Distribution Law – Numerical Part 1

Distribution Law

source :Chromatography-online.org

Numericals of Distribution Law

Q.1      From the following data for concentration of succinic acid in water & ether at 25⁰C, find the value of K of succinic acid between water & ether?

Conc. in Water (in gm/20ml)          0.0244            0.071              0.121

Conc. in ether (in gm/20ml)           0.0046            0.013              0.022

Prove that this data follow the distribution law.

Ans.

 k₁ =C_water / C_ether

=   0.0244/.0046

k₁ =5.30

k₂ = C_{water /  Cether}   

  =0.071 /0.013

k₂= 5,46

k₃ = C_{water /  Cether}

=0.121 /0.022  

k₃ = 5.5

k =( k₁+k₂+k₃ ) /3

= (5.30 +5.46 +5.5 )/3

=16.26/3

K=5.42

This data follows the distribution law because value of K₁ , K₂ & K₃ are nearly equal

Q.2.     In one experiment, the concentration of the acid in water & ether were found as follows-

Conc. in Water (in gm/20ml)          25.4                33.2                42.6

Conc. in ether (in gm/20ml)           4.2                   5.5                   7.1

show that the above results are in favour of distribution law.

Ans.

   K₁ = C_water /  C_ether

=25.4 / 4.2 =6.05

K₂ = 33,2/5.5 =6.04

K₃ = 42.6 / 7.1 =6.00

The above results are in favour of distribution law because values of K₁ , K₂ & K₃ are nearly equal.

Q.3      Iodine (5.0 gm) was dissolved in a mixture containing equal volumes of water & CCl₄. If K of iodine between CCl₄ & H₂O is 82, find the amount of I₂ in aqueous layer?

Ans.

Suppose,

Amount of I₂ in aqueous layer = x

Amount of I₂ in aqueous CCl₄ layer =5- x

K =C _CCl4 / C _H2O

82  = ( 5-x) /x

82 x =5-x

83 x =5

x=5/83 =0.0602  Ans.

Q.4      Solubility of I₂ in water is 0.8 gm/litre. If distribution coefficient of I₂ between CCl₄ & H₂O is 82. Find the solubility of I₂ in CCl₄?

Ans.

  S_Water               = 0.8 gm/l

S_CCl4     =          ? gm/l

K=  S_CCI4  / S_water

82 = S_CCI4 /0.8

S_CCI4  =82 X0.8 =65.6 gm. / l   Ans.

Q 5) Succinic acid is distributed between water and ether  at 18 ⁰ C . If ether layer has 0.046 gm. of acid in 10 ml. and K for this system is 5.2. What will be the concentration of acid in 25 ml. water layer ?

Solution )

Distribution coefficient , K = C_W / C_E

K = 5.2

C_W = x  gm / 25 ml

Given ,C_E  = 0.046 gm / 10 ml

C_E  = 0.046 x 25 / 10 = 0.115 gm / 25 ml

K = C_W / C_E

5.2 = x / 0.115

x = 5.2 x 0.115= 0.598

x ( conc. of acid in water layer )   = 0.598  gm / 25 ml Ans.