Qualitative analysis of V group cations

Group 5 cations are magnesium (II) Mg²⁺, potassium (I) K⁺ and sodium (I) Na⁺. These cations do not react with hydrochloric acid HCl, hydrogen sulphide H₂S, ammonium sulphide and ammonium carbonate (NH₄)₂CO₃. 

Magnesium does show similar reactions to IV^th group cations; it forms basic magnesium carbonate MgCO₃.Mg(OH)­₂.5H₂O with IVth group reagent ammonium carbonate (NH₄)₂CO₃. But this basic magnesium carbonate is soluble in presence of ammonium salts and therefore it doesn’t precipitate with IV group cations.

5Mg²⁺ + 6CO₃^2- + 7H₂O ⟶ 4 MgCO₃.Mg(OH)­₂.5H₂O ↓ + 2HCO₃^-

NH₄⁺ + CO₃² ⇌ NH₃ + HCO₃^-

Magnesium carbonate doesn’t precipitate in the presence of ammonium salts due to common ion effect. Solubility product of magnesium carbonate is quite high and cannot be achieved with lower concentration of carbonate ions. High concentration of ammonium ions shifts the equilibrium in forward direction which decreases the concentration of carbonate ions causing the basic magnesium carbonate to remain soluble.

Take the filtrate of IV group in a porcelain dish and evaporate it to a pasty mass. Add 3ml concentrated nitric acid HNO₃ to dissolve it, evaporate again to dryness and heat until white fumes of ammonium salts cease to evolve. If you get a white residue, it means group V is present.

Add 4ml water to the residue, stir and warm it up for 1minute and then filter. We will test for Mg(II) in the residue, and for K(I) and Na(I) in the filtrate. 

Confirmatory test for Mg²⁺

Dissolve the residue in a few drops of dil HCl and add 2-3ml water. Divide the solution in two parts.

Part 1

Add a little ammonium chloride NH₃Cl solution followed by ammonical oxine reagent (take 1ml 2% 8-hydroxyquinoline solution and add 2M acetic acid followed by 5ml 2M ammonia solution, warm to dissolve any precipitated oxine) and heat to boiling for 1-2minutes or till the odour of ammonia becomes noticeable. You will get a pale yellow precipitate of magnesium oxine Mg(C₉H₆ON)₂.4H₂O which confirms the Mg²⁺ ion.

Part 2

Take 1-2 drops of test solution in a spot plate and add 2-3 drops of magneson I reagent (4-(4-Nitrophenylazo)-resorcinol) and add 1 drop of 2M sodium hydroxide NaOH to make it alkaline. Blue colouration or blue precipitate is formed depending on the concentration of magnesium.

We will test for K(I) and Na(I) in the filtrate we got above. If the residue of V^th group dissolves completely, dilute it up to 6ml and filter if necessary. Divide this solution into three equal parts to test magnesium (II) Mg²⁺, potassium (I) K⁺ and sodium (I) Na⁺. In first part, directly apply magneson test for the confirmation of Mg(II) ion and in other two parts test for K(I) and Na(I).

Confirmatory test for Na⁺

Add a little uranyl magnesium acetate reagent, shake and allow to stand for few minutes. Yellow crystalline precipitate of sodium magnesium uranyl acetate is formed. If precipitation doesn’t occur, add 1/3^rdvolume of ethanol; it helps in precipitation.

Na⁺ + Mg²⁺ + 3UO₂²⁺+ 9CH₃COO^- ⟶NaMg(UO₂)₃(CH₃COO)₉ ↓

If you perform flame test persistent yellow flame confirms Na⁺.

Confirmatory test for K⁺

Add a little sodium hexanitritocobaltate(III) solution and a few drops of 2M acetic acid. Stir and then allow it to stand for 1-2 minutes. Yellow precipitate of potassium hexanitritocobaltate(III) is obtained. If precipitation doesn’t occur immediately, warm it a little; it will accelerate the precipitation.

3K⁺ + [Co(NO₂)₆]^3- ⟶  K₃[Co(NO₂)₆] ↓

The precipitate is insoluble in dilute acetic acid. If larger amount of sodium is present or you have added excess of reagent, then a mixed salt K₂Na[Co(NO₂)₆] is formed.

We have successfully separated the metal cations. Unlike cations, there is no well-defined system for analysis of anions. In the coming posts of analytical chemistry we will discuss the tests for anions.

