.e. from Raoult’s law is called maximum boiling azeotropes and those azeotropes which show negative deviation from Raoult’s law is called maximum boiling azeotropes.Minimum boiling azeotropes having lower boiling point than either of the two liquid pairs and maximum boiling azeotropes  having maximum boiling point than either of the two liquid pairs.

  ·       Colliative properties: A colliative property of a solution is one that depends on the number of particles dissolved in it, rather than on the type of particles.Colliative properties are the properties of only dilute solution which are supposed to behave as ideal solution i.e solution in which the activity of the solute is equal to mole fraction.

The colliative properties are:

i)- lowering in vapour pressure.

ii)- Elevation of boiling point.

iii)- Depression of freezing point.

iv)- Osmosis.

  ·       Lowering in vapours pressure:When a solid dissolves in water,its ions or molecules become surrounded by water molecules; we say that the particles are hydrated . In case of an ionic solid,water molecules are attracted to the positive or negative charges on the ions. For a covalent substance like sugar, the attraction are due to the hydrogen bonds made between water and sugar molecules.Owing to the extra attraction that the water molecules feel for the dissolve particles, they find it harder to escape from a solution of an pure water. By comparing the vapour pressure of pure water with the vapour pressure of a solution of an involatile solute, we can compare the ease with which water molecules can escape into the vapours.The vapours pressure of a solution is always lower than that of pure water.

      “The relative lowering of vapours pressure is equal to the mole fraction of the solute.”

                                      P-P_S / P = _WM / W_M

Where w = weight of solute; W = of pure solvent, m = molecule weight of solute, M = molecule weight of solvent.

              The above expression can be used in the molecule weight determination of non-volatile substance.

·       Elevation of Boiling Point: The boiling point of a liquid is defined as the temperature at which its vapour pressure becomes equal to the atmospheric pressure. Since the addition of a non-volatile solute lowers the vapours pressure of the solvent so the solution boils at a high temperature than the pure sovent.

          An elevation in temperature causes a rise in the vapours pressure  of a liquid because at higher temperature, the escaping tendency of the molecule increases due to great average kinetic energy. Liquid with weak intermolecule attractive forces have low pressure. If T_b is the boiling point of solvent and T is the boiling point of  solution, the difference in boiling point (ΔT_b) is called the elevation of boiling point.

                                          T – T_b = ΔT_b

          The elevation of boiling point is directly proportional to the lowering of vapour pressure.

                                               ΔT_b α p⁰ – p

The elevation of boiling point is also directly proportional to the concentration of the solution expressed as molality i.e. ΔT_b α m or ΔT_b = k_b × m. where K_b is the proportionality constant called the ebullioscopic constant or molal elevation constant.

         K_b is the characteristic of the solvent (independent of the nature of solute) and may be definedas the elevation in the boiling point which could be produced by dissolving one mole of any solute in 1000 grams of pure solvent. Thus,

                         ΔT_b = K_b × m or ΔT_b= 1000× K_b ᵡ w / m ᵡ w or m= 1000×K_bᵡ w / ΔT_b ᵡ w

Where w & m = weight and formula weight of solute. W = weight of solvent.

Depression of Freezing Point: Freezing point is the temperature at which liquid and solid states of a substance have the same vapours pressure. Since the vapours of a solvent is lowered by the addition of non-volatile solute, the freezing point of the solution is always lower than freezing point of the pure solvent.

           The depression in freezing point ΔT_ƒ is directly proportion to the lowering of vapour pressure which in turn is proportional to n/N (where n= w/m & N = W/M).

Therefore, ΔT_ƒ α P⁰ – P or ΔT_ƒα ΔPα n/N α wM/mW.

The lowering or depressing of freezing point (ΔT₁) is related to the molarity (m) of the solution.

i.e. ΔT₁ = K₁ × m

k_ƒ is the proportionality constant known as the cryoscopic constant or molal freezing point depression constant, K_ƒ may be defined as the depression in freezing point which may theoretically by produced by dissolving one mole of the solute in 1000 grams of the solvent.

Molality of the solution= w/m ᵡ 1000/ W/

Where w & m are the weight and formula weight of the solute in gram and W is the weight of solvent.

ΔT_ƒ  = K_ƒ × m

Or  ΔT_ƒ = K_ƒ ᵡwᵡ1000/mᵡw or 1000ᵡ Kƒ ᵡw /ΔT_ƒ ᵪW

Osmosis And Osmotic Pressure: When a solution is separated from a pure solvent by a membrane, it is observed that the solvent tends to pass through the membrane into the solution. “A membrane which permits the solvent and not and not the solute to pass through it is known as semipermeable membrane”. If two solutions of different concentration are separated from each other by a semipermeable, it is fond that “the solvent flows spontaneously by through the membrane from a solution of lower concentration to one of higher concentration till the solution on both sides of the membrane attain uniform concentration. This phenomenon is termed as Osmosis (Greek osmos = a push)”.

The type of the membrane employed in experiments on osmosis depends on the nature of the solvent and solute. Some semipermeable membranes include animal membrances and thin films of cellulose and cellulose nitrate.

It must be noted that there is no perfect universal semipermeable membrane applicable for all systems or for a particular system at all temperatures.

Osmotic Pressure: It may be defined as the equivalent of maximum hydrostatic pressure which is produced when a solution is separated from the solvent by a semipermable membrane.

·       Osmotic pressure may be defined as the equivalent of excess of pressure which must be applied to the solution in order to prevent the passage of solvent into it through a semipermeable membrane.