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Collision Theory

Max Trautz and William Cudmore McCullgh Lewis gave collision theory to interpret the exponential factor in the Arrhenius equation. Their theory was based on kinetic theory of gases. They assumed that the molecules are hard spheres and when they collide, the product is formed. It means that the rate depends on total number of collisions per unit volume, which is termed as collision number Z.

You can understand it by taking the example of Pool or Billiards. To sink a pool ball into the pocket, it is necessary to hit it by cue ball with desired kinetic energy. For a successful shot, the orientation of cue ball is as important as the kinetic energy.

Let’s take an example of a real reaction, the formation of methanol from methyl bromide.

CH₃Br + OH^- ⟶ CH₃OH +  Br ^–

As you know, the hybridization of methylbromide is sp³ and its shape is tetrahedral, but it gains inverted umbrella shape for this reaction. Formation of methanol depends on the orientation of methylbromide when OH^-collides with it.   If OH^- attacks from the methyl side, it leads to the formation of methanol. If OH^-attacks from the bromide side, it bounces back and no product is formed.

Right now I am trying to explain the importance of orientation in any reaction. We will discuss the detailed reaction mechanisms in our future posts of organic reaction mechanisms.

Trautz and Lewis first took a simple reaction between similar molecules to calculate the collision factor Z.

2A(g) ⟶ Product

Collision between A-A is given by equation:

Z_A-A  = ½ √2π  σ²ū N²_A              .......(1)

where π= 3.14,

σ is the distance,

N_Ais the number of molecules per unit volume,

ū is molecular mean velocity = (8k_BT/πm)^1/2

where ,

k_Bis the Boltzmann constant,

T is the temperature in Kelvin,

m is the molecular mass,

On putting the value of ū in equation 1:

Z_A-A  = ½ √2 πσ²(8k_BT/π m)^1/2 N²_A

Z_A-A  = 2 σ² N²_A(π k_B T/m)^1/2                  .......(2)

This quantity is known as collision number Z and its unit is m^-3 s^-1. This equation is restricted to the reactions between same molecules. They modified the equation of collision number Z for the reactions which involve two different molecules like A and B.

For the collision between two different molecules like:

A + B ⟶ Product

Z_A-B  = d ² N_A N_B (8π k_BT)^1/2                 .......(3)

                                    µ

Where d is the distance between the centres of A and B when collision occurs or it is the sum of the radii of A and B.

µ is the reduced mass =  m_A m_B

                                       m_A + m_B

On putting the value of µ in equation 3, we get:

Z_A-B  = d ² N_A N_B (8π k_BT m_A + m_B)^1/2    

                                               m_A m_B

Trautz and Lewis suggested that multiplying collision number with Arrhenius Factor gives the rate of formation of product (ν) in terms of number of molecules formed per unit volume and per unit time.

ν  =  d ² N_A N_B (8π k_BT)^1/2  e^{-Ea / RT}         

                               µ

And to get the rate constant, they divided the above equation by N_A N_B and multiplied it by Avogadro constant L,

k = L d ² (8π k_BT)^1/2  e^{-Ea / RT}      

                     µ

k = Z_AB e^{-Ea / RT}

The pre-exponential factor in this equation is called the collision frequency factor and is denoted by symbols Z_AA (for same molecules) or Z_AB(for different molecules). They applied this theory to the following reaction:

2HI ⟶ H₂ + I₂

And the calculated value of Z was quite closer to the experimental value. This theory gained confidence but when it was applied to other reactions, the difference between experimental and calculated values was quite considerable. By a lucky coincidence,  Lewis and Trautz picked the reaction which gave them accurate results. In order to resolve the discrepancies, they introduced another pre-exponential factor known as the steric factor P, which represents the fraction of the total number of collisions that are effective and from correct orientation.

 k = PZ_ABe^{-Ea / RT}

The introduction of P did improve the collision theory, but it is quite complicated to estimate the value of P as it involves the orientation.

The hard sphere collision theory may give satisfactory explanation to the reactions which involve gaseous reactants and products but it fails to explain the reactions between ions or in solutions. In our next post of chemical kinetics, we will discuss yet another theory to decipher the chemical reactions, the Transition State Theory.

This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Collision Theory

Max Trautz and William Cudmore McCullgh Lewis gave collision theory to interpret the exponential factor in the Arrhenius equation. Their theory was based on kinetic theory of gases. They assumed that the molecules are hard spheres and when they collide, the product is formed. It means that the rate depends on total number of collisions per unit volume, which is termed as collision number Z.

You can understand it by taking the example of Pool or Billiards. To sink a pool ball into the pocket, it is necessary to hit it by cue ball with desired kinetic energy. For a successful shot, the orientation of cue ball is as important as the kinetic energy.

Let’s take an example of a real reaction, the formation of methanol from methyl bromide.

CH₃Br + OH^- ⟶ CH₃OH +  Br ^–

As you know, the hybridization of methylbromide is sp³ and its shape is tetrahedral, but it gains inverted umbrella shape for this reaction. Formation of methanol depends on the orientation of methylbromide when OH^-collides with it.   If OH^- attacks from the methyl side, it leads to the formation of methanol. If OH^-attacks from the bromide side, it bounces back and no product is formed.

Right now I am trying to explain the importance of orientation in any reaction. We will discuss the detailed reaction mechanisms in our future posts of organic reaction mechanisms.

Trautz and Lewis first took a simple reaction between similar molecules to calculate the collision factor Z.

2A(g) ⟶ Product

Collision between A-A is given by equation:

Z_A-A  = ½ √2π  σ²ū N²_A              .......(1)

where π= 3.14,

σ is the distance,

N_Ais the number of molecules per unit volume,

ū is molecular mean velocity = (8k_BT/πm)^1/2

where ,

k_Bis the Boltzmann constant,

T is the temperature in Kelvin,

m is the molecular mass,

On putting the value of ū in equation 1:

Z_A-A  = ½ √2 πσ²(8k_BT/π m)^1/2 N²_A

Z_A-A  = 2 σ² N²_A(π k_B T/m)^1/2                  .......(2)

This quantity is known as collision number Z and its unit is m^-3 s^-1. This equation is restricted to the reactions between same molecules. They modified the equation of collision number Z for the reactions which involve two different molecules like A and B.

For the collision between two different molecules like:

A + B ⟶ Product

Z_A-B  = d ² N_A N_B (8π k_BT)^1/2                 .......(3)

                                    µ

Where d is the distance between the centres of A and B when collision occurs or it is the sum of the radii of A and B.

µ is the reduced mass =  m_A m_B

                                       m_A + m_B

On putting the value of µ in equation 3, we get:

Z_A-B  = d ² N_A N_B (8π k_BT m_A + m_B)^1/2    

                                               m_A m_B

Trautz and Lewis suggested that multiplying collision number with Arrhenius Factor gives the rate of formation of product (ν) in terms of number of molecules formed per unit volume and per unit time.

ν  =  d ² N_A N_B (8π k_BT)^1/2  e^{-Ea / RT}         

                               µ

And to get the rate constant, they divided the above equation by N_A N_B and multiplied it by Avogadro constant L,

k = L d ² (8π k_BT)^1/2  e^{-Ea / RT}      

                     µ

k = Z_AB e^{-Ea / RT}

The pre-exponential factor in this equation is called the collision frequency factor and is denoted by symbols Z_AA (for same molecules) or Z_AB(for different molecules). They applied this theory to the following reaction:

2HI ⟶ H₂ + I₂

And the calculated value of Z was quite closer to the experimental value. This theory gained confidence but when it was applied to other reactions, the difference between experimental and calculated values was quite considerable. By a lucky coincidence,  Lewis and Trautz picked the reaction which gave them accurate results. In order to resolve the discrepancies, they introduced another pre-exponential factor known as the steric factor P, which represents the fraction of the total number of collisions that are effective and from correct orientation.

 k = PZ_ABe^{-Ea / RT}

The introduction of P did improve the collision theory, but it is quite complicated to estimate the value of P as it involves the orientation.

The hard sphere collision theory may give satisfactory explanation to the reactions which involve gaseous reactants and products but it fails to explain the reactions between ions or in solutions. In our next post of chemical kinetics, we will discuss yet another theory to decipher the chemical reactions, the Transition State Theory.