·       It may also be defined as the excess of pressure which must be applied to the solution in order to increase its vapour pressure so that it become equal to that of the solvent.

Hydration: when ionic compound are dissolved in water, they are dissociated into ions. Both positive and negative ions are hydrated in aqueous solution. This means that they are surround by an approximately spherical shell of water dipoles, each with its oxygen end pointing in toward positive ion or its hydrogen end pointing in toward a negative ion. The extent of hydration of an ion can be measured by the hydration energy of the ion, ΔH_hyd.

Heat of hydration is the energy released when the ions leave the gas phase and enters water to become hydrated. Hydration energies are always negative and depend upon ionic size and charge. Hydration energies are high for an ion, which has a small size and/or a high charge.

In water, all ions are hydrated i.e. surrounded by a shell of water molecules. The hydrogen ion is very strongly hydrated because of its small size; it is often represented in solution as H₂O^- called the hydronium ion.

·       Hydrolysis: When the salt NaCl is dissolved in water, the resulting solution is neutral i.e. the concentration of each of H⁺ and OH^- ions are equal to 10^-7M as in pure water. But some salts, upon dissolving in water, do not always form neutral solution. Some salts like NH₄CL, ALCL₃, CuSO₄ give acidic solution in water, and some salt like Na₂CO₃ form basic solution in water. These interactions between salt and water are called hydrolytic reaction and the phenomenon is known as hydrolysis.

   “The reaction of cation or anion (or both) with water so as to change                            its pH  known as hydrolysis”.

·       Arrhenius Theory of Ionization: Electrolytes are the substances containing electrically changed particles called ions. These changes are positive for H^- ion or ions derived from metals and negative for ions derived from non-metals.

·       Numbers of electrical changes carried by an ion is equal to the valency of corresponding atom.

·       The number of negative and positive charges on the ions must be equal so that the solution as a whole remains neutral.

·       In solution, ions move randomly. On collision, they may combine to give unionized molecules. Ionization is a reversible process in which solution contain ions of electrolyte together with unionized molecules.

·       The degree of ionization depends upon the nature of electrolyte. Weak electrolytes ionize only slightly.

·       Ionization is not affected by electric current. When electric current is passed an electrolytic solution, the positive ions (cations) migrate towards cathode and the negative ions (anions) migrate towards anode. On reaching the electrodes, the ions lose their charge and change into neutral species by the gain or loss of electrons.

·       pH: In pure water at 25⁰C; [H⁺][OH^-] = 1 ᵡ 10^-14

                                               [H^-][OH^-] = 1ᵡ 10^-7M.

   In acidic solution, [H^-] is more than 1ᵡ 10^-7M and [OH^-] is less than 1ᵡ 10^-7 M.

In basic solution, [H^-]will be less than and [OH^-] more than 1ᵡ 10^-7 M. the actual values of these concentration are too small to be used for practical work. Therefore, a Danish chemist S.P.L. Sorenson introduced the term pH value to express H^- ion concentration.

          “The pH value of an aqueous solution is the negative logarithm of the hydrogen ion concentration in mole per dm³ in the solution”.

                                               pH = log [H]

   We known that in any aqueous solution;

                                                   [H^-] [OH^-] = 1ᵡ10^-14

Using pOH = - log [OH^-]

                                          pH = pOH = 14

Since in pure water or neutral solution, pH + pOH = 14, so pH = pOH = 7. acid solution,pH < 7.0 and in base solution pH > 7.0.

 [H^-] (mol/dm³) 10⁰ 10^-1 10^-2 10^-3 10^-4 10^-5 10^-6 10^-7 10^-8 10^-9 10^-10 10¹¹ 10^-12 10^-1310^-14                                                           

            pH          0      1     2     3     4     5     6      7    8      9     10    11

      12      13    14  

Acid                                                     Neutral  Basic

Buffer: It is the solution which does not change its pH value either on keeping it for long or on adding to it water or acid or a base or the solution which resists change in its pH value.

 There are two types of buffer solutions:

a). Acidic buffers: Weak acid + salt of same acid with strong base.

E.g.; CH₃ COOH + CH₃ COONa.

b). Basic buffers: Weak base + salt of same base with strong acid.

E.g.; NH₄OH + NH₄CL.

Acid-Base Indicators: Acid-base indicators such as methyl orange, phenolphthalein and bromothymol blue are the substances which change colour according to the hydrogen ion concentration of the solution to which they are added. Consequently , they are used to test for acidity and alkalinity. They are also used to detect the end point in acid-base titrations.

 Most indicators can be regarded as weak acids of which either the undissociated molecule or the dissociated anion, or both, are coloured. If we take methyl orange as our example and write the undissociated molecule as HY,

                             HY           =             H^-               +                           Y

                          Red                       Colourless                                Yellow

Addition of acid (i.e.   H+ ions) displaces this equilibrium to left. When this happens [HY]>> [Y] and the solution becomes red. On the other hand, when alkali (containing OH^-ions) is added to methyl orange, it removes H^- ion forming water. The equilibrium in the above system moves to the right in order to replace some of the H^-  ions. In this cause [Y]>> [HY], and solution truns yellow.

The range of an Indicator: The colour change of an indicator is due to the change from one coloured from to another. Near the end point, both coloured froms will be present in appreciable quantities. It is not possible to say precisely when the two froms are at equal concentration. Experiment shows that our eyes cannot judge the exact end point, and indicators effectively change colour over a range of about 2 pH units.

   “the range of an indicator is the pH range over which it changes colour”.

The end point of each indicator is in the center of its pH range. 

Sher Afzal Ranais

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