This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Arrhenius Equation: Temperature Dependence of Rate of Reaction

Rate of reaction is greatly affected by rise in temperature; we mark it in our daily life too. On a hotter day yoghurt gets sour; dough gets fermented and cooked food goes bad a lot faster than on a colder day. It has beenfound experimentally that rising the temperature by 10°C nearly doubles the rate constant. Before we go into complicated terms and equations, let’s try to understand what happens at the molecular level on rising the temperature? Let’s take an example of a simple reaction:

H₂ + I₂ ⟶2HI

H-H + I-I ⟶2(H-I)

For any reaction to happen, collision of reactant molecules is required.  When reactant molecules collide, old bonds (H-H and I-I) are broken and new bonds (H-I) are formed. But the reaction doesn’t happen all of a sudden. The reaction follows a course where folloing two processes take place simultaneously.

H-H + I-I ⟶ H ⋯ I  ⟶ 2 (H-I)

                          ⋮       ⋮

                         H ⋯ I

An intermediate complex is formed which exists for a fraction of time. It is known as an activated complex. It creates an energy barrier that reactant molecules need to achieve to complete the reaction and form the product. The energy gap between reactant and activated complex is called as activation energy E_a.

It is not possible for every reactant molecule to jump over this barrier. Only few reactant molecules have enough kinetic energy to collide with other reactant molecules and not all collisions are effective enough to form the activated complex or intermediate complex. It means that there are limited numbers of molecules which can overcome all barriers and form the product.

Rise in temperature adds extra kinetic energy to all the molecules enabling some more molecules to collide with enough kinetic energy to form activated complex so that more product will be formed. It means that on raising the temperature rate of reaction increases.

Temperature dependence of rate of reaction has been observed by a number of scientists, such as Wilhelmy in 1850, Berthelot in 1862, J. J. Hood in 1885. They all tried to set an equation relating the rate constant to the temperature, however none of them could give a satisfactory  equation.

In 1884 Van’t Hoff gave the equation for temperature dependence of equilibrium constants:

(𝜕 ln K_c)_p = ΔU^°                                             .........(1)

    𝜕T            RT²

where k_c is equilibrium constant

ΔU^° is standard internal energy change.

A + B ⇌ C + D

Rate of forward reaction = k₁[A][B]

Rate of backward reaction = k_-1[C][D]

So,

k_c = k₁/k_-1

Equation 1 can be written as:

d ln k₁ -  d lnk_-1   =   ΔU^°                                           .........(2)

    dT         dT              RT²

Van’t Hoff suggested thatthe rate constants k₁ and k_-1 are influenced by two different energy factors E₁ and E_-1, therefore he split equation 2 in two equations:

d ln k₁   =  E₁                                   .........(3)

 dT          RT²

d ln k_-1   =  E_-1                                 .........(4)

    dT          RT²

These two energies E₁ and E_-1must be such that E₁ - E_-1 = ΔU^°.

Van’t Hoff was aware that ΔU° is not always temperature independent; therefore E₁and E_-1 might be temperature dependentas well. He also considered the possibility of temperature independence of E.

for an event when E₁ is independent of temperature, equation 3 can be integrated

ln k  = constant -  E₁                                   

                             RT²

k = A e^-E/RT                                                    .........(5)

where,

E = B + DT²

where B and D are temperature independent. And equation 4 will become:

d ln k_-1   =  B + DT²                                     

    dT              RT²

ln k   = A’ - B + DT²                                   

                       RT²

k = A e^-(B-DT2)/RT                                        .........(6)

where A= e^A’

This equation received much experimental support, but in most of his equations, temperature dependence was special case of the equation. In 1889 Arrhenius took Van’t Hoff’ssimplest equation 5 as starting equation and proposed a general concept of how reactions occur. That equation is now known as Arrhenius equation.

k = A e^-Ea/RT                 

where A is known as Arrhenius factor or Frequency factor or Pre exponential factor. It gives the number of collision per second and its unit is (s-1). It is a constant, specific for a particular reaction.

E_a is activation energy, it is measured in Joules/mole and its unit is J mol^-1.

R is gas constant and k is the rate constant.

It has been observed that rising the temperature causes the reaction medium to become less viscous, which gives the molecules more freedom to move and increases the chances of them to collide and react. This was a basic observation but Arrhenius gave an insight to it.

Factor e^-Ea/RT in his equation corresponds to the fraction of molecules that have kinetic energy greater than activation energy E_a.

taking natural log of both side of Arrhenius equation

ln k = - E_a  +  ln A                                .........(7)

             RT

On plotting this equation ln k verses 1/T we get a straight line with slope -E_a/R and intercept ln A. It shows that on increasing temperature or decreasing the activation energy, rate of reaction increases.

Maxwell Boltzmann distribution curve

Arrhenius theory gained support by James Clark Maxwell and Ludwig Boltzmann. They used statistics to predict the behaviour of large number of molecules. Usually, a number of molecules are present in a reaction mixture and they may have different levels of kinetic energy. It is difficult to measure the kinetic energy of each molecule. Boltzmann and Maxwell suggested that we can find a fraction of molecules with a given kinetic energy by plotting the fraction of molecule (N_E/N_T) against Kinetic energy (K.E). When they plotted the same graph at different temperatures (t) and (t+10), they found that the fraction of molecules having energy ≥ E_a was doubled at (t+10) temperature. That’s why on increasing the temperature by 10 units, rate of reaction gets doubled.

Let’s practice few problems:

Q. The rate constant of a reaction at 500K and 700K are 0.02s^-1 and 0.07s^-1respectively. Calculate the values of E_a and A.

At temperature T₁

ln k₁ = - E_a  +  ln A                               .........(8)

             RT₁

At temperature T₂

ln k₂ = - E_a  +  ln A                               .........(9)

             RT₂

Since E_a and A are constant for a given reaction.

Subtracting equation 8 from 9:

ln k₁ – ln k₂  =  E_a -    E_a                                  

                         RT₁    RT

ln k₂  =  E_a  [1  - 1]

    k₁       R   T₁     T₂

log k₂  =      E_a       [T₂ – T₁]                  .........(10)

       k₁     2.303R       T₁ T₂

on putting values in the equation 10 we can find E_a and then using Arrhenius equation we can calculate A. value of R = 8.314 JK^-1mol^-1.

log 0.07  =          E_a                [700– 500]                       .........(10)

      0.02       2.303 × 8.314     700×500

E_a = 18230 J mol^-1

k = A e^-Ea/RT

0.02 = A e^{-18230/8.314× 500}

0.02 = A 0.012

A = 1.66

Q.  A first order reaction whose rate constant at 80°C was found to be 5.0 × 10^-3 s^-1. has an activation energy of 45 kJ mol^-1. What is the value of the rate constant at 875°C?

log k₂  =      E_a       [T₂ – T₁]                  .........(10)

      k₁     2.303R       T₁ T₂

log k₂   =  (4.5 × 10⁴ J mol^-1)               [1148K – 1073K]             

      k₁      2.303× (8.314 J K^-1 mol^-1)    1148K×1073K

log k₂   =  0.143

      k₁     

 k₂   =  1.39      

 k₁     

value of k₁ is given 5.0 × 10^-3 s^-1

k₂= 1.39 × (5.0 × 10^-3 s^-1)

k₂= 7.0 × 10^-3 s^-1

Q. the rate constant for the first order decomposition of H₂O₂is given by the following equation:

log k = 14.34 – 1.25×10⁴ K/T

calculate E_a for this reaction and what temperature will its half life be 256min?

Arrhenius equation

ln k = - E_a  +  ln A                               

             RT

or

log k = log A -       E_a      

                           2.303 RT

on comparing the given equation with this form of Arrhenius equation:

log A = 14.34 s^-1

and

-        E_a            =   – 1.25×10⁴ K

   2.303 RT                T

E_a           =   1.25×10⁴ K × 2.303 × 8.314 J K^-1 mol^-1

E_a      = 1.25×10⁴ K × 2.303 × 8.314 J K^-1 mol^-1

E_a       =  2.39×10⁵ J K^-1 mol^-1

Halflife of first order reaction is

t_1/2  = 0.693

            k

(256× 60)s = 0.693

                         k

k = 4.5 × 10^-5 s^-1

Now calculate T by equation given in the question:

log k = 14.34 – 1.25×10⁴ K/T

log 4.5 × 10^-5 s^-1  = 14.34 s^-1 - 1.25×10⁴K

         T

T = 669 K

Arrhenius theory received great acceptance by scientists but as we know, there is always a possibility of improvement in science. In 1916 Max Trautz and William Lewis gave a new theory known as Collision Theory which modifies the Arrhenius equation. in the next post of Chemical Kinetics we will study Collision Theory in detail.

This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